Daily Papers

In the domain of black-box model extraction, conventional methods reliant on soft labels or surrogate datasets struggle with scaling to high-dimensional input spaces and managing the complexity of an extensive array of interrelated classes. In this work, we present a novel approach that utilizes SHAP (SHapley Additive exPlanations) to enhance synthetic data generation. SHAP quantifies the individual contributions of each input feature towards the victim model's output, facilitating the optimization of an energy-based GAN towards a desirable output. This method significantly boosts performance, achieving a 16.45% increase in the accuracy of image classification models and extending to video classification models with an average improvement of 26.11% and a maximum of 33.36% on challenging datasets such as UCF11, UCF101, Kinetics 400, Kinetics 600, and Something-Something V2. We further demonstrate the effectiveness and practical utility of our method under various scenarios, including the availability of top-k prediction probabilities, top-k prediction labels, and top-1 labels.

A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically infinite-dimensional, deep learning has predominantly advanced through applications in computer vision and natural language processing that focus on mappings between finite-dimensional spaces. Such fundamental disparities in the nature of the data have limited neural networks from achieving a comparable level of success in scientific applications as seen in other fields. Neural operators are a principled way to generalize neural networks to mappings between function spaces, offering a pathway to replicate deep learning's transformative impact on scientific problems. For instance, neural operators can learn solution operators for entire classes of PDEs, e.g., physical systems with different boundary conditions, coefficient functions, and geometries. A key factor in deep learning's success has been the careful engineering of neural architectures through extensive empirical testing. Translating these neural architectures into neural operators allows operator learning to enjoy these same empirical optimizations. However, prior neural operator architectures have often been introduced as standalone models, not directly derived as extensions of existing neural network architectures. In this paper, we identify and distill the key principles for constructing practical implementations of mappings between infinite-dimensional function spaces. Using these principles, we propose a recipe for converting several popular neural architectures into neural operators with minimal modifications. This paper aims to guide practitioners through this process and details the steps to make neural operators work in practice. Our code can be found at https://github.com/neuraloperator/NNs-to-NOs

Adapting pre-trained foundation models for various downstream tasks has been prevalent in artificial intelligence. Due to the vast number of tasks and high costs, adjusting all parameters becomes unfeasible. To mitigate this, several fine-tuning techniques have been developed to update the pre-trained model weights in a more resource-efficient manner, such as through low-rank adjustments. Yet, almost all of these methods focus on linear weights, neglecting the intricacies of parameter spaces in higher dimensions like 4D. Alternatively, some methods can be adapted for high-dimensional parameter space by compressing changes in the original space into two dimensions and then employing low-rank matrix decomposition. However, these approaches destructs the structural integrity of the involved high-dimensional spaces. To tackle the diversity of dimensional spaces across different foundation models and provide a more precise representation of the changes within these spaces, this paper introduces a generalized parameter-efficient fine-tuning framework, FLoRA, designed for various dimensional parameter space. Specifically, utilizing Tucker decomposition, FLoRA asserts that changes in each dimensional parameter space are based on a low-rank core space which maintains the consistent topological structure with the original space. It then models the changes through this core space alongside corresponding weights to reconstruct alterations in the original space. FLoRA effectively preserves the structural integrity of the change of original N-dimensional parameter space, meanwhile decomposes it via low-rank tensor decomposition. Extensive experiments on computer vision, natural language processing and multi-modal tasks validate FLoRA's effectiveness. Codes are available at https://github.com/SJTU-DeepVisionLab/FLoRA.

The autoencoder is an unsupervised learning paradigm that aims to create a compact latent representation of data by minimizing the reconstruction loss. However, it tends to overlook the fact that most data (images) are embedded in a lower-dimensional space, which is crucial for effective data representation. To address this limitation, we propose a novel approach called Low-Rank Autoencoder (LoRAE). In LoRAE, we incorporated a low-rank regularizer to adaptively reconstruct a low-dimensional latent space while preserving the basic objective of an autoencoder. This helps embed the data in a lower-dimensional space while preserving important information. It is a simple autoencoder extension that learns low-rank latent space. Theoretically, we establish a tighter error bound for our model. Empirically, our model's superiority shines through various tasks such as image generation and downstream classification. Both theoretical and practical outcomes highlight the importance of acquiring low-dimensional embeddings.

Target encoding plays a central role when learning Convolutional Neural Networks. In this realm, One-hot encoding is the most prevalent strategy due to its simplicity. However, this so widespread encoding schema assumes a flat label space, thus ignoring rich relationships existing among labels that can be exploited during training. In large-scale datasets, data does not span the full label space, but instead lies in a low-dimensional output manifold. Following this observation, we embed the targets into a low-dimensional space, drastically improving convergence speed while preserving accuracy. Our contribution is two fold: (i) We show that random projections of the label space are a valid tool to find such lower dimensional embeddings, boosting dramatically convergence rates at zero computational cost; and (ii) we propose a normalized eigenrepresentation of the class manifold that encodes the targets with minimal information loss, improving the accuracy of random projections encoding while enjoying the same convergence rates. Experiments on CIFAR-100, CUB200-2011, Imagenet, and MIT Places demonstrate that the proposed approach drastically improves convergence speed while reaching very competitive accuracy rates.

The advancement of makeup transfer, editing, and image encoding has demonstrated their effectiveness and superior quality. However, existing makeup works primarily focus on low-dimensional features such as color distributions and patterns, limiting their versatillity across a wide range of makeup applications. Futhermore, existing high-dimensional latent encoding methods mainly target global features such as structure and style, and are less effective for tasks that require detailed attention to local color and pattern features of makeup. To overcome these limitations, we propose BeautyBank, a novel makeup encoder that disentangles pattern features of bare and makeup faces. Our method encodes makeup features into a high-dimensional space, preserving essential details necessary for makeup reconstruction and broadening the scope of potential makeup research applications. We also propose a Progressive Makeup Tuning (PMT) strategy, specifically designed to enhance the preservation of detailed makeup features while preventing the inclusion of irrelevant attributes. We further explore novel makeup applications, including facial image generation with makeup injection and makeup similarity measure. Extensive empirical experiments validate that our method offers superior task adaptability and holds significant potential for widespread application in various makeup-related fields. Furthermore, to address the lack of large-scale, high-quality paired makeup datasets in the field, we constructed the Bare-Makeup Synthesis Dataset (BMS), comprising 324,000 pairs of 512x512 pixel images of bare and makeup-enhanced faces.

We frame the problem of unifying representations in neural models as one of sparse model recovery and introduce a framework that extends sparse autoencoders (SAEs) to lifted spaces and infinite-dimensional function spaces, enabling mechanistic interpretability of large neural operators (NO). While the Platonic Representation Hypothesis suggests that neural networks converge to similar representations across architectures, the representational properties of neural operators remain underexplored despite their growing importance in scientific computing. We compare the inference and training dynamics of SAEs, lifted-SAE, and SAE neural operators. We highlight how lifting and operator modules introduce beneficial inductive biases, enabling faster recovery, improved recovery of smooth concepts, and robust inference across varying resolutions, a property unique to neural operators.

Neural networks embed the geometric structure of a data manifold lying in a high-dimensional space into latent representations. Ideally, the distribution of the data points in the latent space should depend only on the task, the data, the loss, and other architecture-specific constraints. However, factors such as the random weights initialization, training hyperparameters, or other sources of randomness in the training phase may induce incoherent latent spaces that hinder any form of reuse. Nevertheless, we empirically observe that, under the same data and modeling choices, the angles between the encodings within distinct latent spaces do not change. In this work, we propose the latent similarity between each sample and a fixed set of anchors as an alternative data representation, demonstrating that it can enforce the desired invariances without any additional training. We show how neural architectures can leverage these relative representations to guarantee, in practice, invariance to latent isometries and rescalings, effectively enabling latent space communication: from zero-shot model stitching to latent space comparison between diverse settings. We extensively validate the generalization capability of our approach on different datasets, spanning various modalities (images, text, graphs), tasks (e.g., classification, reconstruction) and architectures (e.g., CNNs, GCNs, transformers).

We perform an average case analysis of the generalization dynamics of large neural networks trained using gradient descent. We study the practically-relevant "high-dimensional" regime where the number of free parameters in the network is on the order of or even larger than the number of examples in the dataset. Using random matrix theory and exact solutions in linear models, we derive the generalization error and training error dynamics of learning and analyze how they depend on the dimensionality of data and signal to noise ratio of the learning problem. We find that the dynamics of gradient descent learning naturally protect against overtraining and overfitting in large networks. Overtraining is worst at intermediate network sizes, when the effective number of free parameters equals the number of samples, and thus can be reduced by making a network smaller or larger. Additionally, in the high-dimensional regime, low generalization error requires starting with small initial weights. We then turn to non-linear neural networks, and show that making networks very large does not harm their generalization performance. On the contrary, it can in fact reduce overtraining, even without early stopping or regularization of any sort. We identify two novel phenomena underlying this behavior in overcomplete models: first, there is a frozen subspace of the weights in which no learning occurs under gradient descent; and second, the statistical properties of the high-dimensional regime yield better-conditioned input correlations which protect against overtraining. We demonstrate that naive application of worst-case theories such as Rademacher complexity are inaccurate in predicting the generalization performance of deep neural networks, and derive an alternative bound which incorporates the frozen subspace and conditioning effects and qualitatively matches the behavior observed in simulation.

Transformers and Mamba, initially invented for natural language processing, have inspired backbone architectures for visual recognition. Recent studies integrated Local Attention Transformers with Mamba to capture both local details and global contexts. Despite competitive performance, these methods are limited to simple stacking of Transformer and Mamba layers without any interaction mechanism between them. Thus, deep integration between Transformer and Mamba layers remains an open problem. We address this problem by proposing A2Mamba, a powerful Transformer-Mamba hybrid network architecture, featuring a new token mixer termed Multi-scale Attention-augmented State Space Model (MASS), where multi-scale attention maps are integrated into an attention-augmented SSM (A2SSM). A key step of A2SSM performs a variant of cross-attention by spatially aggregating the SSM's hidden states using the multi-scale attention maps, which enhances spatial dependencies pertaining to a two-dimensional space while improving the dynamic modeling capabilities of SSMs. Our A2Mamba outperforms all previous ConvNet-, Transformer-, and Mamba-based architectures in visual recognition tasks. For instance, A2Mamba-L achieves an impressive 86.1% top-1 accuracy on ImageNet-1K. In semantic segmentation, A2Mamba-B exceeds CAFormer-S36 by 2.5% in mIoU, while exhibiting higher efficiency. In object detection and instance segmentation with Cascade Mask R-CNN, A2Mamba-S surpasses MambaVision-B by 1.2%/0.9% in AP^b/AP^m, while having 40% less parameters. Code is publicly available at https://github.com/LMMMEng/A2Mamba.

Recent work in unsupervised multi-object segmentation shows impressive results by predicting motion from a single image despite the inherent ambiguity in predicting motion without the next image. On the other hand, the set of possible motions for an image can be constrained to a low-dimensional space by considering the scene structure and moving objects in it. We propose to model pixel-wise geometry and object motion to remove ambiguity in reconstructing flow from a single image. Specifically, we divide the image into coherently moving regions and use depth to construct flow bases that best explain the observed flow in each region. We achieve state-of-the-art results in unsupervised multi-object segmentation on synthetic and real-world datasets by modeling the scene structure and object motion. Our evaluation of the predicted depth maps shows reliable performance in monocular depth estimation.

Reinforcement learning often needs to deal with the exponential growth of states and actions when exploring optimal control in high-dimensional spaces (often known as the curse of dimensionality). In this work, we address this issue by learning the inherent structure of action-wise similar MDP to appropriately balance the performance degradation versus sample/computational complexity. In particular, we partition the action spaces into multiple groups based on the similarity in transition distribution and reward function, and build a linear decomposition model to capture the difference between the intra-group transition kernel and the intra-group rewards. Both our theoretical analysis and experiments reveal a surprising and counter-intuitive result: while a more refined grouping strategy can reduce the approximation error caused by treating actions in the same group as identical, it also leads to increased estimation error when the size of samples or the computation resources is limited. This finding highlights the grouping strategy as a new degree of freedom that can be optimized to minimize the overall performance loss. To address this issue, we formulate a general optimization problem for determining the optimal grouping strategy, which strikes a balance between performance loss and sample/computational complexity. We further propose a computationally efficient method for selecting a nearly-optimal grouping strategy, which maintains its computational complexity independent of the size of the action space.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

In this paper, we introduce fastHDMI, a Python package designed for efficient variable screening in high-dimensional datasets, particularly neuroimaging data. This work pioneers the application of three mutual information estimation methods for neuroimaging variable selection, a novel approach implemented via fastHDMI. These advancements enhance our ability to analyze the complex structures of neuroimaging datasets, providing improved tools for variable selection in high-dimensional spaces. Using the preprocessed ABIDE dataset, we evaluate the performance of these methods through extensive simulations. The tests cover a range of conditions, including linear and nonlinear associations, as well as continuous and binary outcomes. Our results highlight the superiority of the FFTKDE-based mutual information estimation for feature screening in continuous nonlinear outcomes, while binning-based methods outperform others for binary outcomes with nonlinear probability preimages. For linear simulations, both Pearson correlation and FFTKDE-based methods show comparable performance for continuous outcomes, while Pearson excels in binary outcomes with linear probability preimages. A comprehensive case study using the ABIDE dataset further demonstrates fastHDMI's practical utility, showcasing the predictive power of models built from variables selected using our screening techniques. This research affirms the computational efficiency and methodological strength of fastHDMI, significantly enriching the toolkit available for neuroimaging analysis.

In variational inference, the benefits of Bayesian models rely on accurately capturing the true posterior distribution. We propose using neural samplers that specify implicit distributions, which are well-suited for approximating complex multimodal and correlated posteriors in high-dimensional spaces. Our approach introduces novel bounds for approximate inference using implicit distributions by locally linearising the neural sampler. This is distinct from existing methods that rely on additional discriminator networks and unstable adversarial objectives. Furthermore, we present a new sampler architecture that, for the first time, enables implicit distributions over tens of millions of latent variables, addressing computational concerns by using differentiable numerical approximations. We empirically show that our method is capable of recovering correlations across layers in large Bayesian neural networks, a property that is crucial for a network's performance but notoriously challenging to achieve. To the best of our knowledge, no other method has been shown to accomplish this task for such large models. Through experiments in downstream tasks, we demonstrate that our expressive posteriors outperform state-of-the-art uncertainty quantification methods, validating the effectiveness of our training algorithm and the quality of the learned implicit approximation.

Bayesian Optimization (BO) is typically used to optimize an unknown function f that is noisy and costly to evaluate, by exploiting an acquisition function that must be maximized at each optimization step. Even if provably asymptotically optimal BO algorithms are efficient at optimizing low-dimensional functions, scaling them to high-dimensional spaces remains an open problem, often tackled by assuming an additive structure for f. By doing so, BO algorithms typically introduce additional restrictive assumptions on the additive structure that reduce their applicability domain. This paper contains two main contributions: (i) we relax the restrictive assumptions on the additive structure of f without weakening the maximization guarantees of the acquisition function, and (ii) we address the over-exploration problem for decentralized BO algorithms. To these ends, we propose DuMBO, an asymptotically optimal decentralized BO algorithm that achieves very competitive performance against state-of-the-art BO algorithms, especially when the additive structure of f comprises high-dimensional factors.

Tracking objects in three-dimensional space is critical for autonomous driving. To ensure safety while driving, the tracker must be able to reliably track objects across frames and accurately estimate their states such as velocity and acceleration in the present. Existing works frequently focus on the association task while either neglecting the model performance on state estimation or deploying complex heuristics to predict the states. In this paper, we propose STT, a Stateful Tracking model built with Transformers, that can consistently track objects in the scenes while also predicting their states accurately. STT consumes rich appearance, geometry, and motion signals through long term history of detections and is jointly optimized for both data association and state estimation tasks. Since the standard tracking metrics like MOTA and MOTP do not capture the combined performance of the two tasks in the wider spectrum of object states, we extend them with new metrics called S-MOTA and MOTPS that address this limitation. STT achieves competitive real-time performance on the Waymo Open Dataset.

The analysis of emotions expressed in text has numerous applications. In contrast to categorical analysis, focused on classifying emotions according to a pre-defined set of common classes, dimensional approaches can offer a more nuanced way to distinguish between different emotions. Still, dimensional methods have been less studied in the literature. Considering a valence-arousal dimensional space, this work assesses the use of pre-trained Transformers to predict these two dimensions on a continuous scale, with input texts from multiple languages and domains. We specifically combined multiple annotated datasets from previous studies, corresponding to either emotional lexica or short text documents, and evaluated models of multiple sizes and trained under different settings. Our results show that model size can have a significant impact on the quality of predictions, and that by fine-tuning a large model we can confidently predict valence and arousal in multiple languages. We make available the code, models, and supporting data.

Multi-layer perceptrons (MLPs) conventionally follow a narrow-wide-narrow design where skip connections operate at the input/output dimensions while processing occurs in expanded hidden spaces. We challenge this convention by proposing wide-narrow-wide (Hourglass) MLP blocks where skip connections operate at expanded dimensions while residual computation flows through narrow bottlenecks. This inversion leverages higher-dimensional spaces for incremental refinement while maintaining computational efficiency through parameter-matched designs. Implementing Hourglass MLPs requires an initial projection to lift input signals to expanded dimensions. We propose that this projection can remain fixed at random initialization throughout training, enabling efficient training and inference implementations. We evaluate both architectures on generative tasks over popular image datasets, characterizing performance-parameter Pareto frontiers through systematic architectural search. Results show that Hourglass architectures consistently achieve superior Pareto frontiers compared to conventional designs. As parameter budgets increase, optimal Hourglass configurations favor deeper networks with wider skip connections and narrower bottlenecks-a scaling pattern distinct from conventional MLPs. Our findings suggest reconsidering skip connection placement in modern architectures, with potential applications extending to Transformers and other residual networks.

As artificial intelligence models have exploded in scale and capability, understanding of their internal mechanisms remains a critical challenge. Inspired by the success of dynamical systems approaches in neuroscience, here we propose a novel framework for studying computations in deep learning systems. We focus on the residual stream (RS) in transformer models, conceptualizing it as a dynamical system evolving across layers. We find that activations of individual RS units exhibit strong continuity across layers, despite the RS being a non-privileged basis. Activations in the RS accelerate and grow denser over layers, while individual units trace unstable periodic orbits. In reduced-dimensional spaces, the RS follows a curved trajectory with attractor-like dynamics in the lower layers. These insights bridge dynamical systems theory and mechanistic interpretability, establishing a foundation for a "neuroscience of AI" that combines theoretical rigor with large-scale data analysis to advance our understanding of modern neural networks.

We curate a comprehensive dataset of 4,550 questions and solutions from problem sets, midterm exams, and final exams across all MIT Mathematics and Electrical Engineering and Computer Science (EECS) courses required for obtaining a degree. We evaluate the ability of large language models to fulfill the graduation requirements for any MIT major in Mathematics and EECS. Our results demonstrate that GPT-3.5 successfully solves a third of the entire MIT curriculum, while GPT-4, with prompt engineering, achieves a perfect solve rate on a test set excluding questions based on images. We fine-tune an open-source large language model on this dataset. We employ GPT-4 to automatically grade model responses, providing a detailed performance breakdown by course, question, and answer type. By embedding questions in a low-dimensional space, we explore the relationships between questions, topics, and classes and discover which questions and classes are required for solving other questions and classes through few-shot learning. Our analysis offers valuable insights into course prerequisites and curriculum design, highlighting language models' potential for learning and improving Mathematics and EECS education.

We propose SPARC, a lightweight continual learning framework for large language models (LLMs) that enables efficient task adaptation through prompt tuning in a lower-dimensional space. By leveraging principal component analysis (PCA), we identify a compact subspace of the training data. Optimizing prompts in this lower-dimensional space enhances training efficiency, as it focuses updates on the most relevant features while reducing computational overhead. Furthermore, since the model's internal structure remains unaltered, the extensive knowledge gained from pretraining is fully preserved, ensuring that previously learned information is not compromised during adaptation. Our method achieves high knowledge retention in both task-incremental and domain-incremental continual learning setups while fine-tuning only 0.04% of the model's parameters. Additionally, by integrating LoRA, we enhance adaptability to computational constraints, allowing for a tradeoff between accuracy and training cost. Experiments on the SuperGLUE benchmark demonstrate that our PCA-based prompt tuning combined with LoRA maintains full knowledge retention while improving accuracy, utilizing only 1% of the model's parameters. These results establish our approach as a scalable and resource-efficient solution for continual learning in LLMs.

We ask whether multilingual language models trained on unbalanced, English-dominated corpora use English as an internal pivot language -- a question of key importance for understanding how language models function and the origins of linguistic bias. Focusing on the Llama-2 family of transformer models, our study uses carefully constructed non-English prompts with a unique correct single-token continuation. From layer to layer, transformers gradually map an input embedding of the final prompt token to an output embedding from which next-token probabilities are computed. Tracking intermediate embeddings through their high-dimensional space reveals three distinct phases, whereby intermediate embeddings (1) start far away from output token embeddings; (2) already allow for decoding a semantically correct next token in the middle layers, but give higher probability to its version in English than in the input language; (3) finally move into an input-language-specific region of the embedding space. We cast these results into a conceptual model where the three phases operate in "input space", "concept space", and "output space", respectively. Crucially, our evidence suggests that the abstract "concept space" lies closer to English than to other languages, which may have important consequences regarding the biases held by multilingual language models.

In this study, we present an model-based approach to recognize full 26 degrees of freedom of a human hand. Input data include RGB-D images acquired from a Kinect camera and a 3D model of the hand constructed from its anatomy and graphical matrices. A cost function is then defined so that its minimum value is achieved when the model and observation images are matched. To solve the optimization problem in 26 dimensional space, the particle swarm optimization algorimth with improvements are used. In addition, parallel computation in graphical processing units (GPU) is utilized to handle computationally expensive tasks. Simulation and experimental results show that the system can recognize 26 degrees of freedom of hands with the processing time of 0.8 seconds per frame. The algorithm is robust to noise and the hardware requirement is simple with a single camera.

Dimensionality reduction methods are unsupervised approaches which learn low-dimensional spaces where some properties of the initial space, typically the notion of "neighborhood", are preserved. Such methods usually require propagation on large k-NN graphs or complicated optimization solvers. On the other hand, self-supervised learning approaches, typically used to learn representations from scratch, rely on simple and more scalable frameworks for learning. In this paper, we propose TLDR, a dimensionality reduction method for generic input spaces that is porting the recent self-supervised learning framework of Zbontar et al. (2021) to the specific task of dimensionality reduction, over arbitrary representations. We propose to use nearest neighbors to build pairs from a training set and a redundancy reduction loss to learn an encoder that produces representations invariant across such pairs. TLDR is a method that is simple, easy to train, and of broad applicability; it consists of an offline nearest neighbor computation step that can be highly approximated, and a straightforward learning process. Aiming for scalability, we focus on improving linear dimensionality reduction, and show consistent gains on image and document retrieval tasks, e.g. gaining +4% mAP over PCA on ROxford for GeM- AP, improving the performance of DINO on ImageNet or retaining it with a 10x compression.

Human perception integrates multiple modalities, such as vision, hearing, and language, into a unified understanding of the surrounding reality. While recent multimodal models have achieved significant progress by aligning pairs of modalities via contrastive learning, their solutions are unsuitable when scaling to multiple modalities. These models typically align each modality to a designated anchor without ensuring the alignment of all modalities with each other, leading to suboptimal performance in tasks requiring a joint understanding of multiple modalities. In this paper, we structurally rethink the pairwise conventional approach to multimodal learning and we present the novel Gramian Representation Alignment Measure (GRAM), which overcomes the above-mentioned limitations. GRAM learns and then aligns n modalities directly in the higher-dimensional space in which modality embeddings lie by minimizing the Gramian volume of the k-dimensional parallelotope spanned by the modality vectors, ensuring the geometric alignment of all modalities simultaneously. GRAM can replace cosine similarity in any downstream method, holding for 2 to n modalities and providing more meaningful alignment with respect to previous similarity measures. The novel GRAM-based contrastive loss function enhances the alignment of multimodal models in the higher-dimensional embedding space, leading to new state-of-the-art performance in downstream tasks such as video-audio-text retrieval and audio-video classification. The project page, the code, and the pretrained models are available at https://ispamm.github.io/GRAM/.

We introduce Audio Atlas, an interactive web application for visualizing audio data using text-audio embeddings. Audio Atlas is designed to facilitate the exploration and analysis of audio datasets using a contrastive embedding model and a vector database for efficient data management and semantic search. The system maps audio embeddings into a two-dimensional space and leverages DeepScatter for dynamic visualization. Designed for extensibility, Audio Atlas allows easy integration of new datasets, enabling users to better understand their audio data and identify both patterns and outliers. We open-source the codebase of Audio Atlas, and provide an initial implementation containing various audio and music datasets.

Given a K-vertex simplex in a d-dimensional space, suppose we measure n points on the simplex with noise (hence, some of the observed points fall outside the simplex). Vertex hunting is the problem of estimating the K vertices of the simplex. A popular vertex hunting algorithm is successive projection algorithm (SPA). However, SPA is observed to perform unsatisfactorily under strong noise or outliers. We propose pseudo-point SPA (pp-SPA). It uses a projection step and a denoise step to generate pseudo-points and feed them into SPA for vertex hunting. We derive error bounds for pp-SPA, leveraging on extreme value theory of (possibly) high-dimensional random vectors. The results suggest that pp-SPA has faster rates and better numerical performances than SPA. Our analysis includes an improved non-asymptotic bound for the original SPA, which is of independent interest.

Grid-based structures are commonly used to encode explicit features for graphics primitives such as images, signed distance functions (SDF), and neural radiance fields (NeRF) due to their simple implementation. However, in n-dimensional space, calculating the value of a sampled point requires interpolating the values of its 2^n neighboring vertices. The exponential scaling with dimension leads to significant computational overheads. To address this issue, we propose a simplex-based approach for encoding graphics primitives. The number of vertices in a simplex-based structure increases linearly with dimension, making it a more efficient and generalizable alternative to grid-based representations. Using the non-axis-aligned simplicial structure property, we derive and prove a coordinate transformation, simplicial subdivision, and barycentric interpolation scheme for efficient sampling, which resembles transformation procedures in the simplex noise algorithm. Finally, we use hash tables to store multiresolution features of all interest points in the simplicial grid, which are passed into a tiny fully connected neural network to parameterize graphics primitives. We implemented a detailed simplex-based structure encoding algorithm in C++ and CUDA using the methods outlined in our approach. In the 2D image fitting task, the proposed method is capable of fitting a giga-pixel image with 9.4% less time compared to the baseline method proposed by instant-ngp, while maintaining the same quality and compression rate. In the volumetric rendering setup, we observe a maximum 41.2% speedup when the samples are dense enough.

Denoising diffusion models enable conditional generation and density modeling of complex relationships like images and text. However, the nature of the learned relationships is opaque making it difficult to understand precisely what relationships between words and parts of an image are captured, or to predict the effect of an intervention. We illuminate the fine-grained relationships learned by diffusion models by noticing a precise relationship between diffusion and information decomposition. Exact expressions for mutual information and conditional mutual information can be written in terms of the denoising model. Furthermore, pointwise estimates can be easily estimated as well, allowing us to ask questions about the relationships between specific images and captions. Decomposing information even further to understand which variables in a high-dimensional space carry information is a long-standing problem. For diffusion models, we show that a natural non-negative decomposition of mutual information emerges, allowing us to quantify informative relationships between words and pixels in an image. We exploit these new relations to measure the compositional understanding of diffusion models, to do unsupervised localization of objects in images, and to measure effects when selectively editing images through prompt interventions.

The accurate modeling of dynamics in interactive environments is critical for successful long-range prediction. Such a capability could advance Reinforcement Learning (RL) and Planning algorithms, but achieving it is challenging. Inaccuracies in model estimates can compound, resulting in increased errors over long horizons. We approach this problem from the lens of Koopman theory, where the nonlinear dynamics of the environment can be linearized in a high-dimensional latent space. This allows us to efficiently parallelize the sequential problem of long-range prediction using convolution while accounting for the agent's action at every time step. Our approach also enables stability analysis and better control over gradients through time. Taken together, these advantages result in significant improvement over the existing approaches, both in the efficiency and the accuracy of modeling dynamics over extended horizons. We also show that this model can be easily incorporated into dynamics modeling for model-based planning and model-free RL and report promising experimental results.

Automatic International Classification of Diseases (ICD) coding aims to assign multiple ICD codes to a medical note with average length of 3,000+ tokens. This task is challenging due to a high-dimensional space of multi-label assignment (tens of thousands of ICD codes) and the long-tail challenge: only a few codes (common diseases) are frequently assigned while most codes (rare diseases) are infrequently assigned. This study addresses the long-tail challenge by adapting a prompt-based fine-tuning technique with label semantics, which has been shown to be effective under few-shot setting. To further enhance the performance in medical domain, we propose a knowledge-enhanced longformer by injecting three domain-specific knowledge: hierarchy, synonym, and abbreviation with additional pretraining using contrastive learning. Experiments on MIMIC-III-full, a benchmark dataset of code assignment, show that our proposed method outperforms previous state-of-the-art method in 14.5% in marco F1 (from 10.3 to 11.8, P<0.001). To further test our model on few-shot setting, we created a new rare diseases coding dataset, MIMIC-III-rare50, on which our model improves marco F1 from 17.1 to 30.4 and micro F1 from 17.2 to 32.6 compared to previous method.

Instance selection (IS) is important in machine learning for reducing dataset size while keeping key characteristics. Current IS methods often struggle with capturing complex relationships in high-dimensional spaces and scale with large datasets. This paper introduces a graph attention-based instance selection (GAIS) method that uses attention mechanisms to identify informative instances through their structural relationships in graph representations. We present two approaches for scalable graph construction: a distance-based mini-batch sampling technique that reduces computation through strategic batch processing, and a hierarchical hashing approach that allows for efficient similarity computation through random projections. The mini-batch approach keeps class distributions through stratified sampling, while the hierarchical hashing method captures relationships at multiple granularities through single-level, multi-level, and multi-view variants. Experiments across 39 datasets show that GAIS achieves reduction rates above 96\% while maintaining or improving model performance relative to state-of-the-art IS methods. The findings shows that the distance-based mini-batch approach offers an optimal balance of efficiency and effectiveness for large-scale datasets, while multi-view variants provide superior performance for complex, high-dimensional data, demonstrating that attention-based importance scoring can effectively identify instances crucial for maintaining decision boundaries without requiring exhaustive pairwise comparisons.

Image research has shown substantial attention in deblurring networks in recent years. Yet, their practical usage in real-world deblurring, especially motion blur, remains limited due to the lack of pixel-aligned training triplets (background, blurred image, and blur heat map) and restricted information inherent in blurred images. This paper presents a simple yet efficient framework to synthetic and restore motion blur images using Inertial Measurement Unit (IMU) data. Notably, the framework includes a strategy for training triplet generation, and a Gyroscope-Aided Motion Deblurring (GAMD) network for blurred image restoration. The rationale is that through harnessing IMU data, we can determine the transformation of the camera pose during the image exposure phase, facilitating the deduction of the motion trajectory (aka. blur trajectory) for each point inside the three-dimensional space. Thus, the synthetic triplets using our strategy are inherently close to natural motion blur, strictly pixel-aligned, and mass-producible. Through comprehensive experiments, we demonstrate the advantages of the proposed framework: only two-pixel errors between our synthetic and real-world blur trajectories, a marked improvement (around 33.17%) of the state-of-the-art deblurring method MIMO on Peak Signal-to-Noise Ratio (PSNR).

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several extensions to derive practical training objectives. These include infinite-dimensional versions of Girsanov theorem, in order to be able to compute an ELBO, and of the sampling theorem, in order to guarantee that functional evaluations in a countable set of points are equivalent to infinite-dimensional functions. We use FDPs to build a new breed of generative models in function spaces, which do not require specialized network architectures, and that can work with any kind of continuous data. Our results on real data show that FDPs achieve high-quality image generation, using a simple MLP architecture with orders of magnitude fewer parameters than existing diffusion models.

Self-Attentive Sequential Recommendation (SASRec) effectively captures long-term user preferences by applying attention mechanisms to historical interactions. Concurrently, the rise of Large Language Models (LLMs) has motivated research into LLM-based recommendation, which leverages their powerful generalization and language understanding capabilities. However, LLMs often lack the domain-specific knowledge and collaborative signals essential for high-quality recommendations when relying solely on textual prompts. To address this limitation, this study proposes SASRecLLM, a novel framework that integrates SASRec as a collaborative encoder with an LLM fine-tuned using Low-Rank Adaptation (LoRA). The components are connected via a mapping layer to align their dimensional spaces, and three targeted training strategies are designed to optimize the hybrid architecture. Extensive experiments on multiple datasets demonstrate that SASRecLLM achieves robust and consistent improvements over strong baselines in both cold-start and warm-start scenarios. This work advances the field of LLM-based recommendation by presenting a modular and effective paradigm for fusing structured collaborative filtering with the semantic power of fine-tuned LLMs. The implementation is available on GitHub: https://github.com/kechenkristin/RecLLM

We introduce a gradient-free framework for Bayesian Optimal Experimental Design (BOED) in sequential settings, aimed at complex systems where gradient information is unavailable. Our method combines Ensemble Kalman Inversion (EKI) for design optimization with the Affine-Invariant Langevin Dynamics (ALDI) sampler for efficient posterior sampling-both of which are derivative-free and ensemble-based. To address the computational challenges posed by nested expectations in BOED, we propose variational Gaussian and parametrized Laplace approximations that provide tractable upper and lower bounds on the Expected Information Gain (EIG). These approximations enable scalable utility estimation in high-dimensional spaces and PDE-constrained inverse problems. We demonstrate the performance of our framework through numerical experiments ranging from linear Gaussian models to PDE-based inference tasks, highlighting the method's robustness, accuracy, and efficiency in information-driven experimental design.

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we show that the OT map itself can be used as a generative model, providing comparable performance. Previous analogous approaches consider OT maps as generative models only in the latent spaces due to their poor performance in the original high-dimensional ambient space. In contrast, we apply OT maps directly in the ambient space, e.g., a space of high-dimensional images. First, we derive a min-max optimization algorithm to efficiently compute OT maps for the quadratic cost (Wasserstein-2 distance). Next, we extend the approach to the case when the input and output distributions are located in the spaces of different dimensions and derive error bounds for the computed OT map. We evaluate the algorithm on image generation and unpaired image restoration tasks. In particular, we consider denoising, colorization, and inpainting, where the optimality of the restoration map is a desired attribute, since the output (restored) image is expected to be close to the input (degraded) one.

We study several aspects of charged dilaton black holes with planar symmetry in (d+2)-dimensional spacetime, generalizing the four-dimensional results investigated in arXiv:0911.3586 [hep-th]. We revisit the exact solutions with both zero and finite temperature and discuss the thermodynamics of the near-extremal black holes. We calculate the AC conductivity in the zero-temperature background by solving the corresponding Schr\"{o}dinger equation and find that the AC conductivity behaves like omega^{delta}, where the exponent delta is determined by the dilaton coupling alpha and the spacetime dimension parameter d. Moreover, we also study the Gauss-Bonnet corrections to eta/s in a five-dimensional finite-temperature background.

We introduce a new family of physics-inspired generative models termed PFGM++ that unifies diffusion models and Poisson Flow Generative Models (PFGM). These models realize generative trajectories for N dimensional data by embedding paths in N{+}D dimensional space while still controlling the progression with a simple scalar norm of the D additional variables. The new models reduce to PFGM when D{=}1 and to diffusion models when D{to}infty. The flexibility of choosing D allows us to trade off robustness against rigidity as increasing D results in more concentrated coupling between the data and the additional variable norms. We dispense with the biased large batch field targets used in PFGM and instead provide an unbiased perturbation-based objective similar to diffusion models. To explore different choices of D, we provide a direct alignment method for transferring well-tuned hyperparameters from diffusion models (D{to} infty) to any finite D values. Our experiments show that models with finite D can be superior to previous state-of-the-art diffusion models on CIFAR-10/FFHQ 64{times}64 datasets, with FID scores of 1.91/2.43 when D{=}2048/128. In class-conditional setting, D{=}2048 yields current state-of-the-art FID of 1.74 on CIFAR-10. In addition, we demonstrate that models with smaller D exhibit improved robustness against modeling errors. Code is available at https://github.com/Newbeeer/pfgmpp

Vision tokenizers have gained a lot of attraction due to their scalability and compactness; previous works depend on old-school GAN-based hyperparameters, biased comparisons, and a lack of comprehensive analysis of the scaling behaviours. To tackle those issues, we introduce Grouped Spherical Quantization (GSQ), featuring spherical codebook initialization and lookup regularization to constrain codebook latent to a spherical surface. Our empirical analysis of image tokenizer training strategies demonstrates that GSQ-GAN achieves superior reconstruction quality over state-of-the-art methods with fewer training iterations, providing a solid foundation for scaling studies. Building on this, we systematically examine the scaling behaviours of GSQ, specifically in latent dimensionality, codebook size, and compression ratios, and their impact on model performance. Our findings reveal distinct behaviours at high and low spatial compression levels, underscoring challenges in representing high-dimensional latent spaces. We show that GSQ can restructure high-dimensional latent into compact, low-dimensional spaces, thus enabling efficient scaling with improved quality. As a result, GSQ-GAN achieves a 16x down-sampling with a reconstruction FID (rFID) of 0.50.

Dimensionality reduction techniques are fundamental for analyzing and visualizing high-dimensional data. With established methods like t-SNE and PCA presenting a trade-off between representational power and interpretability. This paper introduces a novel approach that bridges this gap by combining the interpretability of linear methods with the expressiveness of non-linear transformations. The proposed algorithm constructs a non-linear mapping between high-dimensional and low-dimensional spaces through a combination of linear transformations, each weighted by Gaussian functions. This architecture enables complex non-linear transformations while preserving the interpretability advantages of linear methods, as each transformation can be analyzed independently. The resulting model provides both powerful dimensionality reduction and transparent insights into the transformed space. Techniques for interpreting the learned transformations are presented, including methods for identifying suppressed dimensions and how space is expanded and contracted. These tools enable practitioners to understand how the algorithm preserves and modifies geometric relationships during dimensionality reduction. To ensure the practical utility of this algorithm, the creation of user-friendly software packages is emphasized, facilitating its adoption in both academia and industry.

Low-rank adaptation (LoRA) reduces the computational and memory demands of fine-tuning large language models (LLMs) by approximating updates with low-rank matrices. However, low-rank approximation in two-dimensional space fails to capture high-dimensional structures within the target matrix. Recently, tensor decomposition methods have been explored for fine-tuning LLMs, leveraging their ability to extract structured information. Yet, these approaches primarily rely on random initialization, and the impact of initialization on tensor adaptation remains underexplored. In this paper, we reveal that random initialization significantly diverges from the validation loss achieved by full fine-tuning. To address this, we propose Weight-Decomposed Tensor Adaptation (DoTA), which leverages the Matrix Product Operator (MPO) decomposition of pre-trained weights for effective initialization in fine-tuning LLMs. Additionally, we introduce QDoTA, a quantized version of DoTA designed for 4-bit quantization. Experiments on commonsense and arithmetic reasoning tasks show that DoTA outperforms random initialization methods with fewer parameters. QDoTA further reduces memory consumption and achieves comparable performance to DoTA on commonsense reasoning tasks. We will release our code to support future research.

Inference on large language models can be expensive in terms of the compute and memory costs involved, especially when long sequence lengths are used. In particular, the self-attention mechanism used in such models contributes significantly to these costs, which has resulted in several recent works that propose sparse attention approximations for inference. In this work, we propose to approximate the self-attention computation by focusing on the dimensionality of key vectors computed in the attention block. Our analysis reveals that the key vectors lie in a significantly lower-dimensional space, consistently across several datasets and models. Exploiting this observation, we propose Loki, a novel sparse attention method that ranks and selects tokens in the KV-cache based on attention scores computed in low-dimensional space. Our evaluations show that Loki is able to maintain the efficacy of the models better than other popular approximation methods, while speeding up the attention computation due to reduced data movement (load/store) and compute costs.

Word embeddings improve generalization over lexical features by placing each word in a lower-dimensional space, using distributional information obtained from unlabeled data. However, the effectiveness of word embeddings for downstream NLP tasks is limited by out-of-vocabulary (OOV) words, for which embeddings do not exist. In this paper, we present MIMICK, an approach to generating OOV word embeddings compositionally, by learning a function from spellings to distributional embeddings. Unlike prior work, MIMICK does not require re-training on the original word embedding corpus; instead, learning is performed at the type level. Intrinsic and extrinsic evaluations demonstrate the power of this simple approach. On 23 languages, MIMICK improves performance over a word-based baseline for tagging part-of-speech and morphosyntactic attributes. It is competitive with (and complementary to) a supervised character-based model in low-resource settings.

Implicit policies parameterized by generative models, such as Diffusion Policy, have become the standard for policy learning and Vision-Language-Action (VLA) models in robotics. However, these approaches often suffer from high computational cost, exposure bias, and unstable inference dynamics, which lead to divergence under distribution shifts. Energy-Based Models (EBMs) address these issues by learning energy landscapes end-to-end and modeling equilibrium dynamics, offering improved robustness and reduced exposure bias. Yet, policies parameterized by EBMs have historically struggled to scale effectively. Recent work on Energy-Based Transformers (EBTs) demonstrates the scalability of EBMs to high-dimensional spaces, but their potential for solving core challenges in physically embodied models remains underexplored. We introduce a new energy-based architecture, EBT-Policy, that solves core issues in robotic and real-world settings. Across simulated and real-world tasks, EBT-Policy consistently outperforms diffusion-based policies, while requiring less training and inference computation. Remarkably, on some tasks it converges within just two inference steps, a 50x reduction compared to Diffusion Policy's 100. Moreover, EBT-Policy exhibits emergent capabilities not seen in prior models, such as zero-shot recovery from failed action sequences using only behavior cloning and without explicit retry training. By leveraging its scalar energy for uncertainty-aware inference and dynamic compute allocation, EBT-Policy offers a promising path toward robust, generalizable robot behavior under distribution shifts.

In the fields of computational mathematics and artificial intelligence, the need for precise data modeling is crucial, especially for predictive machine learning tasks. This paper explores further XNet, a novel algorithm that employs the complex-valued Cauchy integral formula, offering a superior network architecture that surpasses traditional Multi-Layer Perceptrons (MLPs) and Kolmogorov-Arnold Networks (KANs). XNet significant improves speed and accuracy across various tasks in both low and high-dimensional spaces, redefining the scope of data-driven model development and providing substantial improvements over established time series models like LSTMs.

Multi-modal large language models (MLLMs) have shown incredible capabilities in a variety of 2D vision and language tasks. We extend MLLMs' perceptual capabilities to ground and reason about images in 3-dimensional space. To that end, we first develop a large-scale pre-training dataset for 2D and 3D called LV3D by combining multiple existing 2D and 3D recognition datasets under a common task formulation: as multi-turn question-answering. Next, we introduce a new MLLM named Cube-LLM and pre-train it on LV3D. We show that pure data scaling makes a strong 3D perception capability without 3D specific architectural design or training objective. Cube-LLM exhibits intriguing properties similar to LLMs: (1) Cube-LLM can apply chain-of-thought prompting to improve 3D understanding from 2D context information. (2) Cube-LLM can follow complex and diverse instructions and adapt to versatile input and output formats. (3) Cube-LLM can be visually prompted such as 2D box or a set of candidate 3D boxes from specialists. Our experiments on outdoor benchmarks demonstrate that Cube-LLM significantly outperforms existing baselines by 21.3 points of AP-BEV on the Talk2Car dataset for 3D grounded reasoning and 17.7 points on the DriveLM dataset for complex reasoning about driving scenarios, respectively. Cube-LLM also shows competitive results in general MLLM benchmarks such as refCOCO for 2D grounding with (87.0) average score, as well as visual question answering benchmarks such as VQAv2, GQA, SQA, POPE, etc. for complex reasoning. Our project is available at https://janghyuncho.github.io/Cube-LLM.

We study the problem of optimally projecting the transition matrix of a finite ergodic multivariate Markov chain onto a lower-dimensional state space. Specifically, we seek to construct a projected Markov chain that optimizes various information-theoretic criteria under cardinality constraints. These criteria include entropy rate, information-theoretic distance to factorizability, independence, and stationarity. We formulate these tasks as best subset selection problems over multivariate Markov chains and leverage the submodular (or supermodular) structure of the objective functions to develop efficient greedy-based algorithms with theoretical guarantees. We extend our analysis to k-submodular settings and introduce a generalized version of the distorted greedy algorithm, which may be of independent interest. Finally, we illustrate the theory and algorithms through extensive numerical experiments with publicly available code on multivariate Markov chains associated with the Bernoulli-Laplace and Curie-Weiss model.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

We advance the study of incentivized bandit exploration, in which arm choices are viewed as recommendations and are required to be Bayesian incentive compatible. Recent work has shown under certain independence assumptions that after collecting enough initial samples, the popular Thompson sampling algorithm becomes incentive compatible. We give an analog of this result for linear bandits, where the independence of the prior is replaced by a natural convexity condition. This opens up the possibility of efficient and regret-optimal incentivized exploration in high-dimensional action spaces. In the semibandit model, we also improve the sample complexity for the pre-Thompson sampling phase of initial data collection.

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators between infinite dimensional spaces, leading to discretization invariant representations that scale independently of the sample grid resolution. Here we present Variational Autoencoding Neural Operators (VANO), a general strategy for making a large class of operator learning architectures act as variational autoencoders. For this purpose, we provide a novel rigorous mathematical formulation of the variational objective in function spaces for training. VANO first maps an input function to a distribution over a latent space using a parametric encoder and then decodes a sample from the latent distribution to reconstruct the input, as in classic variational autoencoders. We test VANO with different model set-ups and architecture choices for a variety of benchmarks. We start from a simple Gaussian random field where we can analytically track what the model learns and progressively transition to more challenging benchmarks including modeling phase separation in Cahn-Hilliard systems and real world satellite data for measuring Earth surface deformation.

We introduce the use of reinforcement-learning (RL) techniques to the conformal-bootstrap programme. We demonstrate that suitable soft Actor-Critic RL algorithms can perform efficient, relatively cheap high-dimensional searches in the space of scaling dimensions and OPE-squared coefficients that produce sensible results for tens of CFT data from a single crossing equation. In this paper we test this approach in well-known 2D CFTs, with particular focus on the Ising and tri-critical Ising models and the free compactified boson CFT. We present results of as high as 36-dimensional searches, whose sole input is the expected number of operators per spin in a truncation of the conformal-block decomposition of the crossing equations. Our study of 2D CFTs uses only the global so(2,2) part of the conformal algebra, and our methods are equally applicable to higher-dimensional CFTs. When combined with other, already available, numerical and analytical methods, we expect our approach to yield an exciting new window into the non-perturbative structure of arbitrary (unitary or non-unitary) CFTs.

Weakly supervised semantic segmentation (WSSS) typically utilizes limited semantic annotations to obtain initial Class Activation Maps (CAMs). However, due to the inadequate coupling between class activation responses and semantic information in high-dimensional space, the CAM is prone to object co-occurrence or under-activation, resulting in inferior recognition accuracy. To tackle this issue, we propose DOEI, Dual Optimization of Embedding Information, a novel approach that reconstructs embedding representations through semantic-aware attention weight matrices to optimize the expression capability of embedding information. Specifically, DOEI amplifies tokens with high confidence and suppresses those with low confidence during the class-to-patch interaction. This alignment of activation responses with semantic information strengthens the propagation and decoupling of target features, enabling the generated embeddings to more accurately represent target features in high-level semantic space. In addition, we propose a hybrid-feature alignment module in DOEI that combines RGB values, embedding-guided features, and self-attention weights to increase the reliability of candidate tokens. Comprehensive experiments show that DOEI is an effective plug-and-play module that empowers state-of-the-art visual transformer-based WSSS models to significantly improve the quality of CAMs and segmentation performance on popular benchmarks, including PASCAL VOC (+3.6%, +1.5%, +1.2% mIoU) and MS COCO (+1.2%, +1.6% mIoU). Code will be available at https://github.com/AIGeeksGroup/DOEI.

How to enable robots to predict the outcomes of their own motion intentions in three-dimensional space has been a fundamental problem in embodied intelligence. To explore more general spatial imagination capabilities, here we present AirScape, the first world model designed for six-degree-of-freedom aerial agents. AirScape predicts future observation sequences based on current visual inputs and motion intentions. Specifically, we construct an dataset for aerial world model training and testing, which consists of 11k video-intention pairs. This dataset includes first-person-view videos capturing diverse drone actions across a wide range of scenarios, with over 1,000 hours spent annotating the corresponding motion intentions. Then we develop a two-phase training schedule to train a foundation model -- initially devoid of embodied spatial knowledge -- into a world model that is controllable by motion intentions and adheres to physical spatio-temporal constraints.

Nanorobots are a promising development in targeted drug delivery and the treatment of neurological disorders, with potential for crossing the blood-brain barrier (BBB). These small devices leverage advancements in nanotechnology and bioengineering for precise navigation and targeted payload delivery, particularly for conditions like brain tumors, Alzheimer's disease, and Parkinson's disease. Recent progress in artificial intelligence (AI) and machine learning (ML) has improved the navigation and effectiveness of nanorobots, allowing them to detect and interact with cancer cells through biomarker analysis. This study presents a new reinforcement learning (RL) framework for optimizing nanorobot navigation in complex biological environments, focusing on cancer cell detection by analyzing the concentration gradients of surrounding biomarkers. We utilize a computer simulation model to explore the behavior of nanorobots in a three-dimensional space with cancer cells and biological barriers. The proposed method uses Q-learning to refine movement strategies based on real-time biomarker concentration data, enabling nanorobots to autonomously navigate to cancerous tissues for targeted drug delivery. This research lays the groundwork for future laboratory experiments and clinical applications, with implications for personalized medicine and less invasive cancer treatments. The integration of intelligent nanorobots could revolutionize therapeutic strategies, reducing side effects and enhancing treatment effectiveness for cancer patients. Further research will investigate the practical deployment of these technologies in medical settings, aiming to unlock the full potential of nanorobotics in healthcare.

Precise control over language model generation is vital for ensuring both safety and reliability. Although prompt engineering and steering are commonly used to intervene in model behaviors, the vast number of parameters in models often results in highly intertwined internal representations. This interdependency can limit control precision and sometimes lead to unintended side effects. Recent research has explored the use of sparse autoencoders (SAE) to disentangle knowledge in high-dimensional spaces for steering. However, these applications have been limited to toy tasks owing to the nontrivial issue of locating atomic knowledge components. In this paper, we propose Steering Target Atoms (STA), a novel method that isolates and manipulates disentangled knowledge components to enhance safety. Comprehensive experiments demonstrate the effectiveness of our approach. Further analysis reveals that steering exhibits superior robustness and flexibility, particularly in adversarial scenarios. We also apply the steering strategy to the large reasoning model, confirming its effectiveness in precise reasoning control.

Currently, applying diffusion models in pixel space of high resolution images is difficult. Instead, existing approaches focus on diffusion in lower dimensional spaces (latent diffusion), or have multiple super-resolution levels of generation referred to as cascades. The downside is that these approaches add additional complexity to the diffusion framework. This paper aims to improve denoising diffusion for high resolution images while keeping the model as simple as possible. The paper is centered around the research question: How can one train a standard denoising diffusion models on high resolution images, and still obtain performance comparable to these alternate approaches? The four main findings are: 1) the noise schedule should be adjusted for high resolution images, 2) It is sufficient to scale only a particular part of the architecture, 3) dropout should be added at specific locations in the architecture, and 4) downsampling is an effective strategy to avoid high resolution feature maps. Combining these simple yet effective techniques, we achieve state-of-the-art on image generation among diffusion models without sampling modifiers on ImageNet.

Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks.

Jointly identifying a mixture of discrete and continuous factors of variability without supervision is a key problem in unraveling complex phenomena. Variational inference has emerged as a promising method to learn interpretable mixture representations. However, posterior approximation in high-dimensional latent spaces, particularly for discrete factors remains challenging. Here, we propose an unsupervised variational framework using multiple interacting networks called cpl-mixVAE that scales well to high-dimensional discrete settings. In this framework, the mixture representation of each network is regularized by imposing a consensus constraint on the discrete factor. We justify the use of this framework by providing both theoretical and experimental results. Finally, we use the proposed method to jointly uncover discrete and continuous factors of variability describing gene expression in a single-cell transcriptomic dataset profiling more than a hundred cortical neuron types.

Following the recent popularity of Large Language Models (LLMs), several attempts have been made to extend them to the visual domain. From having a visual assistant that could guide us through unfamiliar environments to generative models that produce images using only a high-level text description, the vision-language model (VLM) applications will significantly impact our relationship with technology. However, there are many challenges that need to be addressed to improve the reliability of those models. While language is discrete, vision evolves in a much higher dimensional space in which concepts cannot always be easily discretized. To better understand the mechanics behind mapping vision to language, we present this introduction to VLMs which we hope will help anyone who would like to enter the field. First, we introduce what VLMs are, how they work, and how to train them. Then, we present and discuss approaches to evaluate VLMs. Although this work primarily focuses on mapping images to language, we also discuss extending VLMs to videos.

Video generative models can be regarded as world simulators due to their ability to capture dynamic, continuous changes inherent in real-world environments. These models integrate high-dimensional information across visual, temporal, spatial, and causal dimensions, enabling predictions of subjects in various status. A natural and valuable research direction is to explore whether a fully trained video generative model in high-dimensional space can effectively support lower-dimensional tasks such as controllable image generation. In this work, we propose a paradigm for video-to-image knowledge compression and task adaptation, termed Dimension-Reduction Attack (DRA-Ctrl), which utilizes the strengths of video models, including long-range context modeling and flatten full-attention, to perform various generation tasks. Specially, to address the challenging gap between continuous video frames and discrete image generation, we introduce a mixup-based transition strategy that ensures smooth adaptation. Moreover, we redesign the attention structure with a tailored masking mechanism to better align text prompts with image-level control. Experiments across diverse image generation tasks, such as subject-driven and spatially conditioned generation, show that repurposed video models outperform those trained directly on images. These results highlight the untapped potential of large-scale video generators for broader visual applications. DRA-Ctrl provides new insights into reusing resource-intensive video models and lays foundation for future unified generative models across visual modalities. The project page is https://dra-ctrl-2025.github.io/DRA-Ctrl/.

Diffusion models have recently emerged as powerful generative priors for solving inverse problems. However, training diffusion models in the pixel space are both data-intensive and computationally demanding, which restricts their applicability as priors for high-dimensional real-world data such as medical images. Latent diffusion models, which operate in a much lower-dimensional space, offer a solution to these challenges. However, incorporating latent diffusion models to solve inverse problems remains a challenging problem due to the nonlinearity of the encoder and decoder. To address these issues, we propose ReSample, an algorithm that can solve general inverse problems with pre-trained latent diffusion models. Our algorithm incorporates data consistency by solving an optimization problem during the reverse sampling process, a concept that we term as hard data consistency. Upon solving this optimization problem, we propose a novel resampling scheme to map the measurement-consistent sample back onto the noisy data manifold and theoretically demonstrate its benefits. Lastly, we apply our algorithm to solve a wide range of linear and nonlinear inverse problems in both natural and medical images, demonstrating that our approach outperforms existing state-of-the-art approaches, including those based on pixel-space diffusion models.

The success of today's large language models (LLMs) depends on the observation that larger models perform better. However, the origin of this neural scaling law -- the finding that loss decreases as a power law with model size -- remains unclear. Starting from two empirical principles -- that LLMs represent more things than the model dimensions (widths) they have (i.e., representations are superposed), and that words or concepts in language occur with varying frequencies -- we constructed a toy model to study the loss scaling with model size. We found that when superposition is weak, meaning only the most frequent features are represented without interference, the scaling of loss with model size depends on the underlying feature frequency; if feature frequencies follow a power law, so does the loss. In contrast, under strong superposition, where all features are represented but overlap with each other, the loss becomes inversely proportional to the model dimension across a wide range of feature frequency distributions. This robust scaling behavior is explained geometrically: when many more vectors are packed into a lower dimensional space, the interference (squared overlaps) between vectors scales inversely with that dimension. We then analyzed four families of open-sourced LLMs and found that they exhibit strong superposition and quantitatively match the predictions of our toy model. The Chinchilla scaling law turned out to also agree with our results. We conclude that representation superposition is an important mechanism underlying the observed neural scaling laws. We anticipate that these insights will inspire new training strategies and model architectures to achieve better performance with less computation and fewer parameters.

Lossless speculative decoding accelerates target large language model (LLM) inference by employing a lightweight draft model for generating tree-structured candidates, which are subsequently verified in parallel by the target LLM. Currently, effective approaches leverage feature-level rather than token-level autoregression within the draft model to facilitate more straightforward predictions and enhanced knowledge distillation. In this paper, we reassess these approaches and propose FSPAD (Feature Sampling and Partial Alignment Distillation for Lossless Speculative Decoding), which introduces two straightforward and effective components within the existing framework to boost lossless speculative decoding. Firstly, FSPAD utilizes token embeddings to sample features of the target LLM in high-dimensional space before feeding them into the draft model, due to the inherent uncertainty of the features preventing the draft model from obtaining the specific token output by the target LLM. Secondly, FSPAD introduces partial alignment distillation to weaken the draft model's connection between features and logits, aiming to reduce the conflict between feature alignment and logit confidence during training. Our experiments include both greedy and non-greedy decoding on the largest and smallest models from the Vicuna and LLaMA3-Instruct series, as well as tasks in multi-turn conversation, translation, summarization, question answering, mathematical reasoning, and retrieval-augmented generation. The results show that FSPAD outperforms the state-of-the-art method across all the aforementioned tasks and target LLMs.

Directly learning to model 4D content, including shape, color and motion, is challenging. Existing methods depend on skeleton-based motion control and offer limited continuity in detail. To address this, we propose a novel framework that generates coherent 4D sequences with animation of 3D shapes under given conditions with dynamic evolution of shape and color over time through integrative latent mapping. We first employ an integrative latent unified representation to encode shape and color information of each detailed 3D geometry frame. The proposed skeleton-free latent 4D sequence joint representation allows us to leverage diffusion models in a low-dimensional space to control the generation of 4D sequences. Finally, temporally coherent 4D sequences are generated conforming well to the input images and text prompts. Extensive experiments on the ShapeNet, 3DBiCar and DeformingThings4D datasets for several tasks demonstrate that our method effectively learns to generate quality 3D shapes with color and 4D mesh animations, improving over the current state-of-the-art. Source code will be released.

Representations learned via self-supervised learning (SSL) can be susceptible to dimensional collapse, where the learned representation subspace is of extremely low dimensionality and thus fails to represent the full data distribution and modalities. Dimensional collapse also known as the "underfilling" phenomenon is one of the major causes of degraded performance on downstream tasks. Previous work has investigated the dimensional collapse problem of SSL at a global level. In this paper, we demonstrate that representations can span over high dimensional space globally, but collapse locally. To address this, we propose a method called local dimensionality regularization (LDReg). Our formulation is based on the derivation of the Fisher-Rao metric to compare and optimize local distance distributions at an asymptotically small radius for each data point. By increasing the local intrinsic dimensionality, we demonstrate through a range of experiments that LDReg improves the representation quality of SSL. The results also show that LDReg can regularize dimensionality at both local and global levels.

We consider the problem of approximating a function from L^2 by an element of a given m-dimensional space V_m, associated with some feature map varphi, using evaluations of the function at random points x_1,dots,x_n. After recalling some results on optimal weighted least-squares using independent and identically distributed points, we consider weighted least-squares using projection determinantal point processes (DPP) or volume sampling. These distributions introduce dependence between the points that promotes diversity in the selected features varphi(x_i). We first provide a generalized version of volume-rescaled sampling yielding quasi-optimality results in expectation with a number of samples n = O(mlog(m)), that means that the expected L^2 error is bounded by a constant times the best approximation error in L^2. Also, further assuming that the function is in some normed vector space H continuously embedded in L^2, we further prove that the approximation is almost surely bounded by the best approximation error measured in the H-norm. This includes the cases of functions from L^infty or reproducing kernel Hilbert spaces. Finally, we present an alternative strategy consisting in using independent repetitions of projection DPP (or volume sampling), yielding similar error bounds as with i.i.d. or volume sampling, but in practice with a much lower number of samples. Numerical experiments illustrate the performance of the different strategies.

While static word embedding models are known to represent linguistic analogies as parallel lines in high-dimensional space, the underlying mechanism as to why they result in such geometric structures remains obscure. We find that an elementary contrastive-style method employed over distributional information performs competitively with popular word embedding models on analogy recovery tasks, while achieving dramatic speedups in training time. Further, we demonstrate that a contrastive loss is sufficient to create these parallel structures in word embeddings, and establish a precise relationship between the co-occurrence statistics and the geometric structure of the resulting word embeddings.

Interactions among features are central to understanding the behavior of machine learning models. Recent research has made significant strides in detecting and quantifying feature interactions in single predictive models. However, we argue that the feature interactions extracted from a single pre-specified model may not be trustworthy since: a well-trained predictive model may not preserve the true feature interactions and there exist multiple well-performing predictive models that differ in feature interaction strengths. Thus, we recommend exploring feature interaction strengths in a model class of approximately equally accurate predictive models. In this work, we introduce the feature interaction score (FIS) in the context of a Rashomon set, representing a collection of models that achieve similar accuracy on a given task. We propose a general and practical algorithm to calculate the FIS in the model class. We demonstrate the properties of the FIS via synthetic data and draw connections to other areas of statistics. Additionally, we introduce a Halo plot for visualizing the feature interaction variance in high-dimensional space and a swarm plot for analyzing FIS in a Rashomon set. Experiments with recidivism prediction and image classification illustrate how feature interactions can vary dramatically in importance for similarly accurate predictive models. Our results suggest that the proposed FIS can provide valuable insights into the nature of feature interactions in machine learning models.

We consider the challenging task of training models for image-to-video deblurring, which aims to recover a sequence of sharp images corresponding to a given blurry image input. A critical issue disturbing the training of an image-to-video model is the ambiguity of the frame ordering since both the forward and backward sequences are plausible solutions. This paper proposes an effective self-supervised ordering scheme that allows training high-quality image-to-video deblurring models. Unlike previous methods that rely on order-invariant losses, we assign an explicit order for each video sequence, thus avoiding the order-ambiguity issue. Specifically, we map each video sequence to a vector in a latent high-dimensional space so that there exists a hyperplane such that for every video sequence, the vectors extracted from it and its reversed sequence are on different sides of the hyperplane. The side of the vectors will be used to define the order of the corresponding sequence. Last but not least, we propose a real-image dataset for the image-to-video deblurring problem that covers a variety of popular domains, including face, hand, and street. Extensive experimental results confirm the effectiveness of our method. Code and data are available at https://github.com/VinAIResearch/HyperCUT.git

Much of the success of deep learning is drawn from building architectures that properly respect underlying symmetry and structure in the data on which they operate - a set of considerations that have been united under the banner of geometric deep learning. Often problems in the physical sciences deal with relatively small sets of points in two- or three-dimensional space wherein translation, rotation, and permutation equivariance are important or even vital for models to be useful in practice. In this work, we present rotation- and permutation-equivariant architectures for deep learning on these small point clouds, composed of a set of products of terms from the geometric algebra and reductions over those products using an attention mechanism. The geometric algebra provides valuable mathematical structure by which to combine vector, scalar, and other types of geometric inputs in a systematic way to account for rotation invariance or covariance, while attention yields a powerful way to impose permutation equivariance. We demonstrate the usefulness of these architectures by training models to solve sample problems relevant to physics, chemistry, and biology.

The problem of visual metamerism is defined as finding a family of perceptually indistinguishable, yet physically different images. In this paper, we propose our NeuroFovea metamer model, a foveated generative model that is based on a mixture of peripheral representations and style transfer forward-pass algorithms. Our gradient-descent free model is parametrized by a foveated VGG19 encoder-decoder which allows us to encode images in high dimensional space and interpolate between the content and texture information with adaptive instance normalization anywhere in the visual field. Our contributions include: 1) A framework for computing metamers that resembles a noisy communication system via a foveated feed-forward encoder-decoder network -- We observe that metamerism arises as a byproduct of noisy perturbations that partially lie in the perceptual null space; 2) A perceptual optimization scheme as a solution to the hyperparametric nature of our metamer model that requires tuning of the image-texture tradeoff coefficients everywhere in the visual field which are a consequence of internal noise; 3) An ABX psychophysical evaluation of our metamers where we also find that the rate of growth of the receptive fields in our model match V1 for reference metamers and V2 between synthesized samples. Our model also renders metamers at roughly a second, presenting a times1000 speed-up compared to the previous work, which allows for tractable data-driven metamer experiments.

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks.

Directly modeling the explicit likelihood of the raw data distribution is key topic in the machine learning area, which achieves the scaling successes in Large Language Models by autoregressive modeling. However, continuous AR modeling over visual pixel data suffer from extremely long sequences and high-dimensional spaces. In this paper, we present FARMER, a novel end-to-end generative framework that unifies Normalizing Flows (NF) and Autoregressive (AR) models for tractable likelihood estimation and high-quality image synthesis directly from raw pixels. FARMER employs an invertible autoregressive flow to transform images into latent sequences, whose distribution is modeled implicitly by an autoregressive model. To address the redundancy and complexity in pixel-level modeling, we propose a self-supervised dimension reduction scheme that partitions NF latent channels into informative and redundant groups, enabling more effective and efficient AR modeling. Furthermore, we design a one-step distillation scheme to significantly accelerate inference speed and introduce a resampling-based classifier-free guidance algorithm to boost image generation quality. Extensive experiments demonstrate that FARMER achieves competitive performance compared to existing pixel-based generative models while providing exact likelihoods and scalable training.

This paper introduces a new model to learn graph neural networks equivariant to rotations, translations, reflections and permutations called E(n)-Equivariant Graph Neural Networks (EGNNs). In contrast with existing methods, our work does not require computationally expensive higher-order representations in intermediate layers while it still achieves competitive or better performance. In addition, whereas existing methods are limited to equivariance on 3 dimensional spaces, our model is easily scaled to higher-dimensional spaces. We demonstrate the effectiveness of our method on dynamical systems modelling, representation learning in graph autoencoders and predicting molecular properties.

Humans rely on multisensory integration to perceive spatial environments, where auditory cues enable sound source localization in three-dimensional space. Despite the critical role of spatial audio in immersive technologies such as VR/AR, most existing multimodal datasets provide only monaural audio, which limits the development of spatial audio generation and understanding. To address these challenges, we introduce MRSAudio, a large-scale multimodal spatial audio dataset designed to advance research in spatial audio understanding and generation. MRSAudio spans four distinct components: MRSLife, MRSSpeech, MRSMusic, and MRSSing, covering diverse real-world scenarios. The dataset includes synchronized binaural and ambisonic audio, exocentric and egocentric video, motion trajectories, and fine-grained annotations such as transcripts, phoneme boundaries, lyrics, scores, and prompts. To demonstrate the utility and versatility of MRSAudio, we establish five foundational tasks: audio spatialization, and spatial text to speech, spatial singing voice synthesis, spatial music generation and sound event localization and detection. Results show that MRSAudio enables high-quality spatial modeling and supports a broad range of spatial audio research. Demos and dataset access are available at https://mrsaudio.github.io.

Large language models (LLMs) often need to incorporate external knowledge to solve theme-specific problems. Retrieval-augmented generation (RAG) has shown its high promise, empowering LLMs to generate more qualified responses with retrieved external data and knowledge. However, most RAG methods retrieve relevant documents based on either sparse or dense retrieval methods or their combinations, which overlooks the essential, multi-dimensional, and structured semantic information present in documents. This structured information plays a critical role in finding concise yet highly relevant information for domain knowledge-intensive tasks, such as scientific question-answering (QA). In this work, we introduce a multi-dimensional (cube) structure, Hypercube, which can index and allocate documents in a pre-defined multi-dimensional space. Built on the hypercube, we further propose Hypercube-RAG, a novel RAG framework for precise and efficient retrieval. Given a query, Hypercube-RAG first decomposes it based on its entities, phrases, and topics along with pre-defined hypercube dimensions, and then retrieves relevant documents from cubes by aligning these decomposed components with corresponding dimensions. Experiments on three datasets across different domains demonstrate that our method improves response accuracy by 3.7% and retrieval accuracy by 5.3% over the strongest RAG baseline. It also boosts retrieval efficiency (speed) by one or two magnitudes faster than graph-based RAG. Notably, our Hypercube-RAG inherently offers explainability by revealing those underlying dimensions used for retrieval. The code and data are available at https://github.com/JimengShi/Hypercube-RAG.

This paper presents a novel approach for similarity search with complex filtering capabilities on billion-scale datasets, optimized for CPU inference. Our method extends the classical IVF-Flat index structure to integrate multi-dimensional filters. The proposed algorithm combines dense embeddings with discrete filtering attributes, enabling fast retrieval in high-dimensional spaces. Designed specifically for CPU-based systems, our disk-based approach offers a cost-effective solution for large-scale similarity search. We demonstrate the effectiveness of our method through a case study, showcasing its potential for various practical uses.

Randomized Smoothing (RS) has been proven a promising method for endowing an arbitrary image classifier with certified robustness. However, the substantial uncertainty inherent in the high-dimensional isotropic Gaussian noise imposes the curse of dimensionality on RS. Specifically, the upper bound of {ell_2} certified robustness radius provided by RS exhibits a diminishing trend with the expansion of the input dimension d, proportionally decreasing at a rate of 1/d. This paper explores the feasibility of providing {ell_2} certified robustness for high-dimensional input through the utilization of dual smoothing in the lower-dimensional space. The proposed Dual Randomized Smoothing (DRS) down-samples the input image into two sub-images and smooths the two sub-images in lower dimensions. Theoretically, we prove that DRS guarantees a tight {ell_2} certified robustness radius for the original input and reveal that DRS attains a superior upper bound on the {ell_2} robustness radius, which decreases proportionally at a rate of (1/sqrt m + 1/sqrt n ) with m+n=d. Extensive experiments demonstrate the generalizability and effectiveness of DRS, which exhibits a notable capability to integrate with established methodologies, yielding substantial improvements in both accuracy and {ell_2} certified robustness baselines of RS on the CIFAR-10 and ImageNet datasets. Code is available at https://github.com/xiasong0501/DRS.

Bayesian filtering approximates the true underlying behavior of a time-varying system by inverting an explicit generative model to convert noisy measurements into state estimates. This process typically requires either storage, inversion, and multiplication of large matrices or Monte Carlo estimation, neither of which are practical in high-dimensional state spaces such as the weight spaces of artificial neural networks. Here, we frame the standard Bayesian filtering problem as optimization over a time-varying objective. Instead of maintaining matrices for the filtering equations or simulating particles, we specify an optimizer that defines the Bayesian filter implicitly. In the linear-Gaussian setting, we show that every Kalman filter has an equivalent formulation using K steps of gradient descent. In the nonlinear setting, our experiments demonstrate that our framework results in filters that are effective, robust, and scalable to high-dimensional systems, comparing well against the standard toolbox of Bayesian filtering solutions. We suggest that it is easier to fine-tune an optimizer than it is to specify the correct filtering equations, making our framework an attractive option for high-dimensional filtering problems.

We propose a goodness-of-fit measure for probability densities modeling observations with varying dimensionality, such as text documents of differing lengths or variable-length sequences. The proposed measure is an instance of the kernel Stein discrepancy (KSD), which has been used to construct goodness-of-fit tests for unnormalized densities. The KSD is defined by its Stein operator: current operators used in testing apply to fixed-dimensional spaces. As our main contribution, we extend the KSD to the variable-dimension setting by identifying appropriate Stein operators, and propose a novel KSD goodness-of-fit test. As with the previous variants, the proposed KSD does not require the density to be normalized, allowing the evaluation of a large class of models. Our test is shown to perform well in practice on discrete sequential data benchmarks.

We introduce a novel neural network-based algorithm to compute optimal transport (OT) plans for general cost functionals. In contrast to common Euclidean costs, i.e., ell^1 or ell^2, such functionals provide more flexibility and allow using auxiliary information, such as class labels, to construct the required transport map. Existing methods for general costs are discrete and have limitations in practice, i.e. they do not provide an out-of-sample estimation. We address the challenge of designing a continuous OT approach for general costs that generalizes to new data points in high-dimensional spaces, such as images. Additionally, we provide the theoretical error analysis for our recovered transport plans. As an application, we construct a cost functional to map data distributions while preserving the class-wise structure.

Recently, large-scale pre-training methods like CLIP have made great progress in multi-modal research such as text-video retrieval. In CLIP, transformers are vital for modeling complex multi-modal relations. However, in the vision transformer of CLIP, the essential visual tokenization process, which produces discrete visual token sequences, generates many homogeneous tokens due to the redundancy nature of consecutive and similar frames in videos. This significantly increases computation costs and hinders the deployment of video retrieval models in web applications. In this paper, to reduce the number of redundant video tokens, we design a multi-segment token clustering algorithm to find the most representative tokens and drop the non-essential ones. As the frame redundancy occurs mostly in consecutive frames, we divide videos into multiple segments and conduct segment-level clustering. Center tokens from each segment are later concatenated into a new sequence, while their original spatial-temporal relations are well maintained. We instantiate two clustering algorithms to efficiently find deterministic medoids and iteratively partition groups in high dimensional space. Through this token clustering and center selection procedure, we successfully reduce computation costs by removing redundant visual tokens. This method further enhances segment-level semantic alignment between video and text representations, enforcing the spatio-temporal interactions of tokens from within-segment frames. Our method, coined as CenterCLIP, surpasses existing state-of-the-art by a large margin on typical text-video benchmarks, while reducing the training memory cost by 35\% and accelerating the inference speed by 14\% at the best case. The code is available at {https://github.com/mzhaoshuai/CenterCLIP}{{https://github.com/mzhaoshuai/CenterCLIP}}.

We present a new methodology for detecting out-of-distribution (OOD) images by utilizing norms of the score estimates at multiple noise scales. A score is defined to be the gradient of the log density with respect to the input data. Our methodology is completely unsupervised and follows a straight forward training scheme. First, we train a deep network to estimate scores for levels of noise. Once trained, we calculate the noisy score estimates for N in-distribution samples and take the L2-norms across the input dimensions (resulting in an NxL matrix). Then we train an auxiliary model (such as a Gaussian Mixture Model) to learn the in-distribution spatial regions in this L-dimensional space. This auxiliary model can now be used to identify points that reside outside the learned space. Despite its simplicity, our experiments show that this methodology significantly outperforms the state-of-the-art in detecting out-of-distribution images. For example, our method can effectively separate CIFAR-10 (inlier) and SVHN (OOD) images, a setting which has been previously shown to be difficult for deep likelihood models.

Motivation: Ab initio protein docking represents a major challenge for optimizing a noisy and costly "black box"-like function in a high-dimensional space. Despite progress in this field, there is no docking method available for rigorous uncertainty quantification (UQ) of its solution quality (e.g. interface RMSD or iRMSD). Results: We introduce a novel algorithm, Bayesian Active Learning (BAL), for optimization and UQ of such black-box functions and flexible protein docking. BAL directly models the posterior distribution of the global optimum (or native structures for protein docking) with active sampling and posterior estimation iteratively feeding each other. Furthermore, we use complex normal modes to represent a homogeneous Euclidean conformation space suitable for high-dimension optimization and construct funnel-like energy models for encounter complexes. Over a protein docking benchmark set and a CAPRI set including homology docking, we establish that BAL significantly improve against both starting points by rigid docking and refinements by particle swarm optimization, providing for one third targets a top-3 near-native prediction. BAL also generates tight confidence intervals with half range around 25% of iRMSD and confidence level at 85%. Its estimated probability of a prediction being native or not achieves binary classification AUROC at 0.93 and AUPRC over 0.60 (compared to 0.14 by chance); and also found to help ranking predictions. To the best of our knowledge, this study represents the first uncertainty quantification solution for protein docking, with theoretical rigor and comprehensive assessment. Source codes are available at https://github.com/Shen-Lab/BAL.

Click-through rate (CTR) prediction, which aims to predict the probability of a user clicking on an ad or an item, is critical to many online applications such as online advertising and recommender systems. The problem is very challenging since (1) the input features (e.g., the user id, user age, item id, item category) are usually sparse and high-dimensional, and (2) an effective prediction relies on high-order combinatorial features (a.k.a. cross features), which are very time-consuming to hand-craft by domain experts and are impossible to be enumerated. Therefore, there have been efforts in finding low-dimensional representations of the sparse and high-dimensional raw features and their meaningful combinations. In this paper, we propose an effective and efficient method called the AutoInt to automatically learn the high-order feature interactions of input features. Our proposed algorithm is very general, which can be applied to both numerical and categorical input features. Specifically, we map both the numerical and categorical features into the same low-dimensional space. Afterwards, a multi-head self-attentive neural network with residual connections is proposed to explicitly model the feature interactions in the low-dimensional space. With different layers of the multi-head self-attentive neural networks, different orders of feature combinations of input features can be modeled. The whole model can be efficiently fit on large-scale raw data in an end-to-end fashion. Experimental results on four real-world datasets show that our proposed approach not only outperforms existing state-of-the-art approaches for prediction but also offers good explainability. Code is available at: https://github.com/DeepGraphLearning/RecommenderSystems.

Document clustering is a text mining technique used to provide better document search and browsing in digital libraries or online corpora. A lot of research has been done on biomedical document clustering that is based on using existing ontology. But, associations and co-occurrences of the medical concepts are not well represented by using ontology. In this research, a vector representation of concepts of diseases and similarity measurement between concepts are proposed. They identify the closest concepts of diseases in the context of a corpus. Each document is represented by using the vector space model. A weight scheme is proposed to consider both local content and associations between concepts. A Self-Organizing Map is used as document clustering algorithm. The vector projection and visualization features of SOM enable visualization and analysis of the clusters distributions and relationships on the two dimensional space. The experimental results show that the proposed document clustering framework generates meaningful clusters and facilitate visualization of the clusters based on the concepts of diseases.

In computer-aided engineering design, the goal of a designer is to find an optimal design on a given requirement using the numerical simulator in loop with an optimization method. In this design optimization process, a good design optimization process is one that can reduce the time from inception to design. In this work, we take a class of design problem, that is computationally cheap to evaluate but has high dimensional design space. In such cases, traditional surrogate-based optimization does not offer any benefits. In this work, we propose an alternative way to use ML model to surrogate the design process that formulates the search problem as an inverse problem and can save time by finding the optimal design or at least a good initial seed design for optimization. By using this trained surrogate model with the traditional optimization method, we can get the best of both worlds. We call this as Surrogate Assisted Optimization (SAO)- a hybrid approach by mixing ML surrogate with the traditional optimization method. Empirical evaluations of propeller design problems show that a better efficient design can be found in fewer evaluations using SAO.

We find and analyse solutions of Einstein's equations in arbitrary d dimensions and in the presence of a scalar field with a Liouville potential coupled to a Maxwell field. We consider spacetimes of cylindrical symmetry or again subspaces of dimension d-2 with constant curvature and analyse in detail the field equations and manifest their symmetries. The field equations of the full system are shown to reduce to a single or couple of ODE's which can be used to solve analytically or numerically the theory for the symmetry at hand. Further solutions can also be generated by a solution generating technique akin to the EM duality in the absence of a cosmological constant. We then find and analyse explicit solutions including black holes and gravitating solitons for the case of four dimensional relativity and the higher-dimensional oxydised 5-dimensional spacetime. The general solution is obtained for a certain relation between couplings in the case of cylindrical symmetry.

Large Language Models (LLMs) have become indispensable in numerous real-world applications. Unfortunately, fine-tuning these models at scale, especially in federated settings where data privacy and communication efficiency are critical, presents significant challenges. Existing methods often resort to parameter-efficient fine-tuning (PEFT) to mitigate communication overhead, but this typically comes at the cost of model accuracy. To address these limitations, we propose federated full-parameter tuning at scale for LLMs (Ferret), the first first-order method with shared randomness to enable scalable full-parameter tuning of LLMs across decentralized data sources while maintaining competitive model accuracy. Ferret accomplishes this through three aspects: (1) it employs widely applied first-order methods for efficient local updates; (2) it projects these updates into a low-dimensional space to considerably reduce communication overhead; and (3) it reconstructs local updates from this low-dimensional space with shared randomness to facilitate effective full-parameter global aggregation, ensuring fast convergence and competitive final performance. Our rigorous theoretical analyses and insights along with extensive experiments, show that Ferret significantly enhances the scalability of existing federated full-parameter tuning approaches by achieving high computational efficiency, reduced communication overhead, and fast convergence, all while maintaining competitive model accuracy. Our implementation is available at https://github.com/allen4747/Ferret.

Normalizing flows (NF) are a class of powerful generative models that have gained popularity in recent years due to their ability to model complex distributions with high flexibility and expressiveness. In this work, we introduce a new type of normalizing flow that is tailored for modeling positions and orientations of multiple objects in three-dimensional space, such as molecules in a crystal. Our approach is based on two key ideas: first, we define smooth and expressive flows on the group of unit quaternions, which allows us to capture the continuous rotational motion of rigid bodies; second, we use the double cover property of unit quaternions to define a proper density on the rotation group. This ensures that our model can be trained using standard likelihood-based methods or variational inference with respect to a thermodynamic target density. We evaluate the method by training Boltzmann generators for two molecular examples, namely the multi-modal density of a tetrahedral system in an external field and the ice XI phase in the TIP4P water model. Our flows can be combined with flows operating on the internal degrees of freedom of molecules and constitute an important step towards the modeling of distributions of many interacting molecules.

We present ReXGroundingCT, the first publicly available dataset to link free-text radiology findings with pixel-level segmentations in 3D chest CT scans that is manually annotated. While prior datasets have relied on structured labels or predefined categories, ReXGroundingCT captures the full expressiveness of clinical language represented in free text and grounds it to spatially localized 3D segmentation annotations in volumetric imaging. This addresses a critical gap in medical AI: the ability to connect complex, descriptive text, such as "3 mm nodule in the left lower lobe", to its precise anatomical location in three-dimensional space, a capability essential for grounded radiology report generation systems. The dataset comprises 3,142 non-contrast chest CT scans paired with standardized radiology reports from the CT-RATE dataset. Using a systematic three-stage pipeline, GPT-4 was used to extract positive lung and pleural findings, which were then manually segmented by expert annotators. A total of 8,028 findings across 16,301 entities were annotated, with quality control performed by board-certified radiologists. Approximately 79% of findings are focal abnormalities, while 21% are non-focal. The training set includes up to three representative segmentations per finding, while the validation and test sets contain exhaustive labels for each finding entity. ReXGroundingCT establishes a new benchmark for developing and evaluating sentence-level grounding and free-text medical segmentation models in chest CT. The dataset can be accessed at https://huggingface.co/datasets/rajpurkarlab/ReXGroundingCT.

We present BimArt, a novel generative approach for synthesizing 3D bimanual hand interactions with articulated objects. Unlike prior works, we do not rely on a reference grasp, a coarse hand trajectory, or separate modes for grasping and articulating. To achieve this, we first generate distance-based contact maps conditioned on the object trajectory with an articulation-aware feature representation, revealing rich bimanual patterns for manipulation. The learned contact prior is then used to guide our hand motion generator, producing diverse and realistic bimanual motions for object movement and articulation. Our work offers key insights into feature representation and contact prior for articulated objects, demonstrating their effectiveness in taming the complex, high-dimensional space of bimanual hand-object interactions. Through comprehensive quantitative experiments, we demonstrate a clear step towards simplified and high-quality hand-object animations that excel over the state-of-the-art in motion quality and diversity.

Joint vision-language models have shown great performance over a diverse set of tasks. However, little is known about their limitations, as the high dimensional space learned by these models makes it difficult to identify semantic errors. Recent work has addressed this problem by designing highly controlled probing task benchmarks. Our paper introduces a more scalable solution that relies on already annotated benchmarks. Our method consists of extracting a large set of diverse features from a vision-language benchmark and measuring their correlation with the output of the target model. We confirm previous findings that CLIP behaves like a bag of words model and performs better with nouns and verbs; we also uncover novel insights such as CLIP getting confused by concrete words. Our framework is available at https://github.com/MichiganNLP/Scalable-VLM-Probing and can be used with other multimodal models and benchmarks.

The Lucas-Kanade (LK) method is a classic iterative homography estimation algorithm for image alignment, but often suffers from poor local optimality especially when image pairs have large distortions. To address this challenge, in this paper we propose a novel Deep Star-Convexified Lucas-Kanade (PRISE) method for multimodel image alignment by introducing strongly star-convex constraints into the optimization problem. Our basic idea is to enforce the neural network to approximately learn a star-convex loss landscape around the ground truth give any data to facilitate the convergence of the LK method to the ground truth through the high dimensional space defined by the network. This leads to a minimax learning problem, with contrastive (hinge) losses due to the definition of strong star-convexity that are appended to the original loss for training. We also provide an efficient sampling based algorithm to leverage the training cost, as well as some analysis on the quality of the solutions from PRISE. We further evaluate our approach on benchmark datasets such as MSCOCO, GoogleEarth, and GoogleMap, and demonstrate state-of-the-art results, especially for small pixel errors. Code can be downloaded from https://github.com/Zhang-VISLab.

Graph-structured scene descriptions can be efficiently used in generative models to control the composition of the generated image. Previous approaches are based on the combination of graph convolutional networks and adversarial methods for layout prediction and image generation, respectively. In this work, we show how employing multi-head attention to encode the graph information, as well as using a transformer-based model in the latent space for image generation can improve the quality of the sampled data, without the need to employ adversarial models with the subsequent advantage in terms of training stability. The proposed approach, specifically, is entirely based on transformer architectures both for encoding scene graphs into intermediate object layouts and for decoding these layouts into images, passing through a lower dimensional space learned by a vector-quantized variational autoencoder. Our approach shows an improved image quality with respect to state-of-the-art methods as well as a higher degree of diversity among multiple generations from the same scene graph. We evaluate our approach on three public datasets: Visual Genome, COCO, and CLEVR. We achieve an Inception Score of 13.7 and 12.8, and an FID of 52.3 and 60.3, on COCO and Visual Genome, respectively. We perform ablation studies on our contributions to assess the impact of each component. Code is available at https://github.com/perceivelab/trf-sg2im

This article presents an in-depth review of the topic of path following for autonomous robotic vehicles, with a specific focus on vehicle motion in two dimensional space (2D). From a control system standpoint, path following can be formulated as the problem of stabilizing a path following error system that describes the dynamics of position and possibly orientation errors of a vehicle with respect to a path, with the errors defined in an appropriate reference frame. In spite of the large variety of path following methods described in the literature we show that, in principle, most of them can be categorized in two groups: stabilization of the path following error system expressed either in the vehicle's body frame or in a frame attached to a "reference point" moving along the path, such as a Frenet-Serret (F-S) frame or a Parallel Transport (P-T) frame. With this observation, we provide a unified formulation that is simple but general enough to cover many methods available in the literature. We then discuss the advantages and disadvantages of each method, comparing them from the design and implementation standpoint. We further show experimental results of the path following methods obtained from field trials testing with under-actuated and fully-actuated autonomous marine vehicles. In addition, we introduce open-source Matlab and Gazebo/ROS simulation toolboxes that are helpful in testing path following methods prior to their integration in the combined guidance, navigation, and control systems of autonomous vehicles.

We present a meta-learning framework for learning new visual concepts quickly, from just one or a few examples, guided by multiple naturally occurring data streams: simultaneously looking at images, reading sentences that describe the objects in the scene, and interpreting supplemental sentences that relate the novel concept with other concepts. The learned concepts support downstream applications, such as answering questions by reasoning about unseen images. Our model, namely FALCON, represents individual visual concepts, such as colors and shapes, as axis-aligned boxes in a high-dimensional space (the "box embedding space"). Given an input image and its paired sentence, our model first resolves the referential expression in the sentence and associates the novel concept with particular objects in the scene. Next, our model interprets supplemental sentences to relate the novel concept with other known concepts, such as "X has property Y" or "X is a kind of Y". Finally, it infers an optimal box embedding for the novel concept that jointly 1) maximizes the likelihood of the observed instances in the image, and 2) satisfies the relationships between the novel concepts and the known ones. We demonstrate the effectiveness of our model on both synthetic and real-world datasets.

Sentiment analysis is a task that may suffer from a lack of data in certain cases, as the datasets are often generated and annotated by humans. In cases where data is inadequate for training discriminative models, generate models may aid training via data augmentation. Generative Adversarial Networks (GANs) are one such model that has advanced the state of the art in several tasks, including as image and text generation. In this paper, I train GAN models on low resource datasets, then use them for the purpose of data augmentation towards improving sentiment classifier generalization. Given the constraints of limited data, I explore various techniques to train the GAN models. I also present an analysis of the quality of generated GAN data as more training data for the GAN is made available. In this analysis, the generated data is evaluated as a test set (against a model trained on real data points) as well as a training set to train classification models. Finally, I also conduct a visual analysis by projecting the generated and the real data into a two-dimensional space using the t-Distributed Stochastic Neighbor Embedding (t-SNE) method.

Visual Spatial Reasoning (VSR) is a core human cognitive ability and a critical requirement for advancing embodied intelligence and autonomous systems. Despite recent progress in Vision-Language Models (VLMs), achieving human-level VSR remains highly challenging due to the complexity of representing and reasoning over three-dimensional space. In this paper, we present a systematic investigation of VSR in VLMs, encompassing a review of existing methodologies across input modalities, model architectures, training strategies, and reasoning mechanisms. Furthermore, we categorize spatial intelligence into three levels of capability, ie, basic perception, spatial understanding, spatial planning, and curate SIBench, a spatial intelligence benchmark encompassing nearly 20 open-source datasets across 23 task settings. Experiments with state-of-the-art VLMs reveal a pronounced gap between perception and reasoning, as models show competence in basic perceptual tasks but consistently underperform in understanding and planning tasks, particularly in numerical estimation, multi-view reasoning, temporal dynamics, and spatial imagination. These findings underscore the substantial challenges that remain in achieving spatial intelligence, while providing both a systematic roadmap and a comprehensive benchmark to drive future research in the field. The related resources of this study are accessible at https://sibench.github.io/Awesome-Visual-Spatial-Reasoning/.

Today's denoising diffusion models do not "denoise" in the classical sense, i.e., they do not directly predict clean images. Rather, the neural networks predict noise or a noised quantity. In this paper, we suggest that predicting clean data and predicting noised quantities are fundamentally different. According to the manifold assumption, natural data should lie on a low-dimensional manifold, whereas noised quantities do not. With this assumption, we advocate for models that directly predict clean data, which allows apparently under-capacity networks to operate effectively in very high-dimensional spaces. We show that simple, large-patch Transformers on pixels can be strong generative models: using no tokenizer, no pre-training, and no extra loss. Our approach is conceptually nothing more than "Just image Transformers", or JiT, as we call it. We report competitive results using JiT with large patch sizes of 16 and 32 on ImageNet at resolutions of 256 and 512, where predicting high-dimensional noised quantities can fail catastrophically. With our networks mapping back to the basics of the manifold, our research goes back to basics and pursues a self-contained paradigm for Transformer-based diffusion on raw natural data.

Creating machines capable of understanding the world in 3D is essential in assisting designers that build and edit 3D environments and robots navigating and interacting within a three-dimensional space. Inspired by advances in language and image modeling, we investigate the potential of autoregressive models for a new modality: structured 3D scenes. To this end, we propose a unified LLM framework that aligns language, images, and 3D scenes and provide a detailed ''cookbook'' outlining critical design choices for achieving optimal training and performance addressing key questions related to data representation, modality-specific objectives, and more. We evaluate performance across four core 3D tasks -- rendering, recognition, instruction-following, and question-answering -- and four 3D datasets, synthetic and real-world. We extend our approach to reconstruct complex 3D object shapes by enriching our 3D modality with quantized shape encodings, and show our model's effectiveness on real-world 3D object recognition tasks. Project webpage: https://glab-caltech.github.io/kyvo/

Low-rank optimization has emerged as a promising direction in training large language models (LLMs) to reduce the memory usage of adaptive optimizers by constraining learning to a lower-dimensional space. Prior work typically projects gradients of linear layers using approaches based on Singular Value Decomposition (SVD). However, applying SVD-based procedures individually to each layer in large models is computationally expensive and incurs additional memory costs due to storing the projection matrices. In this work, we propose a computationally efficient and conceptually simple two-step procedure to approximate SVD-based gradient projections into lower-dimensional spaces. First, we construct a complete orthogonal basis using predefined orthogonal matrices of the Discrete Cosine Transform (DCT). Second, we adaptively select basis columns based on their alignment with the gradient of each layer. Each projection matrix in our method is obtained via a single matrix multiplication followed by a lightweight sorting step to identify the most relevant basis vectors. Due to the predefined nature of the orthogonal bases, they are computed once at the start of training. During training, we store only the indices of the selected columns, avoiding the need to store full projection matrices for each layer. Our numerical experiments on both pre-training and fine-tuning tasks demonstrate the effectiveness of our dual strategy in approximating optimal low-rank projections, matching the performance of costly SVD-based methods while achieving faster runtime and reduced memory usage.

We investigate the relationship between the geometry of token embeddings and their role in the next token prediction within transformer models. An important aspect of this connection uses the notion of empirical measure, which encodes the distribution of token point clouds across transformer layers and drives the evolution of token representations in the mean-field interacting picture. We use metrics such as intrinsic dimension, neighborhood overlap, and cosine similarity to observationally probe these empirical measures across layers. To validate our approach, we compare these metrics to a dataset where the tokens are shuffled, which disrupts the syntactic and semantic structure. Our findings reveal a correlation between the geometric properties of token embeddings and the cross-entropy loss of next token predictions, implying that prompts with higher loss values have tokens represented in higher-dimensional spaces.

Recent success in training deep neural networks have prompted active investigation into the features learned on their intermediate layers. Such research is difficult because it requires making sense of non-linear computations performed by millions of parameters, but valuable because it increases our ability to understand current models and create improved versions of them. In this paper we investigate the extent to which neural networks exhibit what we call convergent learning, which is when the representations learned by multiple nets converge to a set of features which are either individually similar between networks or where subsets of features span similar low-dimensional spaces. We propose a specific method of probing representations: training multiple networks and then comparing and contrasting their individual, learned representations at the level of neurons or groups of neurons. We begin research into this question using three techniques to approximately align different neural networks on a feature level: a bipartite matching approach that makes one-to-one assignments between neurons, a sparse prediction approach that finds one-to-many mappings, and a spectral clustering approach that finds many-to-many mappings. This initial investigation reveals a few previously unknown properties of neural networks, and we argue that future research into the question of convergent learning will yield many more. The insights described here include (1) that some features are learned reliably in multiple networks, yet other features are not consistently learned; (2) that units learn to span low-dimensional subspaces and, while these subspaces are common to multiple networks, the specific basis vectors learned are not; (3) that the representation codes show evidence of being a mix between a local code and slightly, but not fully, distributed codes across multiple units.

Attention sink (AS) is a consistent pattern in transformer attention maps where certain tokens (often special tokens or positional anchors) disproportionately attract attention from other tokens. We show that in transformers, AS is not an architectural artifact, but it is the manifestation of a fundamental geometric principle: the establishment of reference frames that anchor representational spaces. We analyze several architectures and identify three distinct reference frame types, centralized, distributed, and bidirectional, that correlate with the attention sink phenomenon. We show that they emerge during the earliest stages of training as optimal solutions to the problem of establishing stable coordinate systems in high-dimensional spaces. We show the influence of architecture components, particularly position encoding implementations, on the specific type of reference frame. This perspective transforms our understanding of transformer attention mechanisms and provides insights for both architecture design and the relationship with AS.

Flow-based generative models, including diffusion models, excel at modeling continuous distributions in high-dimensional spaces. In this work, we introduce Flow Policy Optimization (FPO), a simple on-policy reinforcement learning algorithm that brings flow matching into the policy gradient framework. FPO casts policy optimization as maximizing an advantage-weighted ratio computed from the conditional flow matching loss, in a manner compatible with the popular PPO-clip framework. It sidesteps the need for exact likelihood computation while preserving the generative capabilities of flow-based models. Unlike prior approaches for diffusion-based reinforcement learning that bind training to a specific sampling method, FPO is agnostic to the choice of diffusion or flow integration at both training and inference time. We show that FPO can train diffusion-style policies from scratch in a variety of continuous control tasks. We find that flow-based models can capture multimodal action distributions and achieve higher performance than Gaussian policies, particularly in under-conditioned settings.

In this study, we present an investigation into the anisotropy dynamics and intrinsic dimension of embeddings in transformer architectures, focusing on the dichotomy between encoders and decoders. Our findings reveal that the anisotropy profile in transformer decoders exhibits a distinct bell-shaped curve, with the highest anisotropy concentrations in the middle layers. This pattern diverges from the more uniformly distributed anisotropy observed in encoders. In addition, we found that the intrinsic dimension of embeddings increases in the initial phases of training, indicating an expansion into higher-dimensional space. Which is then followed by a compression phase towards the end of training with dimensionality decrease, suggesting a refinement into more compact representations. Our results provide fresh insights to the understanding of encoders and decoders embedding properties.

While mel-spectrograms have been widely utilized as intermediate representations in zero-shot text-to-speech (TTS), their inherent redundancy leads to inefficiency in learning text-speech alignment. Compact VAE-based latent representations have recently emerged as a stronger alternative, but they also face a fundamental optimization dilemma: higher-dimensional latent spaces improve reconstruction quality and speaker similarity, but degrade intelligibility, while lower-dimensional spaces improve intelligibility at the expense of reconstruction fidelity. To overcome this dilemma, we propose Semantic-VAE, a novel VAE framework that utilizes semantic alignment regularization in the latent space. This design alleviates the reconstruction-generation trade-off by capturing semantic structure in high-dimensional latent representations. Extensive experiments demonstrate that Semantic-VAE significantly improves synthesis quality and training efficiency. When integrated into F5-TTS, our method achieves 2.10% WER and 0.64 speaker similarity on LibriSpeech-PC, outperforming mel-based systems (2.23%, 0.60) and vanilla acoustic VAE baselines (2.65%, 0.59). We also release the code and models to facilitate further research.

We present a class of novel optimisers for training neural networks that makes use of the Riemannian metric naturally induced when the loss landscape is embedded in higher-dimensional space. This is the same metric that underlies common visualisations of loss landscapes. By taking this geometric perspective literally and using the induced metric, we develop a new optimiser and compare it to existing methods, namely: SGD, Adam, AdamW, and Muon, across a range of tasks and architectures. Empirically, we conclude that this new class of optimisers is highly effective in low dimensional examples, and provides slight improvement over state-of-the-art methods for training neural networks. These new optimisers have theoretically desirable properties. In particular, the effective learning rate is automatically decreased in regions of high curvature acting as a smoothed out form of gradient clipping. Similarly, one variant of these optimisers can also be viewed as inducing an effective scheduled learning rate and decoupled weight decay is the natural choice from our geometric perspective. The basic method can be used to modify any existing preconditioning method. The new optimiser has a computational complexity comparable to that of Adam.

Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the diversity and contextual richness required by applications such as retrieval-augmented generation (RAG), multi-hop QA, and memory-augmented agents. We introduce a new retrieval paradigm: semantic compression, which aims to select a compact, representative set of vectors that captures the broader semantic structure around a query. We formalize this objective using principles from submodular optimization and information geometry, and show that it generalizes traditional top-k retrieval by prioritizing coverage and diversity. To operationalize this idea, we propose graph-augmented vector retrieval, which overlays semantic graphs (e.g., kNN or knowledge-based links) atop vector spaces to enable multi-hop, context-aware search. We theoretically analyze the limitations of proximity-based retrieval under high-dimensional concentration and highlight how graph structures can improve semantic coverage. Our work outlines a foundation for meaning-centric vector search systems, emphasizing hybrid indexing, diversity-aware querying, and structured semantic retrieval. We make our implementation publicly available to foster future research in this area.

We present a method for training multi-task vision-language robotic diffusion policies that reduces training time and memory usage by an order of magnitude. This improvement arises from a previously underexplored distinction between action diffusion and the image diffusion techniques that inspired it: image generation targets are high-dimensional, while robot actions lie in a much lower-dimensional space. Meanwhile, the vision-language conditions for action generation remain high-dimensional. Our approach, Mini-Diffuser, exploits this asymmetry by introducing Level-2 minibatching, which pairs multiple noised action samples with each vision-language condition, instead of the conventional one-to-one sampling strategy. To support this batching scheme, we introduce architectural adaptations to the diffusion transformer that prevent information leakage across samples while maintaining full conditioning access. In RLBench simulations, Mini-Diffuser achieves 95\% of the performance of state-of-the-art multi-task diffusion policies, while using only 5\% of the training time and 7\% of the memory. Real-world experiments further validate that Mini-Diffuser preserves the key strengths of diffusion-based policies, including the ability to model multimodal action distributions and produce behavior conditioned on diverse perceptual inputs. Code available at github.com/utomm/mini-diffuse-actor.

Recently, Large Language Models (LLMs) have achieved significant success, prompting increased interest in expanding their generative capabilities beyond general text into domain-specific areas. This study investigates the generation of parametric sequences for computer-aided design (CAD) models using LLMs. This endeavor represents an initial step towards creating parametric 3D shapes with LLMs, as CAD model parameters directly correlate with shapes in three-dimensional space. Despite the formidable generative capacities of LLMs, this task remains challenging, as these models neither encounter parametric sequences during their pretraining phase nor possess direct awareness of 3D structures. To address this, we present CAD-Llama, a framework designed to enhance pretrained LLMs for generating parametric 3D CAD models. Specifically, we develop a hierarchical annotation pipeline and a code-like format to translate parametric 3D CAD command sequences into Structured Parametric CAD Code (SPCC), incorporating hierarchical semantic descriptions. Furthermore, we propose an adaptive pretraining approach utilizing SPCC, followed by an instruction tuning process aligned with CAD-specific guidelines. This methodology aims to equip LLMs with the spatial knowledge inherent in parametric sequences. Experimental results demonstrate that our framework significantly outperforms prior autoregressive methods and existing LLM baselines.

Parameter-efficient fine-tuning (PEFT) has been widely employed for domain adaptation, with LoRA being one of the most prominent methods due to its simplicity and effectiveness. However, in multi-task learning (MTL) scenarios, LoRA tends to obscure the distinction between tasks by projecting sparse high-dimensional features from different tasks into the same dense low-dimensional intrinsic space. This leads to task interference and suboptimal performance for LoRA and its variants. To tackle this challenge, we propose MTL-LoRA, which retains the advantages of low-rank adaptation while significantly enhancing multi-task learning capabilities. MTL-LoRA augments LoRA by incorporating additional task-adaptive parameters that differentiate task-specific information and effectively capture shared knowledge across various tasks within low-dimensional spaces. This approach enables large language models (LLMs) pre-trained on general corpus to adapt to different target task domains with a limited number of trainable parameters. Comprehensive experimental results, including evaluations on public academic benchmarks for natural language understanding, commonsense reasoning, and image-text understanding, as well as real-world industrial text Ads relevance datasets, demonstrate that MTL-LoRA outperforms LoRA and its various variants with comparable or even fewer learnable parameters in multitask learning.

Recently, State Space Models (SSMs), with Mamba as a prime example, have shown great promise for long-range dependency modeling with linear complexity. Then, Vision Mamba and the subsequent architectures are presented successively, and they perform well on visual tasks. The crucial step of applying Mamba to visual tasks is to construct 2D visual features in sequential manners. To effectively organize and construct visual features within the 2D image space through 1D selective scan, we propose a novel Multi-Head Scan (MHS) module. The embeddings extracted from the preceding layer are projected into multiple lower-dimensional subspaces. Subsequently, within each subspace, the selective scan is performed along distinct scan routes. The resulting sub-embeddings, obtained from the multi-head scan process, are then integrated and ultimately projected back into the high-dimensional space. Moreover, we incorporate a Scan Route Attention (SRA) mechanism to enhance the module's capability to discern complex structures. To validate the efficacy of our module, we exclusively substitute the 2D-Selective-Scan (SS2D) block in VM-UNet with our proposed module, and we train our models from scratch without using any pre-trained weights. The results indicate a significant improvement in performance while reducing the parameters of the original VM-UNet. The code for this study is publicly available at https://github.com/PixDeep/MHS-VM.

Knowledge distillation (KD) has been widely adopted to compress large language models (LLMs). Existing KD methods investigate various divergence measures including the Kullback-Leibler (KL), reverse Kullback-Leibler (RKL), and Jensen-Shannon (JS) divergences. However, due to limitations inherent in their assumptions and definitions, these measures fail to deliver effective supervision when few distribution overlap exists between the teacher and the student. In this paper, we show that the aforementioned KL, RKL, and JS divergences respectively suffer from issues of mode-averaging, mode-collapsing, and mode-underestimation, which deteriorates logits-based KD for diverse NLP tasks. We propose the Sinkhorn Knowledge Distillation (SinKD) that exploits the Sinkhorn distance to ensure a nuanced and precise assessment of the disparity between teacher and student distributions. Besides, profit by properties of the Sinkhorn metric, we can get rid of sample-wise KD that restricts the perception of divergence in each teacher-student sample pair. Instead, we propose a batch-wise reformulation to capture geometric intricacies of distributions across samples in the high-dimensional space. Comprehensive evaluation on GLUE and SuperGLUE, in terms of comparability, validity, and generalizability, highlights our superiority over state-of-the-art methods on all kinds of LLMs with encoder-only, encoder-decoder, and decoder-only architectures.

Neuromorphic computing with spiking neural networks is promising for energy-efficient artificial intelligence (AI) applications. However, different from humans who continually learn different tasks in a lifetime, neural network models suffer from catastrophic forgetting. How could neuronal operations solve this problem is an important question for AI and neuroscience. Many previous studies draw inspiration from observed neuroscience phenomena and propose episodic replay or synaptic metaplasticity, but they are not guaranteed to explicitly preserve knowledge for neuron populations. Other works focus on machine learning methods with more mathematical grounding, e.g., orthogonal projection on high dimensional spaces, but there is no neural correspondence for neuromorphic computing. In this work, we develop a new method with neuronal operations based on lateral connections and Hebbian learning, which can protect knowledge by projecting activity traces of neurons into an orthogonal subspace so that synaptic weight update will not interfere with old tasks. We show that Hebbian and anti-Hebbian learning on recurrent lateral connections can effectively extract the principal subspace of neural activities and enable orthogonal projection. This provides new insights into how neural circuits and Hebbian learning can help continual learning, and also how the concept of orthogonal projection can be realized in neuronal systems. Our method is also flexible to utilize arbitrary training methods based on presynaptic activities/traces. Experiments show that our method consistently solves forgetting for spiking neural networks with nearly zero forgetting under various supervised training methods with different error propagation approaches, and outperforms previous approaches under various settings. Our method can pave a solid path for building continual neuromorphic computing systems.

Interactive motion synthesis is essential in creating immersive experiences in entertainment applications, such as video games and virtual reality. However, generating animations that are both high-quality and contextually responsive remains a challenge. Traditional techniques in the game industry can produce high-fidelity animations but suffer from high computational costs and poor scalability. Trained neural network models alleviate the memory and speed issues, yet fall short on generating diverse motions. Diffusion models offer diverse motion synthesis with low memory usage, but require expensive reverse diffusion processes. This paper introduces the Accelerated Auto-regressive Motion Diffusion Model (AAMDM), a novel motion synthesis framework designed to achieve quality, diversity, and efficiency all together. AAMDM integrates Denoising Diffusion GANs as a fast Generation Module, and an Auto-regressive Diffusion Model as a Polishing Module. Furthermore, AAMDM operates in a lower-dimensional embedded space rather than the full-dimensional pose space, which reduces the training complexity as well as further improves the performance. We show that AAMDM outperforms existing methods in motion quality, diversity, and runtime efficiency, through comprehensive quantitative analyses and visual comparisons. We also demonstrate the effectiveness of each algorithmic component through ablation studies.

Parameter inference, i.e. inferring the posterior distribution of the parameters of a statistical model given some data, is a central problem to many scientific disciplines. Generative models can be used as an alternative to Markov Chain Monte Carlo methods for conducting posterior inference, both in likelihood-based and simulation-based problems. However, assessing the accuracy of posteriors encoded in generative models is not straightforward. In this paper, we introduce `Tests of Accuracy with Random Points' (TARP) coverage testing as a method to estimate coverage probabilities of generative posterior estimators. Our method differs from previously-existing coverage-based methods, which require posterior evaluations. We prove that our approach is necessary and sufficient to show that a posterior estimator is accurate. We demonstrate the method on a variety of synthetic examples, and show that TARP can be used to test the results of posterior inference analyses in high-dimensional spaces. We also show that our method can detect inaccurate inferences in cases where existing methods fail.

We present a novel Learning from Demonstration (LfD) method, Deformable Manipulation from Demonstrations (DMfD), to solve deformable manipulation tasks using states or images as inputs, given expert demonstrations. Our method uses demonstrations in three different ways, and balances the trade-off between exploring the environment online and using guidance from experts to explore high dimensional spaces effectively. We test DMfD on a set of representative manipulation tasks for a 1-dimensional rope and a 2-dimensional cloth from the SoftGym suite of tasks, each with state and image observations. Our method exceeds baseline performance by up to 12.9% for state-based tasks and up to 33.44% on image-based tasks, with comparable or better robustness to randomness. Additionally, we create two challenging environments for folding a 2D cloth using image-based observations, and set a performance benchmark for them. We deploy DMfD on a real robot with a minimal loss in normalized performance during real-world execution compared to simulation (~6%). Source code is on github.com/uscresl/dmfd

Entity resolution is a widely studied problem with several proposals to match records across relations. Matching textual content is a widespread task in many applications, such as question answering and search. While recent methods achieve promising results for these two tasks, there is no clear solution for the more general problem of matching textual content and structured data. We introduce a framework that supports this new task in an unsupervised setting for any pair of corpora, being relational tables or text documents. Our method builds a fine-grained graph over the content of the corpora and derives word embeddings to represent the objects to match in a low dimensional space. The learned representation enables effective and efficient matching at different granularity, from relational tuples to text sentences and paragraphs. Our flexible framework can exploit pre-trained resources, but it does not depends on their existence and achieves better quality performance in matching content when the vocabulary is domain specific. We also introduce optimizations in the graph creation process with an "expand and compress" approach that first identifies new valid relationships across elements, to improve matching, and then prunes nodes and edges, to reduce the graph size. Experiments on real use cases and public datasets show that our framework produces embeddings that outperform word embeddings and fine-tuned language models both in results' quality and in execution times.

Loss landscape is a useful tool to characterize and compare neural network models. The main challenge for analysis of loss landscape for the deep neural networks is that they are generally highly non-convex in very high dimensional space. In this paper, we develop "the roughness"concept for understanding such landscapes in high dimensions and apply this technique to study two neural network models arising from solving differential equations. Our main innovation is the proposal of a well-defined and easy-to-compute roughness index (RI) which is based on the mean and variance of the (normalized) total variation for one-dimensional functions projected on randomly sampled directions. A large RI at the local minimizer hints an oscillatory landscape profile and indicates a severe challenge for the first-order optimization method. Particularly, we observe the increasing-then-decreasing pattern for RI along the gradient descent path in most models. We apply our method to two types of loss functions used to solve partial differential equations (PDEs) when the solution of PDE is parametrized by neural networks. Our empirical results on these PDE problems reveal important and consistent observations that the landscapes from the deep Galerkin method around its local minimizers are less rough than the deep Ritz method.

Non-linear manifold learning enables high-dimensional data analysis, but requires out-of-sample-extension methods to process new data points. In this paper, we propose a manifold learning algorithm based on deep learning to create an encoder, which maps a high-dimensional dataset and its low-dimensional embedding, and a decoder, which takes the embedded data back to the high-dimensional space. Stacking the encoder and decoder together constructs an autoencoder, which we term a diffusion net, that performs out-of-sample-extension as well as outlier detection. We introduce new neural net constraints for the encoder, which preserves the local geometry of the points, and we prove rates of convergence for the encoder. Also, our approach is efficient in both computational complexity and memory requirements, as opposed to previous methods that require storage of all training points in both the high-dimensional and the low-dimensional spaces to calculate the out-of-sample-extension and the pre-image.

A central challenge to many fields of science and engineering involves minimizing non-convex error functions over continuous, high dimensional spaces. Gradient descent or quasi-Newton methods are almost ubiquitously used to perform such minimizations, and it is often thought that a main source of difficulty for the ability of these local methods to find the global minimum is the proliferation of local minima with much higher error than the global minimum. Here we argue, based on results from statistical physics, random matrix theory, and neural network theory, that a deeper and more profound difficulty originates from the proliferation of saddle points, not local minima, especially in high dimensional problems of practical interest. Such saddle points are surrounded by high error plateaus that can dramatically slow down learning, and give the illusory impression of the existence of a local minimum. Motivated by these arguments, we propose a new algorithm, the saddle-free Newton method, that can rapidly escape high dimensional saddle points, unlike gradient descent and quasi-Newton methods. We apply this algorithm to deep neural network training, and provide preliminary numerical evidence for its superior performance.

State-Space Models (SSMs) have recently emerged as a powerful and efficient alternative to the long-standing transformer architecture. However, existing SSM conceptualizations retain deeply rooted biases from their roots in natural language processing. This constrains their ability to appropriately model the spatially-dependent characteristics of visual inputs. In this paper, we address these limitations by re-deriving modern selective state-space techniques, starting from a natively multidimensional formulation. Currently, prior works attempt to apply natively 1D SSMs to 2D data (i.e. images) by relying on arbitrary combinations of 1D scan directions to capture spatial dependencies. In contrast, Mamba2D improves upon this with a single 2D scan direction that factors in both dimensions of the input natively, effectively modelling spatial dependencies when constructing hidden states. Mamba2D shows comparable performance to prior adaptations of SSMs for vision tasks, on standard image classification evaluations with the ImageNet-1K dataset. Source code is available at https://github.com/cocoalex00/Mamba2D.

Modeling multivariate time series is a well-established problem with a wide range of applications from healthcare to financial markets. Traditional State Space Models (SSMs) are classical approaches for univariate time series modeling due to their simplicity and expressive power to represent linear dependencies. They, however, have fundamentally limited expressive power to capture non-linear dependencies, are slow in practice, and fail to model the inter-variate information flow. Despite recent attempts to improve the expressive power of SSMs by using deep structured SSMs, the existing methods are either limited to univariate time series, fail to model complex patterns (e.g., seasonal patterns), fail to dynamically model the dependencies of variate and time dimensions, and/or are input-independent. We present Chimera that uses two input-dependent 2-D SSM heads with different discretization processes to learn long-term progression and seasonal patterns. To improve the efficiency of complex 2D recurrence, we present a fast training using a new 2-dimensional parallel selective scan. We further present and discuss 2-dimensional Mamba and Mamba-2 as the spacial cases of our 2D SSM. Our experimental evaluation shows the superior performance of Chimera on extensive and diverse benchmarks, including ECG and speech time series classification, long-term and short-term time series forecasting, and time series anomaly detection.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

We provide a well-defined variational principle for 3-dimensional flat space Einstein gravity by adding one half of the Gibbons-Hawking-York boundary term to the bulk action. We check the 0-point function, recovering consistency with thermodynamics of flat space cosmologies. We then apply our result to calculate the 1-point functions in flat space Einstein gravity for the vacuum and all flat space cosmologies. The results are compatible with the ones for the zero mode charges obtained by canonical analysis.

While recent advances in deep reinforcement learning have allowed autonomous learning agents to succeed at a variety of complex tasks, existing algorithms generally require a lot of training data. One way to increase the speed at which agents are able to learn to perform tasks is by leveraging the input of human trainers. Although such input can take many forms, real-time, scalar-valued feedback is especially useful in situations where it proves difficult or impossible for humans to provide expert demonstrations. Previous approaches have shown the usefulness of human input provided in this fashion (e.g., the TAMER framework), but they have thus far not considered high-dimensional state spaces or employed the use of deep learning. In this paper, we do both: we propose Deep TAMER, an extension of the TAMER framework that leverages the representational power of deep neural networks in order to learn complex tasks in just a short amount of time with a human trainer. We demonstrate Deep TAMER's success by using it and just 15 minutes of human-provided feedback to train an agent that performs better than humans on the Atari game of Bowling - a task that has proven difficult for even state-of-the-art reinforcement learning methods.

Neural networks transform high-dimensional data into compact, structured representations, often modeled as elements of a lower dimensional latent space. In this paper, we present an alternative interpretation of neural models as dynamical systems acting on the latent manifold. Specifically, we show that autoencoder models implicitly define a latent vector field on the manifold, derived by iteratively applying the encoding-decoding map, without any additional training. We observe that standard training procedures introduce inductive biases that lead to the emergence of attractor points within this vector field. Drawing on this insight, we propose to leverage the vector field as a representation for the network, providing a novel tool to analyze the properties of the model and the data. This representation enables to: (i) analyze the generalization and memorization regimes of neural models, even throughout training; (ii) extract prior knowledge encoded in the network's parameters from the attractors, without requiring any input data; (iii) identify out-of-distribution samples from their trajectories in the vector field. We further validate our approach on vision foundation models, showcasing the applicability and effectiveness of our method in real-world scenarios.

Rapid advances in generative AI have led to increasingly realistic deepfakes, posing growing challenges for law enforcement and public trust. Existing passive deepfake detectors struggle to keep pace, largely due to their dependence on specific forgery artifacts, which limits their ability to generalize to new deepfake types. Proactive deepfake detection using watermarks has emerged to address the challenge of identifying high-quality synthetic media. However, these methods often struggle to balance robustness against benign distortions with sensitivity to malicious tampering. This paper introduces a novel deep learning framework that harnesses high-dimensional latent space representations and the Multi-Agent Adversarial Reinforcement Learning (MAARL) paradigm to develop a robust and adaptive watermarking approach. Specifically, we develop a learnable watermark embedder that operates in the latent space, capturing high-level image semantics, while offering precise control over message encoding and extraction. The MAARL paradigm empowers the learnable watermarking agent to pursue an optimal balance between robustness and fragility by interacting with a dynamic curriculum of benign and malicious image manipulations simulated by an adversarial attacker agent. Comprehensive evaluations on the CelebA and CelebA-HQ benchmarks reveal that our method consistently outperforms state-of-the-art approaches, achieving improvements of over 4.5% on CelebA and more than 5.3% on CelebA-HQ under challenging manipulation scenarios.

Detecting out-of-distribution (OOD) inputs is a central challenge for safely deploying machine learning models in the real world. Existing solutions are mainly driven by small datasets, with low resolution and very few class labels (e.g., CIFAR). As a result, OOD detection for large-scale image classification tasks remains largely unexplored. In this paper, we bridge this critical gap by proposing a group-based OOD detection framework, along with a novel OOD scoring function termed MOS. Our key idea is to decompose the large semantic space into smaller groups with similar concepts, which allows simplifying the decision boundaries between in- vs. out-of-distribution data for effective OOD detection. Our method scales substantially better for high-dimensional class space than previous approaches. We evaluate models trained on ImageNet against four carefully curated OOD datasets, spanning diverse semantics. MOS establishes state-of-the-art performance, reducing the average FPR95 by 14.33% while achieving 6x speedup in inference compared to the previous best method.

While transformer models are widely believed to operate in high-dimensional hidden spaces, we show that attention outputs are confined to a surprisingly low-dimensional subspace, where about 60\% of the directions account for 99\% of the variance--a phenomenon that is induced by the attention output projection matrix and consistently observed across diverse model families and datasets. Critically, we find this low-rank structure as a fundamental cause of the prevalent dead feature problem in sparse dictionary learning, where it creates a mismatch between randomly initialized features and the intrinsic geometry of the activation space. Building on this insight, we propose a subspace-constrained training method for sparse autoencoders (SAEs), initializing feature directions into the active subspace of activations. Our approach reduces dead features from 87\% to below 1\% in Attention Output SAEs with 1M features, and can further extend to other sparse dictionary learning methods. Our findings provide both new insights into the geometry of attention and practical tools for improving sparse dictionary learning in large language models.

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators, that map between infinite dimensional function spaces. We formulate the neural operator as a composition of linear integral operators and nonlinear activation functions. We prove a universal approximation theorem for our proposed neural operator, showing that it can approximate any given nonlinear continuous operator. The proposed neural operators are also discretization-invariant, i.e., they share the same model parameters among different discretization of the underlying function spaces. Furthermore, we introduce four classes of efficient parameterization, viz., graph neural operators, multi-pole graph neural operators, low-rank neural operators, and Fourier neural operators. An important application for neural operators is learning surrogate maps for the solution operators of partial differential equations (PDEs). We consider standard PDEs such as the Burgers, Darcy subsurface flow, and the Navier-Stokes equations, and show that the proposed neural operators have superior performance compared to existing machine learning based methodologies, while being several orders of magnitude faster than conventional PDE solvers.

In this work, we present a new network design paradigm. Our goal is to help advance the understanding of network design and discover design principles that generalize across settings. Instead of focusing on designing individual network instances, we design network design spaces that parametrize populations of networks. The overall process is analogous to classic manual design of networks, but elevated to the design space level. Using our methodology we explore the structure aspect of network design and arrive at a low-dimensional design space consisting of simple, regular networks that we call RegNet. The core insight of the RegNet parametrization is surprisingly simple: widths and depths of good networks can be explained by a quantized linear function. We analyze the RegNet design space and arrive at interesting findings that do not match the current practice of network design. The RegNet design space provides simple and fast networks that work well across a wide range of flop regimes. Under comparable training settings and flops, the RegNet models outperform the popular EfficientNet models while being up to 5x faster on GPUs.

Vision-Language Models (VLMs) encode knowledge and reasoning capabilities for robotic manipulation within high-dimensional representation spaces. However, current approaches often project them into compressed intermediate representations, discarding important task-specific information such as fine-grained spatial or semantic details. To address this, we propose AntiGrounding, a new framework that reverses the instruction grounding process. It lifts candidate actions directly into the VLM representation space, renders trajectories from multiple views, and uses structured visual question answering for instruction-based decision making. This enables zero-shot synthesis of optimal closed-loop robot trajectories for new tasks. We also propose an offline policy refinement module that leverages past experience to enhance long-term performance. Experiments in both simulation and real-world environments show that our method outperforms baselines across diverse robotic manipulation tasks.

Performing Reinforcement Learning in sparse rewards settings, with very little prior knowledge, is a challenging problem since there is no signal to properly guide the learning process. In such situations, a good search strategy is fundamental. At the same time, not having to adapt the algorithm to every single problem is very desirable. Here we introduce TAXONS, a Task Agnostic eXploration of Outcome spaces through Novelty and Surprise algorithm. Based on a population-based divergent-search approach, it learns a set of diverse policies directly from high-dimensional observations, without any task-specific information. TAXONS builds a repertoire of policies while training an autoencoder on the high-dimensional observation of the final state of the system to build a low-dimensional outcome space. The learned outcome space, combined with the reconstruction error, is used to drive the search for new policies. Results show that TAXONS can find a diverse set of controllers, covering a good part of the ground-truth outcome space, while having no information about such space.

We propose a general framework for conditional sampling in PDE-based inverse problems, targeting the recovery of whole solutions from extremely sparse or noisy measurements. This is accomplished by a function-space diffusion model and plug-and-play guidance for conditioning. Our method first trains an unconditional discretization-agnostic denoising model using neural operator architectures. At inference, we refine the samples to satisfy sparse observation data via a gradient-based guidance mechanism. Through rigorous mathematical analysis, we extend Tweedie's formula to infinite-dimensional Hilbert spaces, providing the theoretical foundation for our posterior sampling approach. Our method (FunDPS) accurately captures posterior distributions in function spaces under minimal supervision and severe data scarcity. Across five PDE tasks with only 3% observation, our method achieves an average 32% accuracy improvement over state-of-the-art fixed-resolution diffusion baselines while reducing sampling steps by 4x. Furthermore, multi-resolution fine-tuning ensures strong cross-resolution generalizability. To the best of our knowledge, this is the first diffusion-based framework to operate independently of discretization, offering a practical and flexible solution for forward and inverse problems in the context of PDEs. Code is available at https://github.com/neuraloperator/FunDPS

Diffusion probabilistic models have been shown to generate state-of-the-art results on several competitive image synthesis benchmarks but lack a low-dimensional, interpretable latent space, and are slow at generation. On the other hand, standard Variational Autoencoders (VAEs) typically have access to a low-dimensional latent space but exhibit poor sample quality. We present DiffuseVAE, a novel generative framework that integrates VAE within a diffusion model framework, and leverage this to design novel conditional parameterizations for diffusion models. We show that the resulting model equips diffusion models with a low-dimensional VAE inferred latent code which can be used for downstream tasks like controllable synthesis. The proposed method also improves upon the speed vs quality tradeoff exhibited in standard unconditional DDPM/DDIM models (for instance, FID of 16.47 vs 34.36 using a standard DDIM on the CelebA-HQ-128 benchmark using T=10 reverse process steps) without having explicitly trained for such an objective. Furthermore, the proposed model exhibits synthesis quality comparable to state-of-the-art models on standard image synthesis benchmarks like CIFAR-10 and CelebA-64 while outperforming most existing VAE-based methods. Lastly, we show that the proposed method exhibits inherent generalization to different types of noise in the conditioning signal. For reproducibility, our source code is publicly available at https://github.com/kpandey008/DiffuseVAE.

Coecke, Sadrzadeh, and Clark (arXiv:1003.4394v1 [cs.CL]) developed a compositional model of meaning for distributional semantics, in which each word in a sentence has a meaning vector and the distributional meaning of the sentence is a function of the tensor products of the word vectors. Abstractly speaking, this function is the morphism corresponding to the grammatical structure of the sentence in the category of finite dimensional vector spaces. In this paper, we provide a concrete method for implementing this linear meaning map, by constructing a corpus-based vector space for the type of sentence. Our construction method is based on structured vector spaces whereby meaning vectors of all sentences, regardless of their grammatical structure, live in the same vector space. Our proposed sentence space is the tensor product of two noun spaces, in which the basis vectors are pairs of words each augmented with a grammatical role. This enables us to compare meanings of sentences by simply taking the inner product of their vectors.

Mining data streams with multi-label outputs poses significant challenges due to evolving distributions, high-dimensional label spaces, sparse label occurrences, and complex label dependencies. Moreover, concept drift affects not only input distributions but also label correlations and imbalance ratios over time, complicating model adaptation. To address these challenges, structured learners are categorized into local and global methods. Local methods break down the task into simpler components, while global methods adapt the algorithm to the full output space, potentially yielding better predictions by exploiting label correlations. This work introduces iHOMER (Incremental Hierarchy Of Multi-label Classifiers), an online multi-label learning framework that incrementally partitions the label space into disjoint, correlated clusters without relying on predefined hierarchies. iHOMER leverages online divisive-agglomerative clustering based on Jaccard similarity and a global tree-based learner driven by a multivariate Bernoulli process to guide instance partitioning. To address non-stationarity, it integrates drift detection mechanisms at both global and local levels, enabling dynamic restructuring of label partitions and subtrees. Experiments across 23 real-world datasets show iHOMER outperforms 5 state-of-the-art global baselines, such as MLHAT, MLHT of Pruned Sets and iSOUPT, by 23\%, and 12 local baselines, such as binary relevance transformations of kNN, EFDT, ARF, and ADWIN bagging/boosting ensembles, by 32\%, establishing its robustness for online multi-label classification.

Despite the remarkable progress in deep generative models, synthesizing high-resolution and temporally coherent videos still remains a challenge due to their high-dimensionality and complex temporal dynamics along with large spatial variations. Recent works on diffusion models have shown their potential to solve this challenge, yet they suffer from severe computation- and memory-inefficiency that limit the scalability. To handle this issue, we propose a novel generative model for videos, coined projected latent video diffusion models (PVDM), a probabilistic diffusion model which learns a video distribution in a low-dimensional latent space and thus can be efficiently trained with high-resolution videos under limited resources. Specifically, PVDM is composed of two components: (a) an autoencoder that projects a given video as 2D-shaped latent vectors that factorize the complex cubic structure of video pixels and (b) a diffusion model architecture specialized for our new factorized latent space and the training/sampling procedure to synthesize videos of arbitrary length with a single model. Experiments on popular video generation datasets demonstrate the superiority of PVDM compared with previous video synthesis methods; e.g., PVDM obtains the FVD score of 639.7 on the UCF-101 long video (128 frames) generation benchmark, which improves 1773.4 of the prior state-of-the-art.

Deep models have achieved impressive progress in solving partial differential equations (PDEs). A burgeoning paradigm is learning neural operators to approximate the input-output mappings of PDEs. While previous deep models have explored the multiscale architectures and various operator designs, they are limited to learning the operators as a whole in the coordinate space. In real physical science problems, PDEs are complex coupled equations with numerical solvers relying on discretization into high-dimensional coordinate space, which cannot be precisely approximated by a single operator nor efficiently learned due to the curse of dimensionality. We present Latent Spectral Models (LSM) toward an efficient and precise solver for high-dimensional PDEs. Going beyond the coordinate space, LSM enables an attention-based hierarchical projection network to reduce the high-dimensional data into a compact latent space in linear time. Inspired by classical spectral methods in numerical analysis, we design a neural spectral block to solve PDEs in the latent space that approximates complex input-output mappings via learning multiple basis operators, enjoying nice theoretical guarantees for convergence and approximation. Experimentally, LSM achieves consistent state-of-the-art and yields a relative gain of 11.5% averaged on seven benchmarks covering both solid and fluid physics. Code is available at https://github.com/thuml/Latent-Spectral-Models.

Training generalist agents is difficult across several axes, requiring us to deal with high-dimensional inputs (space), long horizons (time), and generalization to novel tasks. Recent advances with architectures have allowed for improved scaling along one or two of these axes, but are still computationally prohibitive to use. In this paper, we propose to address all three axes by leveraging Language to Control Diffusion models as a hierarchical planner conditioned on language (LCD). We effectively and efficiently scale diffusion models for planning in extended temporal, state, and task dimensions to tackle long horizon control problems conditioned on natural language instructions, as a step towards generalist agents. Comparing LCD with other state-of-the-art models on the CALVIN language robotics benchmark finds that LCD outperforms other SOTA methods in multi-task success rates, whilst improving inference speed over other comparable diffusion models by 3.3x~15x. We show that LCD can successfully leverage the unique strength of diffusion models to produce coherent long range plans while addressing their weakness in generating low-level details and control.

We study the problem of 3D object generation. We propose a novel framework, namely 3D Generative Adversarial Network (3D-GAN), which generates 3D objects from a probabilistic space by leveraging recent advances in volumetric convolutional networks and generative adversarial nets. The benefits of our model are three-fold: first, the use of an adversarial criterion, instead of traditional heuristic criteria, enables the generator to capture object structure implicitly and to synthesize high-quality 3D objects; second, the generator establishes a mapping from a low-dimensional probabilistic space to the space of 3D objects, so that we can sample objects without a reference image or CAD models, and explore the 3D object manifold; third, the adversarial discriminator provides a powerful 3D shape descriptor which, learned without supervision, has wide applications in 3D object recognition. Experiments demonstrate that our method generates high-quality 3D objects, and our unsupervisedly learned features achieve impressive performance on 3D object recognition, comparable with those of supervised learning methods.

Knowledge graph embedding (KGE) is an increasingly popular technique that aims to represent entities and relations of knowledge graphs into low-dimensional semantic spaces for a wide spectrum of applications such as link prediction, knowledge reasoning and knowledge completion. In this paper, we provide a systematic review of existing KGE techniques based on representation spaces. Particularly, we build a fine-grained classification to categorise the models based on three mathematical perspectives of the representation spaces: (1) Algebraic perspective, (2) Geometric perspective, and (3) Analytical perspective. We introduce the rigorous definitions of fundamental mathematical spaces before diving into KGE models and their mathematical properties. We further discuss different KGE methods over the three categories, as well as summarise how spatial advantages work over different embedding needs. By collating the experimental results from downstream tasks, we also explore the advantages of mathematical space in different scenarios and the reasons behind them. We further state some promising research directions from a representation space perspective, with which we hope to inspire researchers to design their KGE models as well as their related applications with more consideration of their mathematical space properties.

Achieving high-resolution, identity consistency, and accurate lip-speech synchronization in face visual dubbing presents significant challenges, particularly for real-time applications like live video streaming. We propose MuseTalk, which generates lip-sync targets in a latent space encoded by a Variational Autoencoder, enabling high-fidelity talking face video generation with efficient inference. Specifically, we project the occluded lower half of the face image and itself as an reference into a low-dimensional latent space and use a multi-scale U-Net to fuse audio and visual features at various levels. We further propose a novel sampling strategy during training, which selects reference images with head poses closely matching the target, allowing the model to focus on precise lip movement by filtering out redundant information. Additionally, we analyze the mechanism of lip-sync loss and reveal its relationship with input information volume. Extensive experiments show that MuseTalk consistently outperforms recent state-of-the-art methods in visual fidelity and achieves comparable lip-sync accuracy. As MuseTalk supports the online generation of face at 256x256 at more than 30 FPS with negligible starting latency, it paves the way for real-time applications.

Variational Autoencoders (VAEs) have gained significant popularity among researchers as a powerful tool for understanding unknown distributions based on limited samples. This popularity stems partly from their impressive performance and partly from their ability to provide meaningful feature representations in the latent space. Wasserstein Autoencoders (WAEs), a variant of VAEs, aim to not only improve model efficiency but also interpretability. However, there has been limited focus on analyzing their statistical guarantees. The matter is further complicated by the fact that the data distributions to which WAEs are applied - such as natural images - are often presumed to possess an underlying low-dimensional structure within a high-dimensional feature space, which current theory does not adequately account for, rendering known bounds inefficient. To bridge the gap between the theory and practice of WAEs, in this paper, we show that WAEs can learn the data distributions when the network architectures are properly chosen. We show that the convergence rates of the expected excess risk in the number of samples for WAEs are independent of the high feature dimension, instead relying only on the intrinsic dimension of the data distribution.

Bimanual dexterous manipulation is a critical yet underexplored area in robotics. Its high-dimensional action space and inherent task complexity present significant challenges for policy learning, and the limited task diversity in existing benchmarks hinders general-purpose skill development. Existing approaches largely depend on reinforcement learning, often constrained by intricately designed reward functions tailored to a narrow set of tasks. In this work, we present a novel approach for efficiently learning diverse bimanual dexterous skills from abundant human demonstrations. Specifically, we introduce BiDexHD, a framework that unifies task construction from existing bimanual datasets and employs teacher-student policy learning to address all tasks. The teacher learns state-based policies using a general two-stage reward function across tasks with shared behaviors, while the student distills the learned multi-task policies into a vision-based policy. With BiDexHD, scalable learning of numerous bimanual dexterous skills from auto-constructed tasks becomes feasible, offering promising advances toward universal bimanual dexterous manipulation. Our empirical evaluation on the TACO dataset, spanning 141 tasks across six categories, demonstrates a task fulfillment rate of 74.59% on trained tasks and 51.07% on unseen tasks, showcasing the effectiveness and competitive zero-shot generalization capabilities of BiDexHD. For videos and more information, visit our project page https://sites.google.com/view/bidexhd.

In this paper, we democratise 3D content creation, enabling precise generation of 3D shapes from abstract sketches while overcoming limitations tied to drawing skills. We introduce a novel part-level modelling and alignment framework that facilitates abstraction modelling and cross-modal correspondence. Leveraging the same part-level decoder, our approach seamlessly extends to sketch modelling by establishing correspondence between CLIPasso edgemaps and projected 3D part regions, eliminating the need for a dataset pairing human sketches and 3D shapes. Additionally, our method introduces a seamless in-position editing process as a byproduct of cross-modal part-aligned modelling. Operating in a low-dimensional implicit space, our approach significantly reduces computational demands and processing time.

The task of manipulating real image attributes through StyleGAN inversion has been extensively researched. This process involves searching latent variables from a well-trained StyleGAN generator that can synthesize a real image, modifying these latent variables, and then synthesizing an image with the desired edits. A balance must be struck between the quality of the reconstruction and the ability to edit. Earlier studies utilized the low-dimensional W-space for latent search, which facilitated effective editing but struggled with reconstructing intricate details. More recent research has turned to the high-dimensional feature space F, which successfully inverses the input image but loses much of the detail during editing. In this paper, we introduce StyleFeatureEditor -- a novel method that enables editing in both w-latents and F-latents. This technique not only allows for the reconstruction of finer image details but also ensures their preservation during editing. We also present a new training pipeline specifically designed to train our model to accurately edit F-latents. Our method is compared with state-of-the-art encoding approaches, demonstrating that our model excels in terms of reconstruction quality and is capable of editing even challenging out-of-domain examples. Code is available at https://github.com/AIRI-Institute/StyleFeatureEditor.

End-to-End (E2E) solutions have emerged as a mainstream approach for autonomous driving systems, with Vision-Language-Action (VLA) models representing a new paradigm that leverages pre-trained multimodal knowledge from Vision-Language Models (VLMs) to interpret and interact with complex real-world environments. However, these methods remain constrained by the limitations of imitation learning, which struggles to inherently encode physical rules during training. Existing approaches often rely on complex rule-based post-refinement, employ reinforcement learning that remains largely limited to simulation, or utilize diffusion guidance that requires computationally expensive gradient calculations. To address these challenges, we introduce ReflectDrive, a novel learning-based framework that integrates a reflection mechanism for safe trajectory generation via discrete diffusion. We first discretize the two-dimensional driving space to construct an action codebook, enabling the use of pre-trained Diffusion Language Models for planning tasks through fine-tuning. Central to our approach is a safety-aware reflection mechanism that performs iterative self-correction without gradient computation. Our method begins with goal-conditioned trajectory generation to model multi-modal driving behaviors. Based on this, we apply local search methods to identify unsafe tokens and determine feasible solutions, which then serve as safe anchors for inpainting-based regeneration. Evaluated on the NAVSIM benchmark, ReflectDrive demonstrates significant advantages in safety-critical trajectory generation, offering a scalable and reliable solution for autonomous driving systems.

Recent advances in Vision-Language Models (VLMs) have enabled unified understanding across text and images, yet equipping these models with robust image generation capabilities remains challenging. Existing approaches often rely on reconstruction-oriented autoencoders or complex bridging mechanisms, leading to misalignment between understanding and generation representations, or architectural complexity. In this work, we propose VUGEN, a novel framework that explicitly leverages VLM's pretrained visual understanding priors for efficient and high-quality image generation. Our approach first transforms the high-dimensional latent space of the VLM's native vision encoder into a lower-dimensional, tractable distribution that maximally preserves visual information. The VLM is then trained to sample within this reduced latent space, ensuring alignment with its visual understanding capabilities. Finally, a dedicated pixel decoder maps these generated latents back to the image space. We find that a VAE-free pixel diffusion decoder to be on par or better than commonly used complex latent diffusion decoders that internally rely on VAE latents. Extensive experiments demonstrate that VUGEN achieves superior image generation performance, improving DPG Bench from 71.17 to 74.32 and FID from 11.86 to 9.06 on COCO, while fully preserving the VLM's original understanding capabilities.

Large Language Models (LLMs) have become foundational to modern AI agent systems, enabling autonomous agents to reason and plan. In most existing systems, inter-agent communication relies primarily on natural language. While this design supports interpretability and human oversight, we argue that it introduces fundamental limitations in agent-to-agent coordination. The semantic space of natural language is structurally misaligned with the high-dimensional vector spaces in which LLMs operate, resulting in information loss and behavioral drift. Beyond surface-level inefficiencies, we highlight a deeper architectural limitation: current LLMs were not trained with the objective of supporting agentic behavior. As such, they lack mechanisms for modeling role continuity, task boundaries, and multi-agent dependencies. The standard next-token prediction paradigm fails to support the structural alignment required for robust, scalable agent coordination. Based on this, we argue that two core questions deserve careful examination: first, given that AI agents fundamentally operate in high-dimensional vector spaces, should they rely on a language system originally designed for human cognition as their communication medium? Second, should we consider developing a new model construction paradigm that builds models from the ground up to natively support structured communication, shared intentionality, and task alignment in multi-role, multi-agent environments? This paper calls for a reconsideration not only of how agents should communicate, but also of what it fundamentally means to train a model that natively supports multi-agent coordination and communication.

This paper presents the results of a Neural Network (NN)-based search for short-duration gravitational-wave transients in data from the third observing run of LIGO, Virgo, and KAGRA. The search targets unmodeled transients with durations of milliseconds to a few seconds in the 30-1500 Hz frequency band, without assumptions about the incoming signal direction, polarization, or morphology. Using the Gravitational Wave Anomalous Knowledge (GWAK) method, three compact binary coalescences (CBCs) identified by existing pipelines are successfully detected, along with a range of detector glitches. The algorithm constructs a low-dimensional embedded space to capture the physical features of signals, enabling the detection of CBCs, detector glitches, and unmodeled transients. This study demonstrates GWAK's ability to enhance gravitational-wave searches beyond the limits of existing pipelines, laying the groundwork for future detection strategies.

Class-Incremental Learning (CIL) requires a learning system to continually learn new classes without forgetting. Despite the strong performance of Pre-Trained Models (PTMs) in CIL, a critical issue persists: learning new classes often results in the overwriting of old ones. Excessive modification of the network causes forgetting, while minimal adjustments lead to an inadequate fit for new classes. As a result, it is desired to figure out a way of efficient model updating without harming former knowledge. In this paper, we propose ExpAndable Subspace Ensemble (EASE) for PTM-based CIL. To enable model updating without conflict, we train a distinct lightweight adapter module for each new task, aiming to create task-specific subspaces. These adapters span a high-dimensional feature space, enabling joint decision-making across multiple subspaces. As data evolves, the expanding subspaces render the old class classifiers incompatible with new-stage spaces. Correspondingly, we design a semantic-guided prototype complement strategy that synthesizes old classes' new features without using any old class instance. Extensive experiments on seven benchmark datasets verify EASE's state-of-the-art performance. Code is available at: https://github.com/sun-hailong/CVPR24-Ease

Human pose and shape (HPS) estimation methods achieve remarkable results. However, current HPS benchmarks are mostly designed to test models in scenarios that are similar to the training data. This can lead to critical situations in real-world applications when the observed data differs significantly from the training data and hence is out-of-distribution (OOD). It is therefore important to test and improve the OOD robustness of HPS methods. To address this fundamental problem, we develop a simulator that can be controlled in a fine-grained manner using interpretable parameters to explore the manifold of images of human pose, e.g. by varying poses, shapes, and clothes. We introduce a learning-based testing method, termed PoseExaminer, that automatically diagnoses HPS algorithms by searching over the parameter space of human pose images to find the failure modes. Our strategy for exploring this high-dimensional parameter space is a multi-agent reinforcement learning system, in which the agents collaborate to explore different parts of the parameter space. We show that our PoseExaminer discovers a variety of limitations in current state-of-the-art models that are relevant in real-world scenarios but are missed by current benchmarks. For example, it finds large regions of realistic human poses that are not predicted correctly, as well as reduced performance for humans with skinny and corpulent body shapes. In addition, we show that fine-tuning HPS methods by exploiting the failure modes found by PoseExaminer improve their robustness and even their performance on standard benchmarks by a significant margin. The code are available for research purposes.

We introduce Psi-Sampler, an SMC-based framework incorporating pCNL-based initial particle sampling for effective inference-time reward alignment with a score-based generative model. Inference-time reward alignment with score-based generative models has recently gained significant traction, following a broader paradigm shift from pre-training to post-training optimization. At the core of this trend is the application of Sequential Monte Carlo (SMC) to the denoising process. However, existing methods typically initialize particles from the Gaussian prior, which inadequately captures reward-relevant regions and results in reduced sampling efficiency. We demonstrate that initializing from the reward-aware posterior significantly improves alignment performance. To enable posterior sampling in high-dimensional latent spaces, we introduce the preconditioned Crank-Nicolson Langevin (pCNL) algorithm, which combines dimension-robust proposals with gradient-informed dynamics. This approach enables efficient and scalable posterior sampling and consistently improves performance across various reward alignment tasks, including layout-to-image generation, quantity-aware generation, and aesthetic-preference generation, as demonstrated in our experiments.

We describe a framework for using natural language to design state abstractions for imitation learning. Generalizable policy learning in high-dimensional observation spaces is facilitated by well-designed state representations, which can surface important features of an environment and hide irrelevant ones. These state representations are typically manually specified, or derived from other labor-intensive labeling procedures. Our method, LGA (language-guided abstraction), uses a combination of natural language supervision and background knowledge from language models (LMs) to automatically build state representations tailored to unseen tasks. In LGA, a user first provides a (possibly incomplete) description of a target task in natural language; next, a pre-trained LM translates this task description into a state abstraction function that masks out irrelevant features; finally, an imitation policy is trained using a small number of demonstrations and LGA-generated abstract states. Experiments on simulated robotic tasks show that LGA yields state abstractions similar to those designed by humans, but in a fraction of the time, and that these abstractions improve generalization and robustness in the presence of spurious correlations and ambiguous specifications. We illustrate the utility of the learned abstractions on mobile manipulation tasks with a Spot robot.

As hyperparameter tuning becomes increasingly costly at scale, efficient tuning methods are essential. Yet principles for guiding hyperparameter tuning remain limited. In this work, we seek to establish such principles by considering a broad range of hyperparameters, including batch size, learning rate, and weight decay. We identify a phenomenon we call trajectory invariance, where pre-training loss curves, gradient noise, and gradient norm exhibit invariance--closely overlapping--with respect to a quantity that combines learning rate and weight decay. This phenomenon effectively reduces the original two-dimensional hyperparameter space to one dimension, yielding an efficient tuning rule: follow the salient direction revealed by trajectory invariance. Furthermore, we refine previous scaling laws and challenge several existing viewpoints. Overall, our work proposes new principles for efficient tuning and inspires future research on scaling laws.

Objective: While recent advances in text-conditioned generative models have enabled the synthesis of realistic medical images, progress has been largely confined to 2D modalities such as chest X-rays. Extending text-to-image generation to volumetric Computed Tomography (CT) remains a significant challenge, due to its high dimensionality, anatomical complexity, and the absence of robust frameworks that align vision-language data in 3D medical imaging. Methods: We introduce a novel architecture for Text-to-CT generation that combines a latent diffusion model with a 3D contrastive vision-language pretraining scheme. Our approach leverages a dual-encoder CLIP-style model trained on paired CT volumes and radiology reports to establish a shared embedding space, which serves as the conditioning input for generation. CT volumes are compressed into a low-dimensional latent space via a pretrained volumetric VAE, enabling efficient 3D denoising diffusion without requiring external super-resolution stages. Results: We evaluate our method on the CT-RATE dataset and conduct a comprehensive assessment of image fidelity, clinical relevance, and semantic alignment. Our model achieves competitive performance across all tasks, significantly outperforming prior baselines for text-to-CT generation. Moreover, we demonstrate that CT scans synthesized by our framework can effectively augment real data, improving downstream diagnostic performance. Conclusion: Our results show that modality-specific vision-language alignment is a key component for high-quality 3D medical image generation. By integrating contrastive pretraining and volumetric diffusion, our method offers a scalable and controllable solution for synthesizing clinically meaningful CT volumes from text, paving the way for new applications in data augmentation, medical education, and automated clinical simulation.

We explore the use of topological data analysis (TDA) combined with machine learning for discriminating standard model backgrounds from the invisible decay of the Z^prime boson associated with monophoton emission at a 3 TeV muon collider. Reconstructed events are mapped into a six-dimensional kinematic space and aggregated into bags of events, from which persistent homology is used to extract Betti number distributions. Within the Multiple Instance Learning paradigm, classifiers trained on these topological descriptors demonstrate significantly improved classification accuracy compared to the conventional ML approaches based on event-wise kinematic inputs. We also draw exclusion contours at 95\% CL in the (m_{Z^prime}, m_chi) parameter space, highlighting the potential of topological features to extend the discovery reach of future collider experiments.

In this research, we explore the integration of quantum computing with classical machine learning for image classification tasks, specifically focusing on the MNIST dataset. We propose a hybrid quantum-classical approach that leverages the strengths of both paradigms. The process begins with preprocessing the MNIST dataset, normalizing the pixel values, and reshaping the images into vectors. An autoencoder compresses these 784-dimensional vectors into a 64-dimensional latent space, effectively reducing the data's dimensionality while preserving essential features. These compressed features are then processed using a quantum circuit implemented on a 5-qubit system. The quantum circuit applies rotation gates based on the feature values, followed by Hadamard and CNOT gates to entangle the qubits, and measurements are taken to generate quantum outcomes. These outcomes serve as input for a classical neural network designed to classify the MNIST digits. The classical neural network comprises multiple dense layers with batch normalization and dropout to enhance generalization and performance. We evaluate the performance of this hybrid model and compare it with a purely classical approach. The experimental results indicate that while the hybrid model demonstrates the feasibility of integrating quantum computing with classical techniques, the accuracy of the final model, trained on quantum outcomes, is currently lower than the classical model trained on compressed features. This research highlights the potential of quantum computing in machine learning, though further optimization and advanced quantum algorithms are necessary to achieve superior performance.

Words have been represented in a high-dimensional vector space that encodes their semantic similarities, enabling downstream applications such as retrieving synonyms, antonyms, and relevant contexts. However, despite recent advances in multilingual language models (LMs), the effectiveness of these models' representations in semantic retrieval contexts has not been comprehensively explored. To fill this gap, this paper introduces the MINERS, a benchmark designed to evaluate the ability of multilingual LMs in semantic retrieval tasks, including bitext mining and classification via retrieval-augmented contexts. We create a comprehensive framework to assess the robustness of LMs in retrieving samples across over 200 diverse languages, including extremely low-resource languages in challenging cross-lingual and code-switching settings. Our results demonstrate that by solely retrieving semantically similar embeddings yields performance competitive with state-of-the-art approaches, without requiring any fine-tuning.

Recently, a new Continual Learning (CL) paradigm was presented to control catastrophic forgetting, called Interval Continual Learning (InterContiNet), which relies on enforcing interval constraints on the neural network parameter space. Unfortunately, InterContiNet training is challenging due to the high dimensionality of the weight space, making intervals difficult to manage. To address this issue, we introduce HyperInterval, a technique that employs interval arithmetic within the embedding space and utilizes a hypernetwork to map these intervals to the target network parameter space. We train interval embeddings for consecutive tasks and train a hypernetwork to transform these embeddings into weights of the target network. An embedding for a given task is trained along with the hypernetwork, preserving the response of the target network for the previous task embeddings. Interval arithmetic works with a more manageable, lower-dimensional embedding space rather than directly preparing intervals in a high-dimensional weight space. Our model allows faster and more efficient training. Furthermore, HyperInterval maintains the guarantee of not forgetting. At the end of training, we can choose one universal embedding to produce a single network dedicated to all tasks. In such a framework, hypernetwork is used only for training and can be seen as a meta-trainer. HyperInterval obtains significantly better results than InterContiNet and gives SOTA results on several benchmarks.

Clustering is central to many data-driven application domains and has been studied extensively in terms of distance functions and grouping algorithms. Relatively little work has focused on learning representations for clustering. In this paper, we propose Deep Embedded Clustering (DEC), a method that simultaneously learns feature representations and cluster assignments using deep neural networks. DEC learns a mapping from the data space to a lower-dimensional feature space in which it iteratively optimizes a clustering objective. Our experimental evaluations on image and text corpora show significant improvement over state-of-the-art methods.

Video Variational Autoencoder (VAE) encodes videos into a low-dimensional latent space, becoming a key component of most Latent Video Diffusion Models (LVDMs) to reduce model training costs. However, as the resolution and duration of generated videos increase, the encoding cost of Video VAEs becomes a limiting bottleneck in training LVDMs. Moreover, the block-wise inference method adopted by most LVDMs can lead to discontinuities of latent space when processing long-duration videos. The key to addressing the computational bottleneck lies in decomposing videos into distinct components and efficiently encoding the critical information. Wavelet transform can decompose videos into multiple frequency-domain components and improve the efficiency significantly, we thus propose Wavelet Flow VAE (WF-VAE), an autoencoder that leverages multi-level wavelet transform to facilitate low-frequency energy flow into latent representation. Furthermore, we introduce a method called Causal Cache, which maintains the integrity of latent space during block-wise inference. Compared to state-of-the-art video VAEs, WF-VAE demonstrates superior performance in both PSNR and LPIPS metrics, achieving 2x higher throughput and 4x lower memory consumption while maintaining competitive reconstruction quality. Our code and models are available at https://github.com/PKU-YuanGroup/WF-VAE.

Word embeddings that map words into a fixed-dimensional vector space are the backbone of modern NLP. Most word embedding methods encode semantic information. However, phonetic information, which is important for some tasks, is often overlooked. In this work, we develop several novel methods which leverage articulatory features to build phonetically informed word embeddings, and present a set of phonetic word embeddings to encourage their community development, evaluation and use. While several methods for learning phonetic word embeddings already exist, there is a lack of consistency in evaluating their effectiveness. Thus, we also proposes several ways to evaluate both intrinsic aspects of phonetic word embeddings, such as word retrieval and correlation with sound similarity, and extrinsic performances, such as rhyme and cognate detection and sound analogies. We hope that our suite of tasks will promote reproducibility and provide direction for future research on phonetic word embeddings.

Synthesizing amyloid PET scans from the more widely available and accessible structural MRI modality offers a promising, cost-effective approach for large-scale Alzheimer's Disease (AD) screening. This is motivated by evidence that, while MRI does not directly detect amyloid pathology, it may nonetheless encode information correlated with amyloid deposition that can be uncovered through advanced modeling. However, the high dimensionality and structural complexity of 3D neuroimaging data pose significant challenges for existing MRI-to-PET translation methods. Modeling the cross-modality relationship in a lower-dimensional latent space can simplify the learning task and enable more effective translation. As such, we present CoCoLIT (ControlNet-Conditioned Latent Image Translation), a diffusion-based latent generative framework that incorporates three main innovations: (1) a novel Weighted Image Space Loss (WISL) that improves latent representation learning and synthesis quality; (2) a theoretical and empirical analysis of Latent Average Stabilization (LAS), an existing technique used in similar generative models to enhance inference consistency; and (3) the introduction of ControlNet-based conditioning for MRI-to-PET translation. We evaluate CoCoLIT's performance on publicly available datasets and find that our model significantly outperforms state-of-the-art methods on both image-based and amyloid-related metrics. Notably, in amyloid-positivity classification, CoCoLIT outperforms the second-best method with improvements of +10.5% on the internal dataset and +23.7% on the external dataset. The code and models of our approach are available at https://github.com/brAIn-science/CoCoLIT.

Recent AI-based 3D content creation has largely evolved along two paths: feed-forward image-to-3D reconstruction approaches and 3D generative models trained with 2D or 3D supervision. In this work, we show that existing feed-forward reconstruction methods can serve as effective latent encoders for training 3D generative models, thereby bridging these two paradigms. By reusing powerful pre-trained reconstruction models, we avoid computationally expensive encoder network training and obtain rich 3D latent features for generative modeling for free. However, the latent spaces of reconstruction models are not well-suited for generative modeling due to their unstructured nature. To enable flow-based model training on these latent features, we develop post-processing pipelines, including protocols to standardize the features and spatial weighting to concentrate on important regions. We further incorporate a 2D image space perceptual rendering loss to handle the high-dimensional latent spaces. Finally, we propose a multi-stream transformer-based rectified flow architecture to achieve linear scaling and high-quality text-conditioned 3D generation. Our framework leverages the advancements of feed-forward reconstruction models to enhance the scalability of 3D generative modeling, achieving both high computational efficiency and state-of-the-art performance in text-to-3D generation.

We propose a novel method called SHS-Net for oriented normal estimation of point clouds by learning signed hyper surfaces, which can accurately predict normals with global consistent orientation from various point clouds. Almost all existing methods estimate oriented normals through a two-stage pipeline, i.e., unoriented normal estimation and normal orientation, and each step is implemented by a separate algorithm. However, previous methods are sensitive to parameter settings, resulting in poor results from point clouds with noise, density variations and complex geometries. In this work, we introduce signed hyper surfaces (SHS), which are parameterized by multi-layer perceptron (MLP) layers, to learn to estimate oriented normals from point clouds in an end-to-end manner. The signed hyper surfaces are implicitly learned in a high-dimensional feature space where the local and global information is aggregated. Specifically, we introduce a patch encoding module and a shape encoding module to encode a 3D point cloud into a local latent code and a global latent code, respectively. Then, an attention-weighted normal prediction module is proposed as a decoder, which takes the local and global latent codes as input to predict oriented normals. Experimental results show that our SHS-Net outperforms the state-of-the-art methods in both unoriented and oriented normal estimation on the widely used benchmarks. The code, data and pretrained models are publicly available.

Recent works in robotic manipulation through reinforcement learning (RL) or imitation learning (IL) have shown potential for tackling a range of tasks e.g., opening a drawer or a cupboard. However, these techniques generalize poorly to unseen objects. We conjecture that this is due to the high-dimensional action space for joint control. In this paper, we take an alternative approach and separate the task of learning 'what to do' from 'how to do it' i.e., whole-body control. We pose the RL problem as one of determining the skill dynamics for a disembodied virtual manipulator interacting with articulated objects. The whole-body robotic kinematic control is optimized to execute the high-dimensional joint motion to reach the goals in the workspace. It does so by solving a quadratic programming (QP) model with robotic singularity and kinematic constraints. Our experiments on manipulating complex articulated objects show that the proposed approach is more generalizable to unseen objects with large intra-class variations, outperforming previous approaches. The evaluation results indicate that our approach generates more compliant robotic motion and outperforms the pure RL and IL baselines in task success rates. Additional information and videos are available at https://kl-research.github.io/decoupskill

Large language models (LLMs) have enabled agents to perform complex reasoning and decision-making through free-form language interactions. However, in open-ended language action environments (e.g., negotiation or question-asking games), the action space can be formulated as a joint distribution over tokens, resulting in an exponentially large action space. Sampling actions in such a space can lead to extreme reward sparsity, which brings large reward variance, hindering effective reinforcement learning (RL). To address this, we propose ARIA, a method that Aggregates Rewards in Intention space to enable efficient and effective language Agents training. ARIA aims to project natural language actions from the high-dimensional joint token distribution space into a low-dimensional intention space, where semantically similar actions are clustered and assigned shared rewards. This intention-aware reward aggregation reduces reward variance by densifying reward signals, fostering better policy optimization. Extensive experiments demonstrate that ARIA not only significantly reduces policy gradient variance, but also delivers substantial performance gains of an average of 9.95% across four downstream tasks, consistently outperforming offline and online RL baselines.

Flow-based latent generative models such as Stable Diffusion 3 are able to generate images with remarkable quality, even enabling photorealistic text-to-image generation. Their impressive performance suggests that these models should also constitute powerful priors for inverse imaging problems, but that approach has not yet led to comparable fidelity. There are several key obstacles: (i) the encoding into a lower-dimensional latent space makes the underlying (forward) mapping non-linear; (ii) the data likelihood term is usually intractable; and (iii) learned generative models struggle to recover rare, atypical data modes during inference. We present FLAIR, a novel training free variational framework that leverages flow-based generative models as a prior for inverse problems. To that end, we introduce a variational objective for flow matching that is agnostic to the type of degradation, and combine it with deterministic trajectory adjustments to recover atypical modes. To enforce exact consistency with the observed data, we decouple the optimization of the data fidelity and regularization terms. Moreover, we introduce a time-dependent calibration scheme in which the strength of the regularization is modulated according to off-line accuracy estimates. Results on standard imaging benchmarks demonstrate that FLAIR consistently outperforms existing diffusion- and flow-based methods in terms of reconstruction quality and sample diversity.

Let T be a rooted and weighted tree, where the weight of any node is equal to the sum of the weights of its children. The popular Treemap algorithm visualizes such a tree as a hierarchical partition of a square into rectangles, where the area of the rectangle corresponding to any node in T is equal to the weight of that node. The aspect ratio of the rectangles in such a rectangular partition necessarily depends on the weights and can become arbitrarily high. We introduce a new hierarchical partition scheme, called a polygonal partition, which uses convex polygons rather than just rectangles. We present two methods for constructing polygonal partitions, both having guarantees on the worst-case aspect ratio of the constructed polygons; in particular, both methods guarantee a bound on the aspect ratio that is independent of the weights of the nodes. We also consider rectangular partitions with slack, where the areas of the rectangles may differ slightly from the weights of the corresponding nodes. We show that this makes it possible to obtain partitions with constant aspect ratio. This result generalizes to hyper-rectangular partitions in R^d. We use these partitions with slack for embedding ultrametrics into d-dimensional Euclidean space: we give a rm polylog(Delta)-approximation algorithm for embedding n-point ultrametrics into R^d with minimum distortion, where Delta denotes the spread of the metric, i.e., the ratio between the largest and the smallest distance between two points. The previously best-known approximation ratio for this problem was polynomial in n. This is the first algorithm for embedding a non-trivial family of weighted-graph metrics into a space of constant dimension that achieves polylogarithmic approximation ratio.

We propose a new method for count-based exploration in high-dimensional state spaces. Unlike previous work which relies on density models, we show that counts can be derived by averaging samples from the Rademacher distribution (or coin flips). This insight is used to set up a simple supervised learning objective which, when optimized, yields a state's visitation count. We show that our method is significantly more effective at deducing ground-truth visitation counts than previous work; when used as an exploration bonus for a model-free reinforcement learning algorithm, it outperforms existing approaches on most of 9 challenging exploration tasks, including the Atari game Montezuma's Revenge.

Multimodal Large Language Models (MLLMs) have demonstrated impressive capabilities across various tasks, but still struggle with complex mathematical reasoning. Existing research primarily focuses on dataset construction and method optimization, often overlooking two critical aspects: comprehensive knowledge-driven design and model-centric data space modeling. In this paper, we introduce We-Math 2.0, a unified system that integrates a structured mathematical knowledge system, model-centric data space modeling, and a reinforcement learning (RL)-based training paradigm to comprehensively enhance the mathematical reasoning abilities of MLLMs. The key contributions of We-Math 2.0 are fourfold: (1) MathBook Knowledge System: We construct a five-level hierarchical system encompassing 491 knowledge points and 1,819 fundamental principles. (2) MathBook-Standard & Pro: We develop MathBook-Standard, a dataset that ensures broad conceptual coverage and flexibility through dual expansion. Additionally, we define a three-dimensional difficulty space and generate 7 progressive variants per problem to build MathBook-Pro, a challenging dataset for robust training. (3) MathBook-RL: We propose a two-stage RL framework comprising: (i) Cold-Start Fine-tuning, which aligns the model with knowledge-oriented chain-of-thought reasoning; and (ii) Progressive Alignment RL, leveraging average-reward learning and dynamic data scheduling to achieve progressive alignment across difficulty levels. (4) MathBookEval: We introduce a comprehensive benchmark covering all 491 knowledge points with diverse reasoning step distributions. Experimental results show that MathBook-RL performs competitively with existing baselines on four widely-used benchmarks and achieves strong results on MathBookEval, suggesting promising generalization in mathematical reasoning.

Personalized text-to-image generation has attracted unprecedented attention in the recent few years due to its unique capability of generating highly-personalized images via using the input concept dataset and novel textual prompt. However, previous methods solely focus on the performance of the reconstruction task, degrading its ability to combine with different textual prompt. Besides, optimizing in the high-dimensional embedding space usually leads to unnecessary time-consuming training process and slow convergence. To address these issues, we propose an efficient method to explore the target embedding in a textual subspace, drawing inspiration from the self-expressiveness property. Additionally, we propose an efficient selection strategy for determining the basis vectors of the textual subspace. The experimental evaluations demonstrate that the learned embedding can not only faithfully reconstruct input image, but also significantly improves its alignment with novel input textual prompt. Furthermore, we observe that optimizing in the textual subspace leads to an significant improvement of the robustness to the initial word, relaxing the constraint that requires users to input the most relevant initial word. Our method opens the door to more efficient representation learning for personalized text-to-image generation.

Generalizable neural surface reconstruction techniques have attracted great attention in recent years. However, they encounter limitations of low confidence depth distribution and inaccurate surface reasoning due to the oversimplified volume rendering process employed. In this paper, we present Reconstruction TRansformer (ReTR), a novel framework that leverages the transformer architecture to redesign the rendering process, enabling complex render interaction modeling. It introduces a learnable meta-ray token and utilizes the cross-attention mechanism to simulate the interaction of rendering process with sampled points and render the observed color. Meanwhile, by operating within a high-dimensional feature space rather than the color space, ReTR mitigates sensitivity to projected colors in source views. Such improvements result in accurate surface assessment with high confidence. We demonstrate the effectiveness of our approach on various datasets, showcasing how our method outperforms the current state-of-the-art approaches in terms of reconstruction quality and generalization ability. Our code is available at https://github.com/YixunLiang/ReTR.

The collisionless Boltzmann equation (CBE) is a fundamental equation that governs the dynamics of a broad range of astrophysical systems from space plasma to star clusters and galaxies. It is computationally expensive to integrate the CBE directly in a multi-dimensional phase space, and thus the applications to realistic astrophysical problems have been limited so far. Recently, Todorova & Steijl (2020) proposed an efficient quantum algorithm to solve the CBE with significantly reduced computational complexity. We extend the algorithm to perform quantum simulations of self-gravitating systems, incorporating the method to calculate gravity with the major Fourier modes of the density distribution extracted from the solution-encoding quantum state. Our method improves the dependency of time and space complexities on Nv , the number of grid points in each velocity coordinate, compared to the classical simulation methods. We then conduct some numerical demonstrations of our method. We first run a 1+1 dimensional test calculation of free streaming motion on 64*64 grids using 13 simulated qubits and validate our method. We then perform simulations of Jeans collapse, and compare the result with analytic and linear theory calculations. It will thus allow us to perform large-scale CBE simulations on future quantum computers.

Both the design and control of a robot play equally important roles in its task performance. However, while optimal control is well studied in the machine learning and robotics community, less attention is placed on finding the optimal robot design. This is mainly because co-optimizing design and control in robotics is characterized as a challenging problem, and more importantly, a comprehensive evaluation benchmark for co-optimization does not exist. In this paper, we propose Evolution Gym, the first large-scale benchmark for co-optimizing the design and control of soft robots. In our benchmark, each robot is composed of different types of voxels (e.g., soft, rigid, actuators), resulting in a modular and expressive robot design space. Our benchmark environments span a wide range of tasks, including locomotion on various types of terrains and manipulation. Furthermore, we develop several robot co-evolution algorithms by combining state-of-the-art design optimization methods and deep reinforcement learning techniques. Evaluating the algorithms on our benchmark platform, we observe robots exhibiting increasingly complex behaviors as evolution progresses, with the best evolved designs solving many of our proposed tasks. Additionally, even though robot designs are evolved autonomously from scratch without prior knowledge, they often grow to resemble existing natural creatures while outperforming hand-designed robots. Nevertheless, all tested algorithms fail to find robots that succeed in our hardest environments. This suggests that more advanced algorithms are required to explore the high-dimensional design space and evolve increasingly intelligent robots -- an area of research in which we hope Evolution Gym will accelerate progress. Our website with code, environments, documentation, and tutorials is available at http://evogym.csail.mit.edu.

We provide a mapping between past null and future null infinity in three-dimensional flat space, using symmetry considerations. From this we derive a mapping between the corresponding asymptotic symmetry groups. By studying the metric at asymptotic regions, we find that the mapping is energy preserving and yields an infinite number of conservation laws.

We investigate equilibration and generalized thermalization of the quantum Harmonic chain under local quantum quench. The quench action we consider is connecting two disjoint harmonic chains of different sizes and the system jumps between two integrable settings. We verify the validity of the Generalized Gibbs Ensemble description for this infinite dimensional Hilbert space system and also identify equilibration between the subsystems as in classical systems. Using Bogoliubov transformations, we show that the eigenstates of the system prior to the quench evolve towards the Gibbs Generalized Ensemble description. Eigenstates that are more delocalized (in the sense of inverse participation ratio) prior to the quench, tend to equilibrate more rapidly. Further, through the phase space properties of a Generalized Gibbs Ensemble and the strength of stimulated emission, we identify the necessary criterion on the initial states for such relaxation at late times and also find out the states which would potentially not be described by the Gibbs Generalized Ensemble description.

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distancex2014a measure of representational dissimilarity proposed by Williams et al. (2021).These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves substantially lower bias than standard estimators in simulation and on neural data, particularly in high-dimensional settings. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method that is well-suited to practical scientific settings.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

Many real-world manipulation tasks consist of a series of subtasks that are significantly different from one another. Such long-horizon, complex tasks highlight the potential of dexterous hands, which possess adaptability and versatility, capable of seamlessly transitioning between different modes of functionality without the need for re-grasping or external tools. However, the challenges arise due to the high-dimensional action space of dexterous hand and complex compositional dynamics of the long-horizon tasks. We present Sequential Dexterity, a general system based on reinforcement learning (RL) that chains multiple dexterous policies for achieving long-horizon task goals. The core of the system is a transition feasibility function that progressively finetunes the sub-policies for enhancing chaining success rate, while also enables autonomous policy-switching for recovery from failures and bypassing redundant stages. Despite being trained only in simulation with a few task objects, our system demonstrates generalization capability to novel object shapes and is able to zero-shot transfer to a real-world robot equipped with a dexterous hand. More details and video results could be found at https://sequential-dexterity.github.io

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

We present an efficient text-to-video generation framework based on latent diffusion models, termed MagicVideo. Given a text description, MagicVideo can generate photo-realistic video clips with high relevance to the text content. With the proposed efficient latent 3D U-Net design, MagicVideo can generate video clips with 256x256 spatial resolution on a single GPU card, which is 64x faster than the recent video diffusion model (VDM). Unlike previous works that train video generation from scratch in the RGB space, we propose to generate video clips in a low-dimensional latent space. We further utilize all the convolution operator weights of pre-trained text-to-image generative U-Net models for faster training. To achieve this, we introduce two new designs to adapt the U-Net decoder to video data: a framewise lightweight adaptor for the image-to-video distribution adjustment and a directed temporal attention module to capture frame temporal dependencies. The whole generation process is within the low-dimension latent space of a pre-trained variation auto-encoder. We demonstrate that MagicVideo can generate both realistic video content and imaginary content in a photo-realistic style with a trade-off in terms of quality and computational cost. Refer to https://magicvideo.github.io/# for more examples.

The presence of distribution shifts poses a significant challenge for deploying modern machine learning models in real-world applications. This work focuses on the target shift problem in a regression setting (Zhang et al., 2013; Nguyen et al., 2016). More specifically, the target variable y (also known as the response variable), which is continuous, has different marginal distributions in the training source and testing domain, while the conditional distribution of features x given y remains the same. While most literature focuses on classification tasks with finite target space, the regression problem has an infinite dimensional target space, which makes many of the existing methods inapplicable. In this work, we show that the continuous target shift problem can be addressed by estimating the importance weight function from an ill-posed integral equation. We propose a nonparametric regularized approach named ReTaSA to solve the ill-posed integral equation and provide theoretical justification for the estimated importance weight function. The effectiveness of the proposed method has been demonstrated with extensive numerical studies on synthetic and real-world datasets.

Latent diffusion models with Transformer architectures excel at generating high-fidelity images. However, recent studies reveal an optimization dilemma in this two-stage design: while increasing the per-token feature dimension in visual tokenizers improves reconstruction quality, it requires substantially larger diffusion models and more training iterations to achieve comparable generation performance. Consequently, existing systems often settle for sub-optimal solutions, either producing visual artifacts due to information loss within tokenizers or failing to converge fully due to expensive computation costs. We argue that this dilemma stems from the inherent difficulty in learning unconstrained high-dimensional latent spaces. To address this, we propose aligning the latent space with pre-trained vision foundation models when training the visual tokenizers. Our proposed VA-VAE (Vision foundation model Aligned Variational AutoEncoder) significantly expands the reconstruction-generation frontier of latent diffusion models, enabling faster convergence of Diffusion Transformers (DiT) in high-dimensional latent spaces. To exploit the full potential of VA-VAE, we build an enhanced DiT baseline with improved training strategies and architecture designs, termed LightningDiT. The integrated system achieves state-of-the-art (SOTA) performance on ImageNet 256x256 generation with an FID score of 1.35 while demonstrating remarkable training efficiency by reaching an FID score of 2.11 in just 64 epochs--representing an over 21 times convergence speedup compared to the original DiT. Models and codes are available at: https://github.com/hustvl/LightningDiT.

Designing biological sequences that satisfy multiple, often conflicting, functional and biophysical criteria remains a central challenge in biomolecule engineering. While discrete flow matching models have recently shown promise for efficient sampling in high-dimensional sequence spaces, existing approaches address only single objectives or require continuous embeddings that can distort discrete distributions. We present Multi-Objective-Guided Discrete Flow Matching (MOG-DFM), a general framework to steer any pretrained discrete-time flow matching generator toward Pareto-efficient trade-offs across multiple scalar objectives. At each sampling step, MOG-DFM computes a hybrid rank-directional score for candidate transitions and applies an adaptive hypercone filter to enforce consistent multi-objective progression. We also trained two unconditional discrete flow matching models, PepDFM for diverse peptide generation and EnhancerDFM for functional enhancer DNA generation, as base generation models for MOG-DFM. We demonstrate MOG-DFM's effectiveness in generating peptide binders optimized across five properties (hemolysis, non-fouling, solubility, half-life, and binding affinity), and in designing DNA sequences with specific enhancer classes and DNA shapes. In total, MOG-DFM proves to be a powerful tool for multi-property-guided biomolecule sequence design.

Generative modeling of complex behaviors from labeled datasets has been a longstanding problem in decision making. Unlike language or image generation, decision making requires modeling actions - continuous-valued vectors that are multimodal in their distribution, potentially drawn from uncurated sources, where generation errors can compound in sequential prediction. A recent class of models called Behavior Transformers (BeT) addresses this by discretizing actions using k-means clustering to capture different modes. However, k-means struggles to scale for high-dimensional action spaces or long sequences, and lacks gradient information, and thus BeT suffers in modeling long-range actions. In this work, we present Vector-Quantized Behavior Transformer (VQ-BeT), a versatile model for behavior generation that handles multimodal action prediction, conditional generation, and partial observations. VQ-BeT augments BeT by tokenizing continuous actions with a hierarchical vector quantization module. Across seven environments including simulated manipulation, autonomous driving, and robotics, VQ-BeT improves on state-of-the-art models such as BeT and Diffusion Policies. Importantly, we demonstrate VQ-BeT's improved ability to capture behavior modes while accelerating inference speed 5x over Diffusion Policies. Videos and code can be found https://sjlee.cc/vq-bet

The classical development of neural networks has primarily focused on learning mappings between finite-dimensional Euclidean spaces. Recently, this has been generalized to neural operators that learn mappings between function spaces. For partial differential equations (PDEs), neural operators directly learn the mapping from any functional parametric dependence to the solution. Thus, they learn an entire family of PDEs, in contrast to classical methods which solve one instance of the equation. In this work, we formulate a new neural operator by parameterizing the integral kernel directly in Fourier space, allowing for an expressive and efficient architecture. We perform experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The Fourier neural operator is the first ML-based method to successfully model turbulent flows with zero-shot super-resolution. It is up to three orders of magnitude faster compared to traditional PDE solvers. Additionally, it achieves superior accuracy compared to previous learning-based solvers under fixed resolution.

Latent variable generative models have emerged as powerful tools for generative tasks including image and video synthesis. These models are enabled by pretrained autoencoders that map high resolution data into a compressed lower dimensional latent space, where the generative models can subsequently be developed while requiring fewer computational resources. Despite their effectiveness, the direct application of latent variable models to higher dimensional domains such as videos continues to pose challenges for efficient training and inference. In this paper, we propose an autoencoder that projects volumetric data onto a four-plane factorized latent space that grows sublinearly with the input size, making it ideal for higher dimensional data like videos. The design of our factorized model supports straightforward adoption in a number of conditional generation tasks with latent diffusion models (LDMs), such as class-conditional generation, frame prediction, and video interpolation. Our results show that the proposed four-plane latent space retains a rich representation needed for high-fidelity reconstructions despite the heavy compression, while simultaneously enabling LDMs to operate with significant improvements in speed and memory.

Kinodynamic motion planning is concerned with computing collision-free trajectories while abiding by the robot's dynamic constraints. This critical problem is often tackled using sampling-based planners (SBPs) that explore the robot's high-dimensional state space by constructing a search tree via action propagations. Although SBPs can offer global guarantees on completeness and solution quality, their performance is often hindered by slow exploration due to uninformed action sampling. Learning-based approaches can yield significantly faster runtimes, yet they fail to generalize to out-of-distribution (OOD) scenarios and lack critical guarantees, e.g., safety, thus limiting their deployment on physical robots. We present Diffusion Tree (DiTree): a provably-generalizable framework leveraging diffusion policies (DPs) as informed samplers to efficiently guide state-space search within SBPs. DiTree combines DP's ability to model complex distributions of expert trajectories, conditioned on local observations, with the completeness of SBPs to yield provably-safe solutions within a few action propagation iterations for complex dynamical systems. We demonstrate DiTree's power with an implementation combining the popular RRT planner with a DP action sampler trained on a single environment. In comprehensive evaluations on OOD scenarios, % DiTree has comparable runtimes to a standalone DP (3x faster than classical SBPs), while improving the average success rate over DP and SBPs. DiTree is on average 3x faster than classical SBPs, and outperforms all other approaches by achieving roughly 30\% higher success rate. Project webpage: https://sites.google.com/view/ditree.

Despite advances in large language models (LLMs) on reasoning and instruction-following benchmarks, it remains unclear whether they can reliably produce outputs aligned with a broad variety of user goals, a concept we refer to as steerability. The abundance of methods proposed to modify LLM behavior makes it unclear whether current LLMs are already steerable, or require further intervention. In particular, LLMs may exhibit (i) poor coverage, where rare user goals are underrepresented; (ii) miscalibration, where models overshoot requests; and (iii) side effects, where changes to one dimension of text inadvertently affect others. To systematically evaluate these failures, we introduce a framework based on a multi-dimensional goal space that models user goals and LLM outputs as vectors with dimensions corresponding to text attributes (e.g., reading difficulty). Applied to a text-rewriting task, we find that current LLMs struggle with steerability, as side effects are persistent. Interventions to improve steerability, such as prompt engineering, best-of-N sampling, and reinforcement learning fine-tuning, have varying effectiveness, yet side effects remain problematic. Our findings suggest that even strong LLMs struggle with steerability, and existing alignment strategies may be insufficient. We open-source our steerability evaluation framework at https://github.com/MLD3/steerability.

We present a novel text-to-speech (TTS) system, namely SupertonicTTS, for improved scalability and efficiency in speech synthesis. SupertonicTTS is comprised of three components: a speech autoencoder for continuous latent representation, a text-to-latent module leveraging flow-matching for text-to-latent mapping, and an utterance-level duration predictor. To enable a lightweight architecture, we employ a low-dimensional latent space, temporal compression of latents, and ConvNeXt blocks. We further simplify the TTS pipeline by operating directly on raw character-level text and employing cross-attention for text-speech alignment, thus eliminating the need for grapheme-to-phoneme (G2P) modules and external aligners. In addition, we introduce context-sharing batch expansion that accelerates loss convergence and stabilizes text-speech alignment. Experimental results demonstrate that SupertonicTTS achieves competitive performance while significantly reducing architectural complexity and computational overhead compared to contemporary TTS models. Audio samples demonstrating the capabilities of SupertonicTTS are available at: https://supertonictts.github.io/.

We develop a portfolio allocation framework that leverages deep learning techniques to address challenges arising from high-dimensional, non-stationary, and low-signal-to-noise market information. Our approach includes a dynamic embedding method that reduces the non-stationary, high-dimensional state space into a lower-dimensional representation. We design a reinforcement learning (RL) framework that integrates generative autoencoders and online meta-learning to dynamically embed market information, enabling the RL agent to focus on the most impactful parts of the state space for portfolio allocation decisions. Empirical analysis based on the top 500 U.S. stocks demonstrates that our framework outperforms common portfolio benchmarks and the predict-then-optimize (PTO) approach using machine learning, particularly during periods of market stress. Traditional factor models do not fully explain this superior performance. The framework's ability to time volatility reduces its market exposure during turbulent times. Ablation studies confirm the robustness of this performance across various reinforcement learning algorithms. Additionally, the embedding and meta-learning techniques effectively manage the complexities of high-dimensional, noisy, and non-stationary financial data, enhancing both portfolio performance and risk management.

One of the primary challenges in brain tumor segmentation arises from the uncertainty of voxels close to tumor boundaries. However, the conventional process of generating ground truth segmentation masks fails to treat such uncertainties properly. Those "hard labels" with 0s and 1s conceptually influenced the majority of prior studies on brain image segmentation. As a result, tumor segmentation is often solved through voxel classification. In this work, we instead view this problem as a voxel-level regression, where the ground truth represents a certainty mapping from any pixel to the border of the tumor. We propose a novel ground truth label transformation, which is based on a signed geodesic transform, to capture the uncertainty in brain tumors' vicinity. We combine this idea with a Focal-like regression L1-loss that enables effective regression learning in high-dimensional output space by appropriately weighting voxels according to their difficulty. We thoroughly conduct an experimental evaluation to validate the components of our proposed method, compare it to a diverse array of state-of-the-art segmentation models, and show that it is architecture-agnostic. The code of our method is made publicly available (https://github.com/Oulu-IMEDS/SiNGR/).

Synthesizing novel 3D models that resemble the input example has long been pursued by graphics artists and machine learning researchers. In this paper, we present Sin3DM, a diffusion model that learns the internal patch distribution from a single 3D textured shape and generates high-quality variations with fine geometry and texture details. Training a diffusion model directly in 3D would induce large memory and computational cost. Therefore, we first compress the input into a lower-dimensional latent space and then train a diffusion model on it. Specifically, we encode the input 3D textured shape into triplane feature maps that represent the signed distance and texture fields of the input. The denoising network of our diffusion model has a limited receptive field to avoid overfitting, and uses triplane-aware 2D convolution blocks to improve the result quality. Aside from randomly generating new samples, our model also facilitates applications such as retargeting, outpainting and local editing. Through extensive qualitative and quantitative evaluation, we show that our method outperforms prior methods in generation quality of 3D shapes.

Understanding and manipulating deformable objects (e.g., ropes and fabrics) is an essential yet challenging task with broad applications. Difficulties come from complex states and dynamics, diverse configurations and high-dimensional action space of deformable objects. Besides, the manipulation tasks usually require multiple steps to accomplish, and greedy policies may easily lead to local optimal states. Existing studies usually tackle this problem using reinforcement learning or imitating expert demonstrations, with limitations in modeling complex states or requiring hand-crafted expert policies. In this paper, we study deformable object manipulation using dense visual affordance, with generalization towards diverse states, and propose a novel kind of foresightful dense affordance, which avoids local optima by estimating states' values for long-term manipulation. We propose a framework for learning this representation, with novel designs such as multi-stage stable learning and efficient self-supervised data collection without experts. Experiments demonstrate the superiority of our proposed foresightful dense affordance. Project page: https://hyperplane-lab.github.io/DeformableAffordance

In this paper, we propose a dimensionless anomaly detection method for multivariate streams. Our method is independent of the unit of measurement for the different stream channels, therefore dimensionless. We first propose the variance norm, a generalisation of Mahalanobis distance to handle infinite-dimensional feature space and singular empirical covariance matrix rigorously. We then combine the variance norm with the path signature, an infinite collection of iterated integrals that provide global features of streams, to propose SigMahaKNN, a method for anomaly detection on (multivariate) streams. We show that SigMahaKNN is invariant to stream reparametrisation, stream concatenation and has a graded discrimination power depending on the truncation level of the path signature. We implement SigMahaKNN as an open-source software, and perform extensive numerical experiments, showing significantly improved anomaly detection on streams compared to isolation forest and local outlier factors in applications ranging from language analysis, hand-writing analysis, ship movement paths analysis and univariate time-series analysis.

We present AnimaX, a feed-forward 3D animation framework that bridges the motion priors of video diffusion models with the controllable structure of skeleton-based animation. Traditional motion synthesis methods are either restricted to fixed skeletal topologies or require costly optimization in high-dimensional deformation spaces. In contrast, AnimaX effectively transfers video-based motion knowledge to the 3D domain, supporting diverse articulated meshes with arbitrary skeletons. Our method represents 3D motion as multi-view, multi-frame 2D pose maps, and enables joint video-pose diffusion conditioned on template renderings and a textual motion prompt. We introduce shared positional encodings and modality-aware embeddings to ensure spatial-temporal alignment between video and pose sequences, effectively transferring video priors to motion generation task. The resulting multi-view pose sequences are triangulated into 3D joint positions and converted into mesh animation via inverse kinematics. Trained on a newly curated dataset of 160,000 rigged sequences, AnimaX achieves state-of-the-art results on VBench in generalization, motion fidelity, and efficiency, offering a scalable solution for category-agnostic 3D animation. Project page: https://anima-x.github.io/{https://anima-x.github.io/}.

This paper describes RETVec, an efficient, resilient, and multilingual text vectorizer designed for neural-based text processing. RETVec combines a novel character encoding with an optional small embedding model to embed words into a 256-dimensional vector space. The RETVec embedding model is pre-trained using pair-wise metric learning to be robust against typos and character-level adversarial attacks. In this paper, we evaluate and compare RETVec to state-of-the-art vectorizers and word embeddings on popular model architectures and datasets. These comparisons demonstrate that RETVec leads to competitive, multilingual models that are significantly more resilient to typos and adversarial text attacks. RETVec is available under the Apache 2 license at https://github.com/google-research/retvec.

We introduce Entropy-Guided Sequence Weighting (EGSW), a novel approach that enhances the exploration-exploitation tradeoff by dynamically assigning weights to generated outputs based on their advantage and entropy for Reinforcement Learning-based Large Language Model fine-tuning. EGSW integrates entropy regularization with advantage-based weighting to balance policy updates, enabling efficient exploration in high-dimensional state spaces. By employing temperature-scaled softmax weighting over sequences, EGSW prioritizing high-reward, high-uncertainty steps while maintaining training stability. Although originally developed to improve Group Relative Policy Optimization (GRPO) during large language model (LLM) fine-tuning, EGSW is generalizable to other reinforcement learning (RL) algorithms and can be implemented in both step-wise and trajectory-wise settings. Empirical evaluations demonstrate that EGSW enhances GRPO reasoning ability, yielding improvements in sample efficiency. Future work will explore the application of EGSW to advanced RL methodologies.

Bimanual manipulation is critical to many robotics applications. In contrast to single-arm manipulation, bimanual manipulation tasks are challenging due to higher-dimensional action spaces. Prior works leverage large amounts of data and primitive actions to address this problem, but may suffer from sample inefficiency and limited generalization across various tasks. To this end, we propose VoxAct-B, a language-conditioned, voxel-based method that leverages Vision Language Models (VLMs) to prioritize key regions within the scene and reconstruct a voxel grid. We provide this voxel grid to our bimanual manipulation policy to learn acting and stabilizing actions. This approach enables more efficient policy learning from voxels and is generalizable to different tasks. In simulation, we show that VoxAct-B outperforms strong baselines on fine-grained bimanual manipulation tasks. Furthermore, we demonstrate VoxAct-B on real-world Open Drawer and Open Jar tasks using two UR5s. Code, data, and videos are available at https://voxact-b.github.io.

I propose a version of quantum mechanics featuring a discrete and finite number of states that is plausibly a model of the real world. The model is based on standard unitary quantum theory of a closed system with a finite-dimensional Hilbert space. Given certain simple conditions on the spectrum of the Hamiltonian, Schr\"odinger evolution is periodic, and it is straightforward to replace continuous time with a discrete version, with the result that the system only visits a discrete and finite set of state vectors. The biggest challenges to the viability of such a model come from cosmological considerations. The theory may have implications for questions of mathematical realism and finitism.

We present Variational Self-Supervised Learning (VSSL), a novel framework that combines variational inference with self-supervised learning to enable efficient, decoder-free representation learning. Unlike traditional VAEs that rely on input reconstruction via a decoder, VSSL symmetrically couples two encoders with Gaussian outputs. A momentum-updated teacher network defines a dynamic, data-dependent prior, while the student encoder produces an approximate posterior from augmented views. The reconstruction term in the ELBO is replaced with a cross-view denoising objective, preserving the analytical tractability of Gaussian KL divergence. We further introduce cosine-based formulations of KL and log-likelihood terms to enhance semantic alignment in high-dimensional latent spaces. Experiments on CIFAR-10, CIFAR-100, and ImageNet-100 show that VSSL achieves competitive or superior performance to leading self-supervised methods, including BYOL and MoCo V3. VSSL offers a scalable, probabilistically grounded approach to learning transferable representations without generative reconstruction, bridging the gap between variational modeling and modern self-supervised techniques.

Hyperbolic geometry is gaining traction in machine learning for its effectiveness at capturing hierarchical structures in real-world data. Hyperbolic spaces, where neighborhoods grow exponentially, offer substantial advantages and consistently deliver state-of-the-art results across diverse applications. However, hyperbolic classifiers often grapple with computational challenges. Methods reliant on Riemannian optimization frequently exhibit sluggishness, stemming from the increased computational demands of operations on Riemannian manifolds. In response to these challenges, we present hyperDT, a novel extension of decision tree algorithms into hyperbolic space. Crucially, hyperDT eliminates the need for computationally intensive Riemannian optimization, numerically unstable exponential and logarithmic maps, or pairwise comparisons between points by leveraging inner products to adapt Euclidean decision tree algorithms to hyperbolic space. Our approach is conceptually straightforward and maintains constant-time decision complexity while mitigating the scalability issues inherent in high-dimensional Euclidean spaces. Building upon hyperDT we introduce hyperRF, a hyperbolic random forest model. Extensive benchmarking across diverse datasets underscores the superior performance of these models, providing a swift, precise, accurate, and user-friendly toolkit for hyperbolic data analysis.

Imbalanced distributions are ubiquitous in real-world data. They create constraints on Deep Neural Networks to represent the minority labels and avoid bias towards majority labels. The extensive body of imbalanced approaches address categorical label spaces but fail to effectively extend to regression problems where the label space is continuous. Local and global correlations among continuous labels provide valuable insights towards effectively modelling relationships in feature space. In this work, we propose ConR, a contrastive regularizer that models global and local label similarities in feature space and prevents the features of minority samples from being collapsed into their majority neighbours. ConR discerns the disagreements between the label space and feature space and imposes a penalty on these disagreements. ConR addresses the continuous nature of label space with two main strategies in a contrastive manner: incorrect proximities are penalized proportionate to the label similarities and the correct ones are encouraged to model local similarities. ConR consolidates essential considerations into a generic, easy-to-integrate, and efficient method that effectively addresses deep imbalanced regression. Moreover, ConR is orthogonal to existing approaches and smoothly extends to uni- and multi-dimensional label spaces. Our comprehensive experiments show that ConR significantly boosts the performance of all the state-of-the-art methods on four large-scale deep imbalanced regression benchmarks. Our code is publicly available in https://github.com/BorealisAI/ConR.

Key information extraction (KIE) from document images requires understanding the contextual and spatial semantics of texts in two-dimensional (2D) space. Many recent studies try to solve the task by developing pre-trained language models focusing on combining visual features from document images with texts and their layout. On the other hand, this paper tackles the problem by going back to the basic: effective combination of text and layout. Specifically, we propose a pre-trained language model, named BROS (BERT Relying On Spatiality), that encodes relative positions of texts in 2D space and learns from unlabeled documents with area-masking strategy. With this optimized training scheme for understanding texts in 2D space, BROS shows comparable or better performance compared to previous methods on four KIE benchmarks (FUNSD, SROIE*, CORD, and SciTSR) without relying on visual features. This paper also reveals two real-world challenges in KIE tasks-(1) minimizing the error from incorrect text ordering and (2) efficient learning from fewer downstream examples-and demonstrates the superiority of BROS over previous methods. Code is available at https://github.com/clovaai/bros.

Vision-based grasping of unknown objects in unstructured environments is a key challenge for autonomous robotic manipulation. A practical grasp synthesis system is required to generate a diverse set of 6-DoF grasps from which a task-relevant grasp can be executed. Although generative models are suitable for learning such complex data distributions, existing models have limitations in grasp quality, long training times, and a lack of flexibility for task-specific generation. In this work, we present GraspLDM- a modular generative framework for 6-DoF grasp synthesis that uses diffusion models as priors in the latent space of a VAE. GraspLDM learns a generative model of object-centric SE(3) grasp poses conditioned on point clouds. GraspLDM's architecture enables us to train task-specific models efficiently by only re-training a small de-noising network in the low-dimensional latent space, as opposed to existing models that need expensive re-training. Our framework provides robust and scalable models on both full and single-view point clouds. GraspLDM models trained with simulation data transfer well to the real world and provide an 80\% success rate for 80 grasp attempts of diverse test objects, improving over existing generative models. We make our implementation available at https://github.com/kuldeepbrd1/graspldm .

The seminal Fast Johnson-Lindenstrauss (Fast JL) transform by Ailon and Chazelle (SICOMP'09) embeds a set of n points in d-dimensional Euclidean space into optimal k=O(varepsilon^{-2} ln n) dimensions, while preserving all pairwise distances to within a factor (1 pm varepsilon). The Fast JL transform supports computing the embedding of a data point in O(d ln d +k ln^2 n) time, where the d ln d term comes from multiplication with a d times d Hadamard matrix and the k ln^2 n term comes from multiplication with a sparse k times d matrix. Despite the Fast JL transform being more than a decade old, it is one of the fastest dimensionality reduction techniques for many tradeoffs between varepsilon, d and n. In this work, we give a surprising new analysis of the Fast JL transform, showing that the k ln^2 n term in the embedding time can be improved to (k ln^2 n)/alpha for an alpha = Omega(min{varepsilon^{-1}ln(1/varepsilon), ln n}). The improvement follows by using an even sparser matrix. We also complement our improved analysis with a lower bound showing that our new analysis is in fact tight.

Latent Diffusion Models (LDMs) enable high-quality image synthesis while avoiding excessive compute demands by training a diffusion model in a compressed lower-dimensional latent space. Here, we apply the LDM paradigm to high-resolution video generation, a particularly resource-intensive task. We first pre-train an LDM on images only; then, we turn the image generator into a video generator by introducing a temporal dimension to the latent space diffusion model and fine-tuning on encoded image sequences, i.e., videos. Similarly, we temporally align diffusion model upsamplers, turning them into temporally consistent video super resolution models. We focus on two relevant real-world applications: Simulation of in-the-wild driving data and creative content creation with text-to-video modeling. In particular, we validate our Video LDM on real driving videos of resolution 512 x 1024, achieving state-of-the-art performance. Furthermore, our approach can easily leverage off-the-shelf pre-trained image LDMs, as we only need to train a temporal alignment model in that case. Doing so, we turn the publicly available, state-of-the-art text-to-image LDM Stable Diffusion into an efficient and expressive text-to-video model with resolution up to 1280 x 2048. We show that the temporal layers trained in this way generalize to different fine-tuned text-to-image LDMs. Utilizing this property, we show the first results for personalized text-to-video generation, opening exciting directions for future content creation. Project page: https://research.nvidia.com/labs/toronto-ai/VideoLDM/

Bimanual robotic manipulation is a long-standing challenge of embodied intelligence due to its characteristics of dual-arm spatial-temporal coordination and high-dimensional action spaces. Previous studies rely on pre-defined action taxonomies or direct teleoperation to alleviate or circumvent these issues, often making them lack simplicity, versatility and scalability. Differently, we believe that the most effective and efficient way for teaching bimanual manipulation is learning from human demonstrated videos, where rich features such as spatial-temporal positions, dynamic postures, interaction states and dexterous transitions are available almost for free. In this work, we propose the YOTO (You Only Teach Once), which can extract and then inject patterns of bimanual actions from as few as a single binocular observation of hand movements, and teach dual robot arms various complex tasks. Furthermore, based on keyframes-based motion trajectories, we devise a subtle solution for rapidly generating training demonstrations with diverse variations of manipulated objects and their locations. These data can then be used to learn a customized bimanual diffusion policy (BiDP) across diverse scenes. In experiments, YOTO achieves impressive performance in mimicking 5 intricate long-horizon bimanual tasks, possesses strong generalization under different visual and spatial conditions, and outperforms existing visuomotor imitation learning methods in accuracy and efficiency. Our project link is https://hnuzhy.github.io/projects/YOTO.

Machine learning models often learn latent embedding representations that capture the domain semantics of their training data. These embedding representations are valuable for interpreting trained models, building new models, and analyzing new datasets. However, interpreting and using embeddings can be challenging due to their opaqueness, high dimensionality, and the large size of modern datasets. To tackle these challenges, we present WizMap, an interactive visualization tool to help researchers and practitioners easily explore large embeddings. With a novel multi-resolution embedding summarization method and a familiar map-like interaction design, WizMap enables users to navigate and interpret embedding spaces with ease. Leveraging modern web technologies such as WebGL and Web Workers, WizMap scales to millions of embedding points directly in users' web browsers and computational notebooks without the need for dedicated backend servers. WizMap is open-source and available at the following public demo link: https://poloclub.github.io/wizmap.

Recent self-supervised learning approaches focus on using a few thousand data points to learn policies for high-level, low-dimensional action spaces. However, scaling this framework for high-dimensional control require either scaling up the data collection efforts or using a clever sampling strategy for training. We present a novel approach - Curriculum Accelerated Self-Supervised Learning (CASSL) - to train policies that map visual information to high-level, higher- dimensional action spaces. CASSL orders the sampling of training data based on control dimensions: the learning and sampling are focused on few control parameters before other parameters. The right curriculum for learning is suggested by variance-based global sensitivity analysis of the control space. We apply our CASSL framework to learning how to grasp using an adaptive, underactuated multi-fingered gripper, a challenging system to control. Our experimental results indicate that CASSL provides significant improvement and generalization compared to baseline methods such as staged curriculum learning (8% increase) and complete end-to-end learning with random exploration (14% improvement) tested on a set of novel objects.

Understanding how language model performance varies with scale is critical to benchmark and algorithm development. Scaling laws are one approach to building this understanding, but the requirement of training models across many different scales has limited their use. We propose an alternative, observational approach that bypasses model training and instead builds scaling laws from ~80 publically available models. Building a single scaling law from multiple model families is challenging due to large variations in their training compute efficiencies and capabilities. However, we show that these variations are consistent with a simple, generalized scaling law where language model performance is a function of a low-dimensional capability space, and model families only vary in their efficiency in converting training compute to capabilities. Using this approach, we show the surprising predictability of complex scaling phenomena: we show that several emergent phenomena follow a smooth, sigmoidal behavior and are predictable from small models; we show that the agent performance of models such as GPT-4 can be precisely predicted from simpler non-agentic benchmarks; and we show how to predict the impact of post-training interventions like Chain-of-Thought and Self-Consistency as language model capabilities continue to improve.

Problems involving geometric data arise in a variety of fields, including computer vision, robotics, chemistry, and physics. Such data can take numerous forms, such as points, direction vectors, planes, or transformations, but to date there is no single architecture that can be applied to such a wide variety of geometric types while respecting their symmetries. In this paper we introduce the Geometric Algebra Transformer (GATr), a general-purpose architecture for geometric data. GATr represents inputs, outputs, and hidden states in the projective geometric algebra, which offers an efficient 16-dimensional vector space representation of common geometric objects as well as operators acting on them. GATr is equivariant with respect to E(3), the symmetry group of 3D Euclidean space. As a transformer, GATr is scalable, expressive, and versatile. In experiments with n-body modeling and robotic planning, GATr shows strong improvements over non-geometric baselines.

This paper introduces Sparsified Late Interaction for Multi-vector (SLIM) retrieval with inverted indexes. Multi-vector retrieval methods have demonstrated their effectiveness on various retrieval datasets, and among them, ColBERT is the most established method based on the late interaction of contextualized token embeddings of pre-trained language models. However, efficient ColBERT implementations require complex engineering and cannot take advantage of off-the-shelf search libraries, impeding their practical use. To address this issue, SLIM first maps each contextualized token vector to a sparse, high-dimensional lexical space before performing late interaction between these sparse token embeddings. We then introduce an efficient two-stage retrieval architecture that includes inverted index retrieval followed by a score refinement module to approximate the sparsified late interaction, which is fully compatible with off-the-shelf lexical search libraries such as Lucene. SLIM achieves competitive accuracy on MS MARCO Passages and BEIR compared to ColBERT while being much smaller and faster on CPUs. To our knowledge, we are the first to explore using sparse token representations for multi-vector retrieval. Source code and data are integrated into the Pyserini IR toolkit.

Mixture of Experts (MoE) has emerged as a pivotal architectural paradigm for efficient scaling of Large Language Models (LLMs), operating through selective activation of parameter subsets for each input token. Nevertheless, conventional MoE architectures encounter substantial challenges, including excessive memory utilization and communication overhead during training and inference, primarily attributable to the proliferation of expert modules. In this paper, we introduce Mixture of Latent Experts (MoLE), a novel parameterization methodology that facilitates the mapping of specific experts into a shared latent space. Specifically, all expert operations are systematically decomposed into two principal components: a shared projection into a lower-dimensional latent space, followed by expert-specific transformations with significantly reduced parametric complexity. This factorized approach substantially diminishes parameter count and computational requirements. Beyond the pretraining implementation of the MoLE architecture, we also establish a rigorous mathematical framework for transforming pre-trained MoE models into the MoLE architecture, characterizing the sufficient conditions for optimal factorization and developing a systematic two-phase algorithm for this conversion process. Our comprehensive theoretical analysis demonstrates that MoLE significantly enhances computational efficiency across multiple dimensions while preserving model representational capacity. Empirical evaluations corroborate our theoretical findings, confirming that MoLE achieves performance comparable to standard MoE implementations while substantially reducing resource requirements.

While the activations of neurons in deep neural networks usually do not have a simple human-understandable interpretation, sparse autoencoders (SAEs) can be used to transform these activations into a higher-dimensional latent space which may be more easily interpretable. However, these SAEs can have millions of distinct latent features, making it infeasible for humans to manually interpret each one. In this work, we build an open-source automated pipeline to generate and evaluate natural language explanations for SAE features using LLMs. We test our framework on SAEs of varying sizes, activation functions, and losses, trained on two different open-weight LLMs. We introduce five new techniques to score the quality of explanations that are cheaper to run than the previous state of the art. One of these techniques, intervention scoring, evaluates the interpretability of the effects of intervening on a feature, which we find explains features that are not recalled by existing methods. We propose guidelines for generating better explanations that remain valid for a broader set of activating contexts, and discuss pitfalls with existing scoring techniques. We use our explanations to measure the semantic similarity of independently trained SAEs, and find that SAEs trained on nearby layers of the residual stream are highly similar. Our large-scale analysis confirms that SAE latents are indeed much more interpretable than neurons, even when neurons are sparsified using top-k postprocessing. Our code is available at https://github.com/EleutherAI/sae-auto-interp, and our explanations are available at https://huggingface.co/datasets/EleutherAI/auto_interp_explanations.

Robotic systems that aspire to operate in uninstrumented real-world environments must perceive the world directly via onboard sensing. Vision-based learning systems aim to eliminate the need for environment instrumentation by building an implicit understanding of the world based on raw pixels, but navigating the contact-rich high-dimensional search space from solely sparse visual reward signals significantly exacerbates the challenge of exploration. The applicability of such systems is thus typically restricted to simulated or heavily engineered environments since agent exploration in the real-world without the guidance of explicit state estimation and dense rewards can lead to unsafe behavior and safety faults that are catastrophic. In this study, we isolate the root causes behind these limitations to develop a system, called MoDem-V2, capable of learning contact-rich manipulation directly in the uninstrumented real world. Building on the latest algorithmic advancements in model-based reinforcement learning (MBRL), demo-bootstrapping, and effective exploration, MoDem-V2 can acquire contact-rich dexterous manipulation skills directly in the real world. We identify key ingredients for leveraging demonstrations in model learning while respecting real-world safety considerations -- exploration centering, agency handover, and actor-critic ensembles. We empirically demonstrate the contribution of these ingredients in four complex visuo-motor manipulation problems in both simulation and the real world. To the best of our knowledge, our work presents the first successful system for demonstration-augmented visual MBRL trained directly in the real world. Visit https://sites.google.com/view/modem-v2 for videos and more details.

Recent advances in generative modeling have enabled the generation of high-quality synthetic data that is applicable in a variety of domains, including face recognition. Here, state-of-the-art generative models typically rely on conditioning and fine-tuning of powerful pretrained diffusion models to facilitate the synthesis of realistic images of a desired identity. Yet, these models often do not consider the identity of subjects during training, leading to poor consistency between generated and intended identities. In contrast, methods that employ identity-based training objectives tend to overfit on various aspects of the identity, and in turn, lower the diversity of images that can be generated. To address these issues, we present in this paper a novel generative diffusion-based framework, called ID-Booth. ID-Booth consists of a denoising network responsible for data generation, a variational auto-encoder for mapping images to and from a lower-dimensional latent space and a text encoder that allows for prompt-based control over the generation procedure. The framework utilizes a novel triplet identity training objective and enables identity-consistent image generation while retaining the synthesis capabilities of pretrained diffusion models. Experiments with a state-of-the-art latent diffusion model and diverse prompts reveal that our method facilitates better intra-identity consistency and inter-identity separability than competing methods, while achieving higher image diversity. In turn, the produced data allows for effective augmentation of small-scale datasets and training of better-performing recognition models in a privacy-preserving manner. The source code for the ID-Booth framework is publicly available at https://github.com/dariant/ID-Booth.

Recent advances in neural surrogate modeling offer the potential for transformative innovations in applications such as automotive aerodynamics. Yet, industrial-scale problems often involve volumetric meshes with cell counts reaching the 100 millions, presenting major scalability challenges. Complex geometries further complicate modeling through intricate surface-volume interactions, while quantities such as vorticity are highly nonlinear and must satisfy strict divergence-free constraints. To address these requirements, we introduce AB-UPT as a novel modeling scheme for building neural surrogates for CFD simulations. AB-UPT is designed to: (i) decouple geometry encoding and prediction tasks via multi-branch operators; (ii) enable scalability to high-resolution outputs via neural simulation in a low-dimensional latent space, coupled with anchored neural field decoders to predict high-fidelity outputs; (iii) enforce physics consistency by a novel divergence-free formulation. We show that AB-UPT yields state-of-the-art predictive accuracy of surface and volume fields on automotive CFD simulations ranging from 33 thousand up to 150 million mesh cells. Furthermore, our anchored neural field architecture enables the enforcement of hard physical constraints on the physics predictions without degradation in performance, exemplified by modeling divergence-free vorticity fields. Notably, the proposed models can be trained on a single GPU in less than a day and predict industry-standard surface and volume fields within seconds. Additionally, we show that the flexible design of our method enables neural simulation from a CAD geometry alone, omitting the need for costly CFD meshing procedures.

Large Language Models (LLMs) often generate inconsistent responses when prompted with semantically equivalent paraphrased inputs. Recently, activation steering, a technique that modulates LLMs' behaviours by adjusting their latent representations during inference time, has been explored to improve the semantic consistency of LLMs. However, these methods typically operate at the model component level, such as layer hidden states or attention head outputs. They face a challenge due to the ``polysemanticity issue'', where the model components of LLMs typically encode multiple entangled features, making precise steering difficult. To address this challenge, we drill down to feature-level representations and propose LF-Steering, a novel activation steering approach to precisely identify latent feature representations responsible for semantic inconsistency. More specifically, our method maps the hidden states of the relevant transformer layer into a sparsely activated, high-dimensional feature space based on a sparse autoencoder (SAE), ensuring model steering based on decoupled feature representations with minimal interference. Comprehensive experiments on NLU and NLG datasets demonstrate the effectiveness of our method in enhancing semantic consistency, resulting in significant performance gains for various NLU and NLG tasks.

In various video-language learning tasks, the challenge of achieving cross-modality alignment with multi-grained data persists. We propose a method to tackle this challenge from two crucial perspectives: data and modeling. Given the absence of a multi-grained video-text pretraining dataset, we introduce a Granularity EXpansion (GEX) method with Integration and Compression operations to expand the granularity of a single-grained dataset. To better model multi-grained data, we introduce an Iterative Approximation Module (IAM), which embeds multi-grained videos and texts into a unified, low-dimensional semantic space while preserving essential information for cross-modal alignment. Furthermore, GEXIA is highly scalable with no restrictions on the number of video-text granularities for alignment. We evaluate our work on three categories of video tasks across seven benchmark datasets, showcasing state-of-the-art or comparable performance. Remarkably, our model excels in tasks involving long-form video understanding, even though the pretraining dataset only contains short video clips.

Deep neural networks have become a standard building block for designing models that can perform multiple dense computer vision tasks such as depth estimation and semantic segmentation thanks to their ability to capture complex correlations in high dimensional feature space across tasks. However, the cross-task correlations that are learned in the unstructured feature space can be extremely noisy and susceptible to overfitting, consequently hurting performance. We propose to address this problem by introducing a structured 3D-aware regularizer which interfaces multiple tasks through the projection of features extracted from an image encoder to a shared 3D feature space and decodes them into their task output space through differentiable rendering. We show that the proposed method is architecture agnostic and can be plugged into various prior multi-task backbones to improve their performance; as we evidence using standard benchmarks NYUv2 and PASCAL-Context.

Text-guided diffusion models (TDMs) are widely applied but can fail unexpectedly. Common failures include: (i) natural-looking text prompts generating images with the wrong content, or (ii) different random samples of the latent variables that generate vastly different, and even unrelated, outputs despite being conditioned on the same text prompt. In this work, we aim to study and understand the failure modes of TDMs in more detail. To achieve this, we propose SAGE, the first adversarial search method on TDMs that systematically explores the discrete prompt space and the high-dimensional latent space, to automatically discover undesirable behaviors and failure cases in image generation. We use image classifiers as surrogate loss functions during searching, and employ human inspections to validate the identified failures. For the first time, our method enables efficient exploration of both the discrete and intricate human language space and the challenging latent space, overcoming the gradient vanishing problem. Then, we demonstrate the effectiveness of SAGE on five widely used generative models and reveal four typical failure modes: (1) We find a variety of natural text prompts that generate images failing to capture the semantics of input texts. We further discuss the underlying causes and potential solutions based on the results. (2) We find regions in the latent space that lead to distorted images independent of the text prompt, suggesting that parts of the latent space are not well-structured. (3) We also find latent samples that result in natural-looking images unrelated to the text prompt, implying a possible misalignment between the latent and prompt spaces. (4) By appending a single adversarial token embedding to any input prompts, we can generate a variety of specified target objects. Project page: https://sage-diffusion.github.io/

The effectiveness and efficiency of 5G software stack vulnerability and unintended behavior detection are essential for 5G assurance, especially for its applications in critical infrastructures. Scalability and automation are the main challenges in testing approaches and cybersecurity research. In this paper, we propose an innovative approach for automatically detecting vulnerabilities, unintended emergent behaviors, and performance degradation in 5G stacks via run-time profiling documents corresponding to fuzz testing in code repositories. Piloting on srsRAN, we map the run-time profiling via Logging Information (LogInfo) generated by fuzzing test to a high dimensional metric space first and then construct feature spaces based on their timestamp information. Lastly, we further leverage machine learning-based classification algorithms, including Logistic Regression, K-Nearest Neighbors, and Random Forest to categorize the impacts on performance and security attributes. The performance of the proposed approach has high accuracy, ranging from 93.4 % to 95.9 % , in detecting the fuzzing impacts. In addition, the proof of concept could identify and prioritize real-time vulnerabilities on 5G infrastructures and critical applications in various verticals.

Systems for language-guided human-robot interaction must satisfy two key desiderata for broad adoption: adaptivity and learning efficiency. Unfortunately, existing instruction-following agents cannot adapt, lacking the ability to incorporate online natural language supervision, and even if they could, require hundreds of demonstrations to learn even simple policies. In this work, we address these problems by presenting Language-Informed Latent Actions with Corrections (LILAC), a framework for incorporating and adapting to natural language corrections - "to the right," or "no, towards the book" - online, during execution. We explore rich manipulation domains within a shared autonomy paradigm. Instead of discrete turn-taking between a human and robot, LILAC splits agency between the human and robot: language is an input to a learned model that produces a meaningful, low-dimensional control space that the human can use to guide the robot. Each real-time correction refines the human's control space, enabling precise, extended behaviors - with the added benefit of requiring only a handful of demonstrations to learn. We evaluate our approach via a user study where users work with a Franka Emika Panda manipulator to complete complex manipulation tasks. Compared to existing learned baselines covering both open-loop instruction following and single-turn shared autonomy, we show that our corrections-aware approach obtains higher task completion rates, and is subjectively preferred by users because of its reliability, precision, and ease of use.

Recognizing and categorizing human actions is an important task with applications in various fields such as human-robot interaction, video analysis, surveillance, video retrieval, health care system and entertainment industry. This thesis presents a novel computational approach for human action recognition through different implementations of multi-layer architectures based on artificial neural networks. Each system level development is designed to solve different aspects of the action recognition problem including online real-time processing, action segmentation and the involvement of objects. The analysis of the experimental results are illustrated and described in six articles. The proposed action recognition architecture of this thesis is composed of several processing layers including a preprocessing layer, an ordered vector representation layer and three layers of neural networks. It utilizes self-organizing neural networks such as Kohonen feature maps and growing grids as the main neural network layers. Thus the architecture presents a biological plausible approach with certain features such as topographic organization of the neurons, lateral interactions, semi-supervised learning and the ability to represent high dimensional input space in lower dimensional maps. For each level of development the system is trained with the input data consisting of consecutive 3D body postures and tested with generalized input data that the system has never met before. The experimental results of different system level developments show that the system performs well with quite high accuracy for recognizing human actions.

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to reduce the dimensionality of data characterized by a large Kolmogorov n-width, they typically lack a straightforward mapping from the latent space to the high-dimensional physical space. Moreover, the realized latent variables are often hard to interpret. Therefore, many of these methods are often dismissed in the reduced order modeling of dynamical systems governed by the partial differential equations (PDEs). Accordingly, we propose an auto-encoder type nonlinear dimensionality reduction algorithm. The unsupervised learning problem trains a diffeomorphic spatio-temporal grid, that registers the output sequence of the PDEs on a non-uniform parameter/time-varying grid, such that the Kolmogorov n-width of the mapped data on the learned grid is minimized. We demonstrate the efficacy and interpretability of our approach to separate convection/advection from diffusion/scaling on various manufactured and physical systems.

Latent generative modeling, where a pretrained autoencoder maps pixels into a latent space for the diffusion process, has become the standard strategy for Diffusion Transformers (DiT); however, the autoencoder component has barely evolved. Most DiTs continue to rely on the original VAE encoder, which introduces several limitations: outdated backbones that compromise architectural simplicity, low-dimensional latent spaces that restrict information capacity, and weak representations that result from purely reconstruction-based training and ultimately limit generative quality. In this work, we explore replacing the VAE with pretrained representation encoders (e.g., DINO, SigLIP, MAE) paired with trained decoders, forming what we term Representation Autoencoders (RAEs). These models provide both high-quality reconstructions and semantically rich latent spaces, while allowing for a scalable transformer-based architecture. Since these latent spaces are typically high-dimensional, a key challenge is enabling diffusion transformers to operate effectively within them. We analyze the sources of this difficulty, propose theoretically motivated solutions, and validate them empirically. Our approach achieves faster convergence without auxiliary representation alignment losses. Using a DiT variant equipped with a lightweight, wide DDT head, we achieve strong image generation results on ImageNet: 1.51 FID at 256x256 (no guidance) and 1.13 at both 256x256 and 512x512 (with guidance). RAE offers clear advantages and should be the new default for diffusion transformer training.

This paper introduces Diffusion Policy, a new way of generating robot behavior by representing a robot's visuomotor policy as a conditional denoising diffusion process. We benchmark Diffusion Policy across 11 different tasks from 4 different robot manipulation benchmarks and find that it consistently outperforms existing state-of-the-art robot learning methods with an average improvement of 46.9%. Diffusion Policy learns the gradient of the action-distribution score function and iteratively optimizes with respect to this gradient field during inference via a series of stochastic Langevin dynamics steps. We find that the diffusion formulation yields powerful advantages when used for robot policies, including gracefully handling multimodal action distributions, being suitable for high-dimensional action spaces, and exhibiting impressive training stability. To fully unlock the potential of diffusion models for visuomotor policy learning on physical robots, this paper presents a set of key technical contributions including the incorporation of receding horizon control, visual conditioning, and the time-series diffusion transformer. We hope this work will help motivate a new generation of policy learning techniques that are able to leverage the powerful generative modeling capabilities of diffusion models. Code, data, and training details will be publicly available.

We present DIMO, a generative approach capable of generating diverse 3D motions for arbitrary objects from a single image. The core idea of our work is to leverage the rich priors in well-trained video models to extract the common motion patterns and then embed them into a shared low-dimensional latent space. Specifically, we first generate multiple videos of the same object with diverse motions. We then embed each motion into a latent vector and train a shared motion decoder to learn the distribution of motions represented by a structured and compact motion representation, i.e., neural key point trajectories. The canonical 3D Gaussians are then driven by these key points and fused to model the geometry and appearance. During inference time with learned latent space, we can instantly sample diverse 3D motions in a single-forward pass and support several interesting applications including 3D motion interpolation and language-guided motion generation. Our project page is available at https://linzhanm.github.io/dimo.

A diffusion probabilistic model (DPM), which constructs a forward diffusion process by gradually adding noise to data points and learns the reverse denoising process to generate new samples, has been shown to handle complex data distribution. Despite its recent success in image synthesis, applying DPMs to video generation is still challenging due to high-dimensional data spaces. Previous methods usually adopt a standard diffusion process, where frames in the same video clip are destroyed with independent noises, ignoring the content redundancy and temporal correlation. This work presents a decomposed diffusion process via resolving the per-frame noise into a base noise that is shared among all frames and a residual noise that varies along the time axis. The denoising pipeline employs two jointly-learned networks to match the noise decomposition accordingly. Experiments on various datasets confirm that our approach, termed as VideoFusion, surpasses both GAN-based and diffusion-based alternatives in high-quality video generation. We further show that our decomposed formulation can benefit from pre-trained image diffusion models and well-support text-conditioned video creation.

Molecule generation with desired properties has grown immensely in popularity by disruptively changing the way scientists design molecular structures and providing support for chemical and materials design. However, despite the promising outcome, previous machine learning-based deep generative models suffer from a reliance on complex, task-specific fine-tuning, limited dimensional latent spaces, or the quality of expert rules. In this work, we propose MolGen, a pre-trained molecular language model that effectively learns and shares knowledge across multiple generation tasks and domains. Specifically, we pre-train MolGen with the chemical language SELFIES on more than 100 million unlabelled molecules. We further propose multi-task molecular prefix tuning across several molecular generation tasks and different molecular domains (synthetic & natural products) with a self-feedback mechanism. Extensive experiments show that MolGen can obtain superior performances on well-known molecular generation benchmark datasets. The further analysis illustrates that MolGen can accurately capture the distribution of molecules, implicitly learn their structural characteristics, and efficiently explore the chemical space with the guidance of multi-task molecular prefix tuning. Codes, datasets, and the pre-trained model will be available in https://github.com/zjunlp/MolGen.

In computer vision, a larger effective receptive field (ERF) is associated with better performance. While attention natively supports global context, its quadratic complexity limits its applicability to tasks that benefit from high-resolution input. In this work, we extend Hyena, a convolution-based attention replacement, from causal sequences to bidirectional data and two-dimensional image space. We scale Hyena's convolution kernels beyond the feature map size, up to 191times191, to maximize ERF while maintaining sub-quadratic complexity in the number of pixels. We integrate our two-dimensional Hyena, HyenaPixel, and bidirectional Hyena into the MetaFormer framework. For image categorization, HyenaPixel and bidirectional Hyena achieve a competitive ImageNet-1k top-1 accuracy of 84.9% and 85.2%, respectively, with no additional training data, while outperforming other convolutional and large-kernel networks. Combining HyenaPixel with attention further improves accuracy. We attribute the success of bidirectional Hyena to learning the data-dependent geometric arrangement of pixels without a fixed neighborhood definition. Experimental results on downstream tasks suggest that HyenaPixel with large filters and a fixed neighborhood leads to better localization performance.

Leveraging human motion data to impart robots with versatile manipulation skills has emerged as a promising paradigm in robotic manipulation. Nevertheless, translating multi-source human hand motions into feasible robot behaviors remains challenging, particularly for robots equipped with multi-fingered dexterous hands characterized by complex, high-dimensional action spaces. Moreover, existing approaches often struggle to produce policies capable of adapting to diverse environmental conditions. In this paper, we introduce HERMES, a human-to-robot learning framework for mobile bimanual dexterous manipulation. First, HERMES formulates a unified reinforcement learning approach capable of seamlessly transforming heterogeneous human hand motions from multiple sources into physically plausible robotic behaviors. Subsequently, to mitigate the sim2real gap, we devise an end-to-end, depth image-based sim2real transfer method for improved generalization to real-world scenarios. Furthermore, to enable autonomous operation in varied and unstructured environments, we augment the navigation foundation model with a closed-loop Perspective-n-Point (PnP) localization mechanism, ensuring precise alignment of visual goals and effectively bridging autonomous navigation and dexterous manipulation. Extensive experimental results demonstrate that HERMES consistently exhibits generalizable behaviors across diverse, in-the-wild scenarios, successfully performing numerous complex mobile bimanual dexterous manipulation tasks. Project Page:https://gemcollector.github.io/HERMES/.

Due to domain shift, machine learning systems typically fail to generalize well to domains different from those of training data, which is what domain generalization (DG) aims to address. Although various DG methods have been developed, most of them lack interpretability and require domain labels that are not available in many real-world scenarios. This paper presents a novel DG method, called HMOE: Hypernetwork-based Mixture of Experts (MoE), which does not rely on domain labels and is more interpretable. MoE proves effective in identifying heterogeneous patterns in data. For the DG problem, heterogeneity arises exactly from domain shift. HMOE uses hypernetworks taking vectors as input to generate experts' weights, which allows experts to share useful meta-knowledge and enables exploring experts' similarities in a low-dimensional vector space. We compare HMOE with other DG algorithms under a fair and unified benchmark-DomainBed. Our extensive experiments show that HMOE can divide mixed-domain data into distinct clusters that are surprisingly more consistent with human intuition than original domain labels. Compared to other DG methods, HMOE shows competitive performance and achieves SOTA results in some cases.

Parameter-efficient fine-tuning (PEFT) has emerged as a practical solution for adapting large language models (LLMs) to custom datasets with significantly reduced computational cost. When carrying out PEFT under collaborative learning scenarios (e.g., federated learning), it is often required to exchange model updates (or gradients) across parties. These gradients, even with limited dimensions, can cause severe breach of data privacy. Recent works have shown that both contextual prefixes and personally identifiable information (PII) can be exposed through gradients. However, simultaneously and accurately recovering both components from the same training instance remains infeasible due to the following challenges: 1) limited number of PEFT parameters; 2) high-dimensional token spaces; and 3) large batch sizes. We propose ReCIT, a novel privacy attack that addresses all challenges, and achieves recovery of full private data from PEFT gradients with high fidelity. Specifically, ReCIT proposes to enhance the memorization capability of the pre-trained model through malicious fine-tuning with Personal Notes; ReCIT also proposes a novel filter-based token extraction technique and a token pairing mechanism, to accurately reconstruct tokens from the training sequences with large batch sizes. Extensive evaluations show that ReCIT consistently outperforms state-of-the-art gradient inversion and memorization-based attacks across different PEFT paradigms. It achieves up to 10times higher PII recovery rates and remains effective across varying batch sizes, especially in settings where prefix reconstruction is intractable for conventional approaches. These findings highlight an urgent need to reassess the privacy guarantees of PEFT, especially in decentralized or shared training environments.

Long-horizon contact-rich tasks are challenging to learn with reinforcement learning, due to ineffective exploration of high-dimensional state spaces with sparse rewards. The learning process often gets stuck in local optimum and demands task-specific reward fine-tuning for complex scenarios. In this work, we propose a structured framework that leverages privileged actions with curriculum learning, enabling the policy to efficiently acquire long-horizon skills without relying on extensive reward engineering or reference trajectories. Specifically, we use privileged actions in simulation with a general training procedure that would be infeasible to implement in real-world scenarios. These privileges include relaxed constraints and virtual forces that enhance interaction and exploration with objects. Our results successfully achieve complex multi-stage long-horizon tasks that naturally combine non-prehensile manipulation with grasping to lift objects from non-graspable poses. We demonstrate generality by maintaining a parsimonious reward structure and showing convergence to diverse and robust behaviors across various environments. Additionally, real-world experiments further confirm that the skills acquired using our approach are transferable to real-world environments, exhibiting robust and intricate performance. Our approach outperforms state-of-the-art methods in these tasks, converging to solutions where others fail.

In recent years, imitation learning has made progress in the field of robotic manipulation. However, it still faces challenges when dealing with complex long-horizon deformable object tasks, such as high-dimensional state spaces, complex dynamics, and multimodal action distributions. Traditional imitation learning methods often require a large amount of data and encounter distributional shifts and accumulative errors in these tasks. To address these issues, we propose a data-efficient general learning framework (DeformPAM) based on preference learning and reward-guided action selection. DeformPAM decomposes long-horizon tasks into multiple action primitives, utilizes 3D point cloud inputs and diffusion models to model action distributions, and trains an implicit reward model using human preference data. During the inference phase, the reward model scores multiple candidate actions, selecting the optimal action for execution, thereby reducing the occurrence of anomalous actions and improving task completion quality. Experiments conducted on three challenging real-world long-horizon deformable object manipulation tasks demonstrate the effectiveness of this method. Results show that DeformPAM improves both task completion quality and efficiency compared to baseline methods even with limited data. Code and data will be available at https://deform-pam.robotflow.ai.

Large Language Models (LLMs) have the potential to automate reward engineering by leveraging their broad domain knowledge across various tasks. However, they often need many iterations of trial-and-error to generate effective reward functions. This process is costly because evaluating every sampled reward function requires completing the full policy optimization process for each function. In this paper, we introduce an LLM-driven reward generation framework that is able to produce state-of-the-art policies on the challenging Bi-DexHands benchmark with 20x fewer reward function samples than the prior state-of-the-art work. Our key insight is that we reduce the problem of generating task-specific rewards to the problem of coarsely estimating task progress. Our two-step solution leverages the task domain knowledge and the code synthesis abilities of LLMs to author progress functions that estimate task progress from a given state. Then, we use this notion of progress to discretize states, and generate count-based intrinsic rewards using the low-dimensional state space. We show that the combination of LLM-generated progress functions and count-based intrinsic rewards is essential for our performance gains, while alternatives such as generic hash-based counts or using progress directly as a reward function fall short.

Creating high-fidelity 3D human head avatars is crucial for applications in VR/AR, telepresence, digital human interfaces, and film production. Recent advances have leveraged morphable face models to generate animated head avatars from easily accessible data, representing varying identities and expressions within a low-dimensional parametric space. However, existing methods often struggle with modeling complex appearance details, e.g., hairstyles and accessories, and suffer from low rendering quality and efficiency. This paper introduces a novel approach, 3D Gaussian Parametric Head Model, which employs 3D Gaussians to accurately represent the complexities of the human head, allowing precise control over both identity and expression. Additionally, it enables seamless face portrait interpolation and the reconstruction of detailed head avatars from a single image. Unlike previous methods, the Gaussian model can handle intricate details, enabling realistic representations of varying appearances and complex expressions. Furthermore, this paper presents a well-designed training framework to ensure smooth convergence, providing a guarantee for learning the rich content. Our method achieves high-quality, photo-realistic rendering with real-time efficiency, making it a valuable contribution to the field of parametric head models.

Neural Radiance Fields (NeRFs) have achieved great success in the past few years. However, most current methods still require intensive resources due to ray marching-based rendering. To construct urban-level radiance fields efficiently, we design Deformable Neural Mesh Primitive~(DNMP), and propose to parameterize the entire scene with such primitives. The DNMP is a flexible and compact neural variant of classic mesh representation, which enjoys both the efficiency of rasterization-based rendering and the powerful neural representation capability for photo-realistic image synthesis. Specifically, a DNMP consists of a set of connected deformable mesh vertices with paired vertex features to parameterize the geometry and radiance information of a local area. To constrain the degree of freedom for optimization and lower the storage budgets, we enforce the shape of each primitive to be decoded from a relatively low-dimensional latent space. The rendering colors are decoded from the vertex features (interpolated with rasterization) by a view-dependent MLP. The DNMP provides a new paradigm for urban-level scene representation with appealing properties: (1) High-quality rendering. Our method achieves leading performance for novel view synthesis in urban scenarios. (2) Low computational costs. Our representation enables fast rendering (2.07ms/1k pixels) and low peak memory usage (110MB/1k pixels). We also present a lightweight version that can run 33times faster than vanilla NeRFs, and comparable to the highly-optimized Instant-NGP (0.61 vs 0.71ms/1k pixels). Project page: https://dnmp.github.io/{https://dnmp.github.io/}.

Recent advancements in generative modeling have made it possible to generate high-quality content from context information, but a key question remains: how to teach models to know when to generate content? To answer this question, this study proposes a novel event generative model that draws its statistical intuition from marked temporal point processes, and offers a clean, flexible, and computationally efficient solution for a wide range of applications involving multi-dimensional marks. We aim to capture the distribution of the point process without explicitly specifying the conditional intensity or probability density. Instead, we use a conditional generator that takes the history of events as input and generates the high-quality subsequent event that is likely to occur given the prior observations. The proposed framework offers a host of benefits, including exceptional efficiency in learning the model and generating samples, as well as considerable representational power to capture intricate dynamics in multi- or even high-dimensional event space. Our numerical results demonstrate superior performance compared to other state-of-the-art baselines.

We study the design of sample-efficient algorithms for reinforcement learning in the presence of rich, high-dimensional observations, formalized via the Block MDP problem. Existing algorithms suffer from either 1) computational intractability, 2) strong statistical assumptions that are not necessarily satisfied in practice, or 3) suboptimal sample complexity. We address these issues by providing the first computationally efficient algorithm that attains rate-optimal sample complexity with respect to the desired accuracy level, with minimal statistical assumptions. Our algorithm, MusIK, combines systematic exploration with representation learning based on multi-step inverse kinematics, a learning objective in which the aim is to predict the learner's own action from the current observation and observations in the (potentially distant) future. MusIK is simple and flexible, and can efficiently take advantage of general-purpose function approximation. Our analysis leverages several new techniques tailored to non-optimistic exploration algorithms, which we anticipate will find broader use.

Semantic segmentation has made significant progress in recent years thanks to deep neural networks, but the common objective of generating a single segmentation output that accurately matches the image's content may not be suitable for safety-critical domains such as medical diagnostics and autonomous driving. Instead, multiple possible correct segmentation maps may be required to reflect the true distribution of annotation maps. In this context, stochastic semantic segmentation methods must learn to predict conditional distributions of labels given the image, but this is challenging due to the typically multimodal distributions, high-dimensional output spaces, and limited annotation data. To address these challenges, we propose a conditional categorical diffusion model (CCDM) for semantic segmentation based on Denoising Diffusion Probabilistic Models. Our model is conditioned to the input image, enabling it to generate multiple segmentation label maps that account for the aleatoric uncertainty arising from divergent ground truth annotations. Our experimental results show that CCDM achieves state-of-the-art performance on LIDC, a stochastic semantic segmentation dataset, and outperforms established baselines on the classical segmentation dataset Cityscapes.

Applying pre-trained generative denoising diffusion models (DDMs) for downstream tasks such as image semantic editing usually requires either fine-tuning DDMs or learning auxiliary editing networks in the existing literature. In this work, we present our BoundaryDiffusion method for efficient, effective and light-weight semantic control with frozen pre-trained DDMs, without learning any extra networks. As one of the first learning-free diffusion editing works, we start by seeking a comprehensive understanding of the intermediate high-dimensional latent spaces by theoretically and empirically analyzing their probabilistic and geometric behaviors in the Markov chain. We then propose to further explore the critical step for editing in the denoising trajectory that characterizes the convergence of a pre-trained DDM and introduce an automatic search method. Last but not least, in contrast to the conventional understanding that DDMs have relatively poor semantic behaviors, we prove that the critical latent space we found already exhibits semantic subspace boundaries at the generic level in unconditional DDMs, which allows us to do controllable manipulation by guiding the denoising trajectory towards the targeted boundary via a single-step operation. We conduct extensive experiments on multiple DPMs architectures (DDPM, iDDPM) and datasets (CelebA, CelebA-HQ, LSUN-church, LSUN-bedroom, AFHQ-dog) with different resolutions (64, 256), achieving superior or state-of-the-art performance in various task scenarios (image semantic editing, text-based editing, unconditional semantic control) to demonstrate the effectiveness.

Voice anti-spoofing systems are crucial auxiliaries for automatic speaker verification (ASV) systems. A major challenge is caused by unseen attacks empowered by advanced speech synthesis technologies. Our previous research on one-class learning has improved the generalization ability to unseen attacks by compacting the bona fide speech in the embedding space. However, such compactness lacks consideration of the diversity of speakers. In this work, we propose speaker attractor multi-center one-class learning (SAMO), which clusters bona fide speech around a number of speaker attractors and pushes away spoofing attacks from all the attractors in a high-dimensional embedding space. For training, we propose an algorithm for the co-optimization of bona fide speech clustering and bona fide/spoof classification. For inference, we propose strategies to enable anti-spoofing for speakers without enrollment. Our proposed system outperforms existing state-of-the-art single systems with a relative improvement of 38% on equal error rate (EER) on the ASVspoof2019 LA evaluation set.

The tremendous progress in neural image generation, coupled with the emergence of seemingly omnipotent vision-language models has finally enabled text-based interfaces for creating and editing images. Handling generic images requires a diverse underlying generative model, hence the latest works utilize diffusion models, which were shown to surpass GANs in terms of diversity. One major drawback of diffusion models, however, is their relatively slow inference time. In this paper, we present an accelerated solution to the task of local text-driven editing of generic images, where the desired edits are confined to a user-provided mask. Our solution leverages a recent text-to-image Latent Diffusion Model (LDM), which speeds up diffusion by operating in a lower-dimensional latent space. We first convert the LDM into a local image editor by incorporating Blended Diffusion into it. Next we propose an optimization-based solution for the inherent inability of this LDM to accurately reconstruct images. Finally, we address the scenario of performing local edits using thin masks. We evaluate our method against the available baselines both qualitatively and quantitatively and demonstrate that in addition to being faster, our method achieves better precision than the baselines while mitigating some of their artifacts.

Hyperdimensional computing (HD), also known as vector symbolic architectures (VSA), is a framework for computing with distributed representations by exploiting properties of random high-dimensional vector spaces. The commitment of the scientific community to aggregate and disseminate research in this particularly multidisciplinary area has been fundamental for its advancement. Joining these efforts, we present Torchhd, a high-performance open source Python library for HD/VSA. Torchhd seeks to make HD/VSA more accessible and serves as an efficient foundation for further research and application development. The easy-to-use library builds on top of PyTorch and features state-of-the-art HD/VSA functionality, clear documentation, and implementation examples from well-known publications. Comparing publicly available code with their corresponding Torchhd implementation shows that experiments can run up to 100x faster. Torchhd is available at: https://github.com/hyperdimensional-computing/torchhd.

We consider the problem of how a teacher algorithm can enable an unknown Deep Reinforcement Learning (DRL) student to become good at a skill over a wide range of diverse environments. To do so, we study how a teacher algorithm can learn to generate a learning curriculum, whereby it sequentially samples parameters controlling a stochastic procedural generation of environments. Because it does not initially know the capacities of its student, a key challenge for the teacher is to discover which environments are easy, difficult or unlearnable, and in what order to propose them to maximize the efficiency of learning over the learnable ones. To achieve this, this problem is transformed into a surrogate continuous bandit problem where the teacher samples environments in order to maximize absolute learning progress of its student. We present a new algorithm modeling absolute learning progress with Gaussian mixture models (ALP-GMM). We also adapt existing algorithms and provide a complete study in the context of DRL. Using parameterized variants of the BipedalWalker environment, we study their efficiency to personalize a learning curriculum for different learners (embodiments), their robustness to the ratio of learnable/unlearnable environments, and their scalability to non-linear and high-dimensional parameter spaces. Videos and code are available at https://github.com/flowersteam/teachDeepRL.

In this paper, we propose a convolutional recurrent neural network for joint sound event localization and detection (SELD) of multiple overlapping sound events in three-dimensional (3D) space. The proposed network takes a sequence of consecutive spectrogram time-frames as input and maps it to two outputs in parallel. As the first output, the sound event detection (SED) is performed as a multi-label classification task on each time-frame producing temporal activity for all the sound event classes. As the second output, localization is performed by estimating the 3D Cartesian coordinates of the direction-of-arrival (DOA) for each sound event class using multi-output regression. The proposed method is able to associate multiple DOAs with respective sound event labels and further track this association with respect to time. The proposed method uses separately the phase and magnitude component of the spectrogram calculated on each audio channel as the feature, thereby avoiding any method- and array-specific feature extraction. The method is evaluated on five Ambisonic and two circular array format datasets with different overlapping sound events in anechoic, reverberant and real-life scenarios. The proposed method is compared with two SED, three DOA estimation, and one SELD baselines. The results show that the proposed method is generic and applicable to any array structures, robust to unseen DOA values, reverberation, and low SNR scenarios. The proposed method achieved a consistently higher recall of the estimated number of DOAs across datasets in comparison to the best baseline. Additionally, this recall was observed to be significantly better than the best baseline method for a higher number of overlapping sound events.

In this paper, we propose a novel approach, 3D-RecGAN++, which reconstructs the complete 3D structure of a given object from a single arbitrary depth view using generative adversarial networks. Unlike existing work which typically requires multiple views of the same object or class labels to recover the full 3D geometry, the proposed 3D-RecGAN++ only takes the voxel grid representation of a depth view of the object as input, and is able to generate the complete 3D occupancy grid with a high resolution of 256^3 by recovering the occluded/missing regions. The key idea is to combine the generative capabilities of autoencoders and the conditional Generative Adversarial Networks (GAN) framework, to infer accurate and fine-grained 3D structures of objects in high-dimensional voxel space. Extensive experiments on large synthetic datasets and real-world Kinect datasets show that the proposed 3D-RecGAN++ significantly outperforms the state of the art in single view 3D object reconstruction, and is able to reconstruct unseen types of objects.

In this paper, we propose a novel 3D-RecGAN approach, which reconstructs the complete 3D structure of a given object from a single arbitrary depth view using generative adversarial networks. Unlike the existing work which typically requires multiple views of the same object or class labels to recover the full 3D geometry, the proposed 3D-RecGAN only takes the voxel grid representation of a depth view of the object as input, and is able to generate the complete 3D occupancy grid by filling in the occluded/missing regions. The key idea is to combine the generative capabilities of autoencoders and the conditional Generative Adversarial Networks (GAN) framework, to infer accurate and fine-grained 3D structures of objects in high-dimensional voxel space. Extensive experiments on large synthetic datasets show that the proposed 3D-RecGAN significantly outperforms the state of the art in single view 3D object reconstruction, and is able to reconstruct unseen types of objects. Our code and data are available at: https://github.com/Yang7879/3D-RecGAN.

In this paper, we propose a unified approach to harness quantum conformal methods for multi-output distributions, with a particular emphasis on two experimental paradigms: (i) a standard 2-qubit circuit scenario producing a four-dimensional outcome distribution, and (ii) a multi-basis measurement setting that concatenates measurement probabilities in different bases (Z, X, Y) into a twelve-dimensional output space. By combining a multioutput regression model (e.g., random forests) with distributional conformal prediction, we validate coverage and interval-set sizes on both simulated quantum data and multi-basis measurement data. Our results confirm that classical conformal prediction can effectively provide coverage guarantees even when the target probabilities derive from inherently quantum processes. Such synergy opens the door to next-generation quantum-classical hybrid frameworks, providing both improved interpretability and rigorous coverage for quantum machine learning tasks. All codes and full reproducible Colab notebooks are made available at https://github.com/detasar/QECMMOU.