Daily Papers

Although transformer architectures have achieved state-of-the-art performance across diverse domains, their quadratic computational complexity with respect to sequence length remains a significant bottleneck, particularly for latency-sensitive long-context applications. While recent linear-complexity alternatives are increasingly powerful, effectively training them from scratch is still resource-intensive. To overcome these limitations, we propose LAWCAT (Linear Attention with Convolution Across Time), a novel linearization framework designed to efficiently transfer the capabilities of pre-trained transformers into a performant linear attention architecture. LAWCAT integrates causal Conv1D layers to enhance local dependency modeling and employs normalized gated linear attention to improve generalization across varying context lengths. Our comprehensive evaluations demonstrate that, distilling Mistral-7B with only 1K-length sequences yields over 90\% passkey retrieval accuracy up to 22K tokens, significantly extending its effective context window. Similarly, Llama3.2-1B LAWCAT variant achieves competitive performance on S-NIAH 1\&2\&3 tasks (1K-8K context length) and BABILong benchmark (QA2\&QA3, 0K-16K context length), requiring less than 0.1\% pre-training tokens compared with pre-training models. Furthermore, LAWCAT exhibits faster prefill speeds than FlashAttention-2 for sequences exceeding 8K tokens. LAWCAT thus provides an efficient pathway to high-performance, long-context linear models suitable for edge deployment, reducing reliance on extensive long-sequence training data and computational resources.

Recent Multimodal Large Language Models (MLLMs) have achieved remarkable performance but face deployment challenges due to their quadratic computational complexity, growing Key-Value cache requirements, and reliance on separate vision encoders. We propose mmMamba, a framework for developing linear-complexity native multimodal state space models through progressive distillation from existing MLLMs using moderate academic computational resources. Our approach enables the direct conversion of trained decoder-only MLLMs to linear-complexity architectures without requiring pre-trained RNN-based LLM or vision encoders. We propose an seeding strategy to carve Mamba from trained Transformer and a three-stage distillation recipe, which can effectively transfer the knowledge from Transformer to Mamba while preserving multimodal capabilities. Our method also supports flexible hybrid architectures that combine Transformer and Mamba layers for customizable efficiency-performance trade-offs. Distilled from the Transformer-based decoder-only HoVLE, mmMamba-linear achieves competitive performance against existing linear and quadratic-complexity VLMs, while mmMamba-hybrid further improves performance significantly, approaching HoVLE's capabilities. At 103K tokens, mmMamba-linear demonstrates 20.6times speedup and 75.8% GPU memory reduction compared to HoVLE, while mmMamba-hybrid achieves 13.5times speedup and 60.2% memory savings. Code and models are released at https://github.com/hustvl/mmMamba

Linear attention has emerged as a viable alternative to softmax attention by reducing complexity from quadratic to linear in sequence length. To preserve two fundamental properties of softmax, non-negativity and entropy reduction, current works employ various linearly separatable kernel functions with L1 normalization instead of softmax operator. However, query norms are neglected by the normalization operation in linear attention, such degradation heavily leads to an entropy gap. Meanwhile, existing works inhibit negative values of query and key vectors resulting in a missing inner-product interactions after being mapped. To address these dual challenges, we propose a novel Norm-Aware Linear Attention mechanism serving to restore norm-guided dynamic spikiness and recover kernel-perturbed norm distributions. Specifically, we first decouple query and key matrices into two components: norm and direction, to achieve norm-aware spikiness control and norm consistency, respectively. We mathematically reveal that the extent of entropy reduction varies with the query norm in softmax normalization, motivating a query-norm aware kernel function for dynamic control over entropy reduction. Furthermore, to ensure norm consistency and enforce non-negativity constraints, we employ a norm-preserving mapping to project all elements of the angular matrix into positive values, leveraging cosine similarity to inhibit dimensions with opposite directions. We conduct extensive experiments demonstrating that the NaLaFormer improves performance on vision and language tasks, enhancing both expressiveness and efficiency by up to 4.2\%.

The time complexity of the standard attention mechanism in a transformer scales quadratically with the length of the sequence. We introduce a method to reduce this to linear scaling with time, based on defining attention via latent vectors. The method is readily usable as a drop-in replacement for the standard attention mechanism. Our "Latte Transformer" model can be implemented for both bidirectional and unidirectional tasks, with the causal version allowing a recurrent implementation which is memory and time-efficient during inference of language generation tasks. Whilst next token prediction scales linearly with the sequence length for a standard transformer, a Latte Transformer requires constant time to compute the next token. The empirical performance of our method is comparable to standard attention, yet allows scaling to context windows much larger than practical in standard attention.

Large transformer models have shown extraordinary success in achieving state-of-the-art results in many natural language processing applications. However, training and deploying these models can be prohibitively costly for long sequences, as the standard self-attention mechanism of the Transformer uses O(n^2) time and space with respect to sequence length. In this paper, we demonstrate that the self-attention mechanism can be approximated by a low-rank matrix. We further exploit this finding to propose a new self-attention mechanism, which reduces the overall self-attention complexity from O(n^2) to O(n) in both time and space. The resulting linear transformer, the Linformer, performs on par with standard Transformer models, while being much more memory- and time-efficient.

Large Language Models (LLMs), epitomized by ChatGPT' s release in late 2022, have revolutionized various industries with their advanced language comprehension. However, their efficiency is challenged by the Transformer architecture' s struggle with handling long texts. KV-Cache has emerged as a pivotal solution to this issue, converting the time complexity of token generation from quadratic to linear, albeit with increased GPU memory overhead proportional to conversation length. With the development of the LLM community and academia, various KV-Cache compression methods have been proposed. In this review, we dissect the various properties of KV-Cache and elaborate on various methods currently used to optimize the KV-Cache space usage of LLMs. These methods span the pre-training phase, deployment phase, and inference phase, and we summarize the commonalities and differences among these methods. Additionally, we list some metrics for evaluating the long-text capabilities of large language models, from both efficiency and capability perspectives. Our review thus sheds light on the evolving landscape of LLM optimization, offering insights into future advancements in this dynamic field.

Many machine learning tasks such as multiple instance learning, 3D shape recognition, and few-shot image classification are defined on sets of instances. Since solutions to such problems do not depend on the order of elements of the set, models used to address them should be permutation invariant. We present an attention-based neural network module, the Set Transformer, specifically designed to model interactions among elements in the input set. The model consists of an encoder and a decoder, both of which rely on attention mechanisms. In an effort to reduce computational complexity, we introduce an attention scheme inspired by inducing point methods from sparse Gaussian process literature. It reduces the computation time of self-attention from quadratic to linear in the number of elements in the set. We show that our model is theoretically attractive and we evaluate it on a range of tasks, demonstrating the state-of-the-art performance compared to recent methods for set-structured data.

Zero-Input AI (ZIA) introduces a novel framework for human-computer interaction by enabling proactive intent prediction without explicit user commands. It integrates gaze tracking, bio-signals (EEG, heart rate), and contextual data (time, location, usage history) into a multi-modal model for real-time inference, targeting <100 ms latency. The proposed architecture employs a transformer-based model with cross-modal attention, variational Bayesian inference for uncertainty estimation, and reinforcement learning for adaptive optimization. To support deployment on edge devices (CPUs, TPUs, NPUs), ZIA utilizes quantization, weight pruning, and linear attention to reduce complexity from quadratic to linear with sequence length. Theoretical analysis establishes an information-theoretic bound on prediction error and demonstrates how multi-modal fusion improves accuracy over single-modal approaches. Expected performance suggests 85-90% accuracy with EEG integration and 60-100 ms inference latency. ZIA provides a scalable, privacy-preserving framework for accessibility, healthcare, and consumer applications, advancing AI toward anticipatory intelligence.

This paper presents ``Stim", a fast simulator for quantum stabilizer circuits. The paper explains how Stim works and compares it to existing tools. With no foreknowledge, Stim can analyze a distance 100 surface code circuit (20 thousand qubits, 8 million gates, 1 million measurements) in 15 seconds and then begin sampling full circuit shots at a rate of 1 kHz. Stim uses a stabilizer tableau representation, similar to Aaronson and Gottesman's CHP simulator, but with three main improvements. First, Stim improves the asymptotic complexity of deterministic measurement from quadratic to linear by tracking the {\em inverse} of the circuit's stabilizer tableau. Second, Stim improves the constant factors of the algorithm by using a cache-friendly data layout and 256 bit wide SIMD instructions. Third, Stim only uses expensive stabilizer tableau simulation to create an initial reference sample. Further samples are collected in bulk by using that sample as a reference for batches of Pauli frames propagating through the circuit.

Transformers have been successful in many vision tasks, thanks to their capability of capturing long-range dependency. However, their quadratic computational complexity poses a major obstacle for applying them to vision tasks requiring dense predictions, such as object detection, feature matching, stereo, etc. We introduce QuadTree Attention, which reduces the computational complexity from quadratic to linear. Our quadtree transformer builds token pyramids and computes attention in a coarse-to-fine manner. At each level, the top K patches with the highest attention scores are selected, such that at the next level, attention is only evaluated within the relevant regions corresponding to these top K patches. We demonstrate that quadtree attention achieves state-of-the-art performance in various vision tasks, e.g. with 4.0% improvement in feature matching on ScanNet, about 50% flops reduction in stereo matching, 0.4-1.5% improvement in top-1 accuracy on ImageNet classification, 1.2-1.8% improvement on COCO object detection, and 0.7-2.4% improvement on semantic segmentation over previous state-of-the-art transformers. The codes are available at https://github.com/Tangshitao/QuadtreeAttention.

In this work we introduce KERNELIZED TRANSFORMER, a generic, scalable, data driven framework for learning the kernel function in Transformers. Our framework approximates the Transformer kernel as a dot product between spectral feature maps and learns the kernel by learning the spectral distribution. This not only helps in learning a generic kernel end-to-end, but also reduces the time and space complexity of Transformers from quadratic to linear. We show that KERNELIZED TRANSFORMERS achieve performance comparable to existing efficient Transformer architectures, both in terms of accuracy as well as computational efficiency. Our study also demonstrates that the choice of the kernel has a substantial impact on performance, and kernel learning variants are competitive alternatives to fixed kernel Transformers, both in long as well as short sequence tasks.

In-context Ranking (ICR) is an emerging paradigm for Information Retrieval (IR), which leverages contextual understanding of LLMs by directly incorporating the task description, candidate documents, and the query into the model's input prompt and tasking the LLM to identify relevant document(s). While it is effective, efficiency is a significant challenge in this paradigm, especially as the candidate list grows due to quadratic/super-linear scaling of attention operation with context length. To this end, this paper first identifies inherent and exploitable structures in the attention of LLMs finetuned for ICR: (1) inter-document block sparsity: attention is dense within each document block but sparse across different documents in the context; and (2) query-document block relevance: the attention scores from certain query tokens to a document block in middle layers strongly correlate with that document's actual relevance. Motivated by these observations, we introduce BlockRank (Blockwise In-context Ranking), a novel method that adapts the attention operation in an LLM by (a) architecturally enforcing the observed inter-document block sparsity, reducing attention complexity from quadratic to linear without loss in performance, and (b) optimizing query-document block relevance for true relevant documents during fine-tuning using an auxiliary contrastive training objective, improving retrieval in attention. Experiments on BEIR, MSMarco and NQ with Mistral-7B demonstrate that FLARE Mistral matches or outperforms existing SOTA listwise rankers and controlled fine-tuned baseline while being significantly more efficient at inference (4.7x for 100 MSMarco documents in context) and scaling gracefully to long-context shortlists, around 500 documents in-context (approximately 100K context length) within a second, presenting a scalable and effective solution for ICR.

Efficiently supporting long context length is crucial for Transformer models. The quadratic complexity of the self-attention computation plagues traditional Transformers. Sliding window-based static sparse attention mitigates the problem by limiting the attention scope of the input tokens, reducing the theoretical complexity from quadratic to linear. Although the sparsity induced by window attention is highly structured, it does not align perfectly with the microarchitecture of the conventional accelerators, leading to suboptimal implementation. In response, we propose a dataflow-aware FPGA-based accelerator design, SWAT, that efficiently leverages the sparsity to achieve scalable performance for long input. The proposed microarchitecture is based on a design that maximizes data reuse by using a combination of row-wise dataflow, kernel fusion optimization, and an input-stationary design considering the distributed memory and computation resources of FPGA. Consequently, it achieves up to 22times and 5.7times improvement in latency and energy efficiency compared to the baseline FPGA-based accelerator and 15times energy efficiency compared to GPU-based solution.

Sparse observations and coarse-resolution climate models limit effective regional decision-making, underscoring the need for robust downscaling. However, existing AI methods struggle with generalization across variables and geographies and are constrained by the quadratic complexity of Vision Transformer (ViT) self-attention. We introduce ORBIT-2, a scalable foundation model for global, hyper-resolution climate downscaling. ORBIT-2 incorporates two key innovations: (1) Residual Slim ViT (Reslim), a lightweight architecture with residual learning and Bayesian regularization for efficient, robust prediction; and (2) TILES, a tile-wise sequence scaling algorithm that reduces self-attention complexity from quadratic to linear, enabling long-sequence processing and massive parallelism. ORBIT-2 scales to 10 billion parameters across 65,536 GPUs, achieving up to 4.1 exaFLOPS sustained throughput and 74--98% strong scaling efficiency. It supports downscaling to 0.9 km global resolution and processes sequences up to 4.2 billion tokens. On 7 km resolution benchmarks, ORBIT-2 achieves high accuracy with R^2 scores in the range of 0.98--0.99 against observational data.

Linear attentions have shown potential for improving Transformer efficiency, reducing attention's quadratic complexity to linear in sequence length. This holds exciting promise for (1) training linear Transformers from scratch, (2) "finetuned-conversion" of task-specific Transformers into linear versions that recover task performance, and (3) "pretrained-conversion" of Transformers such as large language models into linear versions finetunable on downstream tasks. However, linear attentions often underperform standard softmax attention in quality. To close this performance gap, we find prior linear attentions lack key properties of softmax attention tied to good performance: low-entropy (or "spiky") weights and dot-product monotonicity. We further observe surprisingly simple feature maps that retain these properties and match softmax performance, but are inefficient to compute in linear attention. We thus propose Hedgehog, a learnable linear attention that retains the spiky and monotonic properties of softmax attention while maintaining linear complexity. Hedgehog uses simple trainable MLPs to produce attention weights mimicking softmax attention. Experiments show Hedgehog recovers over 99% of standard Transformer quality in train-from-scratch and finetuned-conversion settings, outperforming prior linear attentions up to 6 perplexity points on WikiText-103 with causal GPTs, and up to 8.7 GLUE score points on finetuned bidirectional BERTs. Hedgehog also enables pretrained-conversion. Converting a pretrained GPT-2 into a linear attention variant achieves state-of-the-art 16.7 perplexity on WikiText-103 for 125M subquadratic decoder models. We finally turn a pretrained Llama-2 7B into a viable linear attention Llama. With low-rank adaptation, Hedgehog-Llama2 7B achieves 28.1 higher ROUGE-1 points over the base standard attention model, where prior linear attentions lead to 16.5 point drops.

The quadratic computational complexity in the self-attention mechanism of popular transformer architectures poses significant challenges for training and inference, particularly in terms of efficiency and memory requirements. Towards addressing these challenges, this paper introduces a novel fast computation method for gradient calculation in multi-layer transformer models. Our approach enables the computation of gradients for the entire multi-layer transformer model in almost linear time n^{1+o(1)}, where n is the input sequence length. This breakthrough significantly reduces the computational bottleneck associated with the traditional quadratic time complexity. Our theory holds for any loss function and maintains a bounded approximation error across the entire model. Furthermore, our analysis can hold when the multi-layer transformer model contains many practical sub-modules, such as residual connection, casual mask, and multi-head attention. By improving the efficiency of gradient computation in large language models, we hope that our work will facilitate the more effective training and deployment of long-context language models based on our theoretical results.

Transformers-based models, such as BERT, have been one of the most successful deep learning models for NLP. Unfortunately, one of their core limitations is the quadratic dependency (mainly in terms of memory) on the sequence length due to their full attention mechanism. To remedy this, we propose, BigBird, a sparse attention mechanism that reduces this quadratic dependency to linear. We show that BigBird is a universal approximator of sequence functions and is Turing complete, thereby preserving these properties of the quadratic, full attention model. Along the way, our theoretical analysis reveals some of the benefits of having O(1) global tokens (such as CLS), that attend to the entire sequence as part of the sparse attention mechanism. The proposed sparse attention can handle sequences of length up to 8x of what was previously possible using similar hardware. As a consequence of the capability to handle longer context, BigBird drastically improves performance on various NLP tasks such as question answering and summarization. We also propose novel applications to genomics data.

Ultra-high-resolution text-to-image generation demands both fine-grained texture synthesis and globally coherent structure, yet current diffusion models remain constrained to sub-1K times 1K resolutions due to the prohibitive quadratic complexity of attention and the scarcity of native 4K training data. We present Scale-DiT, a new diffusion framework that introduces hierarchical local attention with low-resolution global guidance, enabling efficient, scalable, and semantically coherent image synthesis at ultra-high resolutions. Specifically, high-resolution latents are divided into fixed-size local windows to reduce attention complexity from quadratic to near-linear, while a low-resolution latent equipped with scaled positional anchors injects global semantics. A lightweight LoRA adaptation bridges global and local pathways during denoising, ensuring consistency across structure and detail. To maximize inference efficiency, we repermute token sequence in Hilbert curve order and implement a fused-kernel for skipping masked operations, resulting in a GPU-friendly design. Extensive experiments demonstrate that Scale-DiT achieves more than 2times faster inference and lower memory usage compared to dense attention baselines, while reliably scaling to 4K times 4K resolution without requiring additional high-resolution training data. On both quantitative benchmarks (FID, IS, CLIP Score) and qualitative comparisons, Scale-DiT delivers superior global coherence and sharper local detail, matching or outperforming state-of-the-art methods that rely on native 4K training. Taken together, these results highlight hierarchical local attention with guided low-resolution anchors as a promising and effective approach for advancing ultra-high-resolution image generation.

Transformers-based models, such as BERT, have dramatically improved the performance for various natural language processing tasks. The clinical knowledge enriched model, namely ClinicalBERT, also achieved state-of-the-art results when performed on clinical named entity recognition and natural language inference tasks. One of the core limitations of these transformers is the substantial memory consumption due to their full self-attention mechanism. To overcome this, long sequence transformer models, e.g. Longformer and BigBird, were proposed with the idea of sparse attention mechanism to reduce the memory usage from quadratic to the sequence length to a linear scale. These models extended the maximum input sequence length from 512 to 4096, which enhanced the ability of modeling long-term dependency and consequently achieved optimal results in a variety of tasks. Inspired by the success of these long sequence transformer models, we introduce two domain enriched language models, namely Clinical-Longformer and Clinical-BigBird, which are pre-trained from large-scale clinical corpora. We evaluate both pre-trained models using 10 baseline tasks including named entity recognition, question answering, and document classification tasks. The results demonstrate that Clinical-Longformer and Clinical-BigBird consistently and significantly outperform ClinicalBERT as well as other short-sequence transformers in all downstream tasks. We have made our source code available at [https://github.com/luoyuanlab/Clinical-Longformer] the pre-trained models available for public download at: [https://huggingface.co/yikuan8/Clinical-Longformer].

As the size of large language models continue to scale, so does the computational resources required to run it. Spiking Neural Networks (SNNs) have emerged as an energy-efficient approach to deep learning that leverage sparse and event-driven activations to reduce the computational overhead associated with model inference. While they have become competitive with non-spiking models on many computer vision tasks, SNNs have also proven to be more challenging to train. As a result, their performance lags behind modern deep learning, and we are yet to see the effectiveness of SNNs in language generation. In this paper, inspired by the Receptance Weighted Key Value (RWKV) language model, we successfully implement `SpikeGPT', a generative language model with binary, event-driven spiking activation units. We train the proposed model on two model variants: 45M and 216M parameters. To the best of our knowledge, SpikeGPT is the largest backpropagation-trained SNN model to date, rendering it suitable for both the generation and comprehension of natural language. We achieve this by modifying the transformer block to replace multi-head self attention to reduce quadratic computational complexity O(N^2) to linear complexity O(N) with increasing sequence length. Input tokens are instead streamed in sequentially to our attention mechanism (as with typical SNNs). Our preliminary experiments show that SpikeGPT remains competitive with non-spiking models on tested benchmarks, while maintaining 20x fewer operations when processed on neuromorphic hardware that can leverage sparse, event-driven activations. Our code implementation is available at https://github.com/ridgerchu/SpikeGPT.

We propose Scalable Mechanistic Neural Network (S-MNN), an enhanced neural network framework designed for scientific machine learning applications involving long temporal sequences. By reformulating the original Mechanistic Neural Network (MNN) (Pervez et al., 2024), we reduce the computational time and space complexities from cubic and quadratic with respect to the sequence length, respectively, to linear. This significant improvement enables efficient modeling of long-term dynamics without sacrificing accuracy or interpretability. Extensive experiments demonstrate that S-MNN matches the original MNN in precision while substantially reducing computational resources. Consequently, S-MNN can drop-in replace the original MNN in applications, providing a practical and efficient tool for integrating mechanistic bottlenecks into neural network models of complex dynamical systems.

Transformer-based video diffusion models (VDMs) deliver state-of-the-art video generation quality but are constrained by the quadratic cost of self-attention, making long sequences and high resolutions computationally expensive. While linear attention offers sub-quadratic complexity, prior attempts fail to match the expressiveness of softmax attention without costly retraining. We introduce Attention Surgery, an efficient framework for linearizing or hybridizing attention in pretrained VDMs without training from scratch. Inspired by recent advances in language models, our method combines a novel hybrid attention mechanism-mixing softmax and linear tokens-with a lightweight distillation and fine-tuning pipeline requiring only a few GPU-days. Additionally, we incorporate a cost-aware block-rate strategy to balance expressiveness and efficiency across layers. Applied to Wan2.1 1.3B, a state-of-the-art DiT-based VDM, Attention Surgery achieves the first competitive sub-quadratic attention video diffusion models, reducing attention cost by up to 40\% in terms of FLOPs, while maintaining generation quality as measured on the standard VBench and VBench-2.0 benchmarks.

The quadratic complexity of the attention mechanism represents one of the biggest hurdles for processing long sequences using Transformers. Current methods, relying on sparse representations or stateful recurrence, sacrifice token-to-token interactions, which ultimately leads to compromises in performance. This paper introduces TaylorShift, a novel reformulation of the Taylor softmax that enables computing full token-to-token interactions in linear time and space. We analytically determine the crossover points where employing TaylorShift becomes more efficient than traditional attention, aligning closely with empirical measurements. Specifically, our findings demonstrate that TaylorShift enhances memory efficiency for sequences as short as 800 tokens and accelerates inference for inputs of approximately 1700 tokens and beyond. For shorter sequences, TaylorShift scales comparably with the vanilla attention. Furthermore, a classification benchmark across five tasks involving long sequences reveals no degradation in accuracy when employing Transformers equipped with TaylorShift. For reproducibility, we provide access to our code under https://github.com/tobna/TaylorShift.

Diffusion Transformers (DiT) have become a leading architecture in image generation. However, the quadratic complexity of attention mechanisms, which are responsible for modeling token-wise relationships, results in significant latency when generating high-resolution images. To address this issue, we aim at a linear attention mechanism in this paper that reduces the complexity of pre-trained DiTs to linear. We begin our exploration with a comprehensive summary of existing efficient attention mechanisms and identify four key factors crucial for successful linearization of pre-trained DiTs: locality, formulation consistency, high-rank attention maps, and feature integrity. Based on these insights, we introduce a convolution-like local attention strategy termed CLEAR, which limits feature interactions to a local window around each query token, and thus achieves linear complexity. Our experiments indicate that, by fine-tuning the attention layer on merely 10K self-generated samples for 10K iterations, we can effectively transfer knowledge from a pre-trained DiT to a student model with linear complexity, yielding results comparable to the teacher model. Simultaneously, it reduces attention computations by 99.5% and accelerates generation by 6.3 times for generating 8K-resolution images. Furthermore, we investigate favorable properties in the distilled attention layers, such as zero-shot generalization cross various models and plugins, and improved support for multi-GPU parallel inference. Models and codes are available here: https://github.com/Huage001/CLEAR.

Transformer-based models are widely used in natural language processing (NLP). Central to the transformer model is the self-attention mechanism, which captures the interactions of token pairs in the input sequences and depends quadratically on the sequence length. Training such models on longer sequences is expensive. In this paper, we show that a Bernoulli sampling attention mechanism based on Locality Sensitive Hashing (LSH), decreases the quadratic complexity of such models to linear. We bypass the quadratic cost by considering self-attention as a sum of individual tokens associated with Bernoulli random variables that can, in principle, be sampled at once by a single hash (although in practice, this number may be a small constant). This leads to an efficient sampling scheme to estimate self-attention which relies on specific modifications of LSH (to enable deployment on GPU architectures). We evaluate our algorithm on the GLUE benchmark with standard 512 sequence length where we see favorable performance relative to a standard pretrained Transformer. On the Long Range Arena (LRA) benchmark, for evaluating performance on long sequences, our method achieves results consistent with softmax self-attention but with sizable speed-ups and memory savings and often outperforms other efficient self-attention methods. Our code is available at https://github.com/mlpen/YOSO

The Transformer architecture has become the de facto standard for Large Language Models (LLMs), demonstrating remarkable capabilities in language understanding and generation. However, its application in conversational AI is fundamentally constrained by its stateless nature and the quadratic computational complexity (O(L^2)) with respect to sequence length L. Current models emulate memory by reprocessing an ever-expanding conversation history with each turn, leading to prohibitive costs and latency in long dialogues. This paper introduces the Reactive Transformer (RxT), a novel architecture designed to overcome these limitations by shifting from a data-driven to an event-driven paradigm. RxT processes each conversational turn as a discrete event in real-time, maintaining context in an integrated, fixed-size Short-Term Memory (STM) system. The architecture features a distinct operational cycle where a generator-decoder produces a response based on the current query and the previous memory state, after which a memory-encoder and a dedicated Memory Attention network asynchronously update the STM with a representation of the complete interaction. This design fundamentally alters the scaling dynamics, reducing the total user-facing cost of a conversation from quadratic (O(N^2 cdot T)) to linear (O(N cdot T)) with respect to the number of interactions N. By decoupling response generation from memory updates, RxT achieves low latency, enabling truly real-time, stateful, and economically viable long-form conversations. We validated our architecture with a series of proof-of-concept experiments on synthetic data, demonstrating superior performance and constant-time inference latency compared to a baseline stateless model of comparable size.

We design and implement AXLearn, a production deep learning system that facilitates scalable and high-performance training of large deep learning models. Compared to other state-of-the-art deep learning systems, AXLearn has a unique focus on modularity and support for heterogeneous hardware infrastructure. AXLearn's internal interfaces between software components follow strict encapsulation, allowing different components to be assembled to facilitate rapid model development and experimentation on heterogeneous compute infrastructure. We introduce a novel method of quantifying modularity via Lines-of-Code (LoC)-complexity, which demonstrates how our system maintains constant complexity as we scale the components in the system, compared to linear or quadratic complexity in other systems. This allows integrating features such as Rotary Position Embeddings (RoPE) into AXLearn across hundred of modules with just 10 lines of code, compared to hundreds as required in other systems. At the same time, AXLearn maintains equivalent performance compared to state-of-the-art training systems. Finally, we share our experience in the development and operation of AXLearn.

The adversarial vulnerability of Deep Neural Networks (DNNs) has been well-known and widely concerned, often under the context of learning top-1 attacks (e.g., fooling a DNN to classify a cat image as dog). This paper shows that the concern is much more serious by learning significantly more aggressive ordered top-K clear-box~ This is often referred to as white/black-box attacks in the literature. We choose to adopt neutral terminology, clear/opaque-box attacks in this paper, and omit the prefix clear-box for simplicity. targeted attacks proposed in Adversarial Distillation. We propose a novel and rigorous quadratic programming (QP) method of learning ordered top-K attacks with low computing cost, dubbed as QuadAttacK. Our QuadAttacK directly solves the QP to satisfy the attack constraint in the feature embedding space (i.e., the input space to the final linear classifier), which thus exploits the semantics of the feature embedding space (i.e., the principle of class coherence). With the optimized feature embedding vector perturbation, it then computes the adversarial perturbation in the data space via the vanilla one-step back-propagation. In experiments, the proposed QuadAttacK is tested in the ImageNet-1k classification using ResNet-50, DenseNet-121, and Vision Transformers (ViT-B and DEiT-S). It successfully pushes the boundary of successful ordered top-K attacks from K=10 up to K=20 at a cheap budget (1times 60) and further improves attack success rates for K=5 for all tested models, while retaining the performance for K=1.

Transformer models are computationally costly on long sequences since regular attention has quadratic O(n^2) time complexity. We introduce Wavelet-Enhanced Random Spectral Attention (WERSA), a novel mechanism of linear O(n) time complexity that is pivotal to enable successful long-sequence processing without the performance trade-off. WERSA merges content-adaptive random spectral features together with multi-resolution Haar wavelets and learnable parameters to selectively attend to informative scales of data while preserving linear efficiency. Large-scale comparisons on single GPU and across various benchmarks (vision, NLP, hierarchical reasoning) and various attention mechanisms (like Multiheaded Attention, Flash-Attention-2, FNet, Linformer, Performer, Waveformer), reveal uniform advantages of WERSA. It achieves best accuracy in all tests. On ArXiv classification, WERSA improves accuracy over vanilla attention by 1.2\% (86.2\% vs 85.0\%) while cutting training time by 81\% (296s vs 1554s) and FLOPS by 73.4\% (26.2G vs 98.4G). Significantly, WERSA excels where vanilla and FlashAttention-2 fail: on ArXiv-128k's extremely lengthy sequences, it achieves best accuracy (79.1\%) and AUC (0.979) among viable methods, operating on data that gives Out-Of-Memory errors to quadratic methods while being twice as fast as Waveformer, its next-best competitor. By significantly reducing computational loads without compromising accuracy, WERSA makes possible more practical, more affordable, long-context models, in particular on low-resource hardware, for more sustainable and more scalable AI development.

Leveraging the in-context learning (ICL) capability of Large Language Models (LLMs) for tabular classification has gained significant attention for its training-free adaptability across diverse datasets. Recent advancements, like TabPFN, excel in small-scale tabular datasets but struggle to scale for large and complex datasets. Our work enhances the efficiency and scalability of TabPFN for larger datasets by incorporating linear attention mechanisms as a scalable alternative to complexity-quadratic self-attention. Our model, TabFlex, efficiently handles tabular datasets with thousands of features and hundreds of classes, scaling seamlessly to millions of samples. For instance, TabFlex processes the poker-hand dataset with over a million samples in just 5 seconds. Our extensive evaluations demonstrate that TabFlex can achieve over a 2x speedup compared to TabPFN and a 1.5x speedup over XGBoost, outperforming 25 tested baselines in terms of efficiency across a diverse range of datasets. Furthermore, TabFlex remains highly effective on large-scale datasets, delivering strong performance with significantly reduced computational costs, especially when combined with data-efficient techniques such as dimensionality reduction and data sampling.

The Transformer architecture, despite its widespread success, struggles with long-context scenarios due to quadratic computation and linear memory growth. While various linear attention variants mitigate these efficiency constraints by compressing context into fixed-size states, they often degrade performance in tasks such as in-context retrieval and reasoning. To address this limitation and achieve more effective context compression, we propose two key innovations. First, we introduce a row-sparse update formulation for linear attention by conceptualizing state updating as information classification. This enables sparse state updates via softmax-based top-k hard classification, thereby extending receptive fields and reducing inter-class interference. Second, we present Sparse State Expansion (SSE) within the sparse framework, which expands the contextual state into multiple partitions, effectively decoupling parameter size from state capacity while maintaining the sparse classification paradigm. Our design, supported by efficient parallelized implementations, yields effective classification and discriminative state representations. We extensively validate SSE in both pure linear and hybrid (SSE-H) architectures across language modeling, in-context retrieval, and mathematical reasoning benchmarks. SSE demonstrates strong retrieval performance and scales favorably with state size. Moreover, after reinforcement learning (RL) training, our 2B SSE-H model achieves state-of-the-art mathematical reasoning performance among small reasoning models, scoring 64.7 on AIME24 and 51.3 on AIME25, significantly outperforming similarly sized open-source Transformers. These results highlight SSE as a promising and efficient architecture for long-context modeling.

Neighborhood attention reduces the cost of self attention by restricting each token's attention span to its nearest neighbors. This restriction, parameterized by a window size and dilation factor, draws a spectrum of possible attention patterns between linear projection and self attention. Neighborhood attention, and more generally sliding window attention patterns, have long been bounded by infrastructure, particularly in higher-rank spaces (2-D and 3-D), calling for the development of custom kernels, which have been limited in either functionality, or performance, if not both. In this work, we first show that neighborhood attention can be represented as a batched GEMM problem, similar to standard attention, and implement it for 1-D and 2-D neighborhood attention. These kernels on average provide 895% and 272% improvement in full precision latency compared to existing naive kernels for 1-D and 2-D neighborhood attention respectively. We find certain inherent inefficiencies in all unfused neighborhood attention kernels that bound their performance and lower-precision scalability. We also developed fused neighborhood attention; an adaptation of fused dot-product attention kernels that allow fine-grained control over attention across different spatial axes. Known for reducing the quadratic time complexity of self attention to a linear complexity, neighborhood attention can now enjoy a reduced and constant memory footprint, and record-breaking half precision latency. We observe that our fused kernels successfully circumvent some of the unavoidable inefficiencies in unfused implementations. While our unfused GEMM-based kernels only improve half precision performance compared to naive kernels by an average of 496% and 113% in 1-D and 2-D problems respectively, our fused kernels improve naive kernels by an average of 1607% and 581% in 1-D and 2-D problems respectively.

Efficient long-context language modeling remains a significant challenge in Natural Language Processing (NLP). While Transformers dominate language tasks, they struggle with long sequences due to quadratic computational complexity in training and linearly scaling memory costs during inference. Recent State Space Models (SSMs) such as Mamba offer alternatives with constant memory usage, but they underperform in tasks requiring extensive in-context retrieval. We introduce Taipan, a novel hybrid architecture that combines Mamba-2 with Selective Attention Layers (SALs). These SALs identify tokens requiring long-range interactions, remove less important features, and then augment their representations using the attention module. This approach balances Mamba's efficiency with Transformer-like performance in memory-intensive tasks. By constraining the attention budget, Taipan extends accurate predictions to context lengths of up to 1 million tokens while preserving computational efficiency. Our experiments demonstrate Taipan's superior performance across various scales and tasks, offering a promising solution for efficient long-context language modeling.

We introduce Performers, Transformer architectures which can estimate regular (softmax) full-rank-attention Transformers with provable accuracy, but using only linear (as opposed to quadratic) space and time complexity, without relying on any priors such as sparsity or low-rankness. To approximate softmax attention-kernels, Performers use a novel Fast Attention Via positive Orthogonal Random features approach (FAVOR+), which may be of independent interest for scalable kernel methods. FAVOR+ can be also used to efficiently model kernelizable attention mechanisms beyond softmax. This representational power is crucial to accurately compare softmax with other kernels for the first time on large-scale tasks, beyond the reach of regular Transformers, and investigate optimal attention-kernels. Performers are linear architectures fully compatible with regular Transformers and with strong theoretical guarantees: unbiased or nearly-unbiased estimation of the attention matrix, uniform convergence and low estimation variance. We tested Performers on a rich set of tasks stretching from pixel-prediction through text models to protein sequence modeling. We demonstrate competitive results with other examined efficient sparse and dense attention methods, showcasing effectiveness of the novel attention-learning paradigm leveraged by Performers.

We propose a novel spectral generative modeling framework for natural language processing that jointly learns a global time varying Fourier dictionary and per token mixing coefficients, replacing the ubiquitous self attention mechanism in transformer architectures. By enforcing reconstruction losses in both the time domain (embedding reconstruction) and the frequency domain (via Short Time Fourier Transform magnitude matching) alongside a standard language modeling objective, and fitting a Gaussian Mixture Model (GMM) prior over the learned mixing vectors, our approach achieves competitive perplexity and generation quality on standard benchmarks such as WikiText2 and Penn Treebank. In contrast to the quadratic computation complexity of self attention, our method operates with linear complexity, delivering substantial efficiency gains. We demonstrate that spectral dictionary models can achieve competitive performance compared to transformer baselines while significantly reducing inference latency and memory footprint, offering a compelling alternative for scalable language modeling.

Transformers achieve remarkable performance in several tasks but due to their quadratic complexity, with respect to the input's length, they are prohibitively slow for very long sequences. To address this limitation, we express the self-attention as a linear dot-product of kernel feature maps and make use of the associativity property of matrix products to reduce the complexity from Oleft(N^2right) to Oleft(Nright), where N is the sequence length. We show that this formulation permits an iterative implementation that dramatically accelerates autoregressive transformers and reveals their relationship to recurrent neural networks. Our linear transformers achieve similar performance to vanilla transformers and they are up to 4000x faster on autoregressive prediction of very long sequences.

The transformer architecture has driven breakthroughs in recent years on tasks which require modeling pairwise relationships between sequential elements, as is the case in natural language understanding. However, long seqeuences pose a problem due to the quadratic complexity of the attention operation. Previous research has aimed to lower the complexity by sparsifying or linearly approximating the attention matrix. Yet, these approaches cannot straightforwardly distill knowledge from a teacher's attention matrix and often require complete retraining from scratch. Furthermore, previous sparse and linear approaches lose interpretability if they cannot produce full attention matrices. To address these challenges, we propose SEA: Sparse linear attention with an Estimated Attention mask. SEA estimates the attention matrix with linear complexity via kernel-based linear attention, then subsequently creates a sparse attention matrix with a top-k selection to perform a sparse attention operation. For language modeling tasks (Wikitext2), previous linear and sparse attention methods show roughly two-fold worse perplexity scores over the quadratic OPT-1.3B baseline, while SEA achieves better perplexity than OPT-1.3B, using roughly half the memory of OPT-1.3B, providing interpretable attention matrix. We believe that our work will have a large practical impact, as it opens the possibility of running large transformers on resource-limited devices with less memory.

We propose Lizard, a linearization framework that transforms pretrained Transformer-based Large Language Models (LLMs) into flexible, subquadratic architectures for infinite-context generation. Transformer-based LLMs face significant memory and computational bottlenecks as context lengths increase, due to the quadratic complexity of softmax attention and the growing key-value (KV) cache. Lizard addresses these limitations by introducing a subquadratic attention mechanism that closely approximates softmax attention while preserving the output quality. Unlike previous linearization methods, which are often limited by fixed model structures and therefore exclude gating mechanisms, Lizard incorporates a gating module inspired by recent state-of-the-art linear models. This enables adaptive memory control, supports constant-memory inference, offers strong length generalization, and allows more flexible model design. Lizard combines gated linear attention for global context compression with sliding window attention enhanced by meta memory, forming a hybrid mechanism that captures both long-range dependencies and fine-grained local interactions. Moreover, we introduce a hardware-aware algorithm that accelerates the training speed of our models. Extensive experiments show that Lizard achieves near-lossless recovery of the teacher model's performance across standard language modeling tasks, while significantly outperforming previous linearization methods. On the 5-shot MMLU benchmark, Lizard improves over prior models by 18 points and shows significant improvements on associative recall tasks.

The Softmax attention mechanism in Transformer models is notoriously computationally expensive, particularly due to its quadratic complexity, posing significant challenges in vision applications. In contrast, linear attention provides a far more efficient solution by reducing the complexity to linear levels. However, compared to Softmax attention, linear attention often experiences significant performance degradation. Our experiments indicate that this performance drop is due to the low-rank nature of linear attention's feature map, which hinders its ability to adequately model complex spatial information. In this paper, to break the low-rank dilemma of linear attention, we conduct rank analysis from two perspectives: the KV buffer and the output features. Consequently, we introduce Rank-Augmented Linear Attention (RALA), which rivals the performance of Softmax attention while maintaining linear complexity and high efficiency. Based on RALA, we construct the Rank-Augmented Vision Linear Transformer (RAVLT). Extensive experiments demonstrate that RAVLT achieves excellent performance across various vision tasks. Specifically, without using any additional labels, data, or supervision during training, RAVLT achieves an 84.4% Top-1 accuracy on ImageNet-1k with only 26M parameters and 4.6G FLOPs. This result significantly surpasses previous linear attention mechanisms, fully illustrating the potential of RALA. Code will be available at https://github.com/qhfan/RALA.

Recent advancements in Large Language Models (LLMs) have set themselves apart with their exceptional performance in complex language modelling tasks. However, these models are also known for their significant computational and storage requirements, primarily due to the quadratic computation complexity of softmax attention. To mitigate this issue, linear attention has been designed to reduce the quadratic space-time complexity that is inherent in standard transformers. In this work, we embarked on a comprehensive exploration of three key components that substantially impact the performance of the Gated Linear Attention module: feature maps, normalization, and the gating mechanism. We developed a feature mapping function to address some crucial issues that previous suggestions overlooked. Then we offered further rationale for the integration of normalization layers to stabilize the training process. Moreover, we explored the saturation phenomenon of the gating mechanism and augmented it with a refining module. We conducted extensive experiments and showed our architecture outperforms previous Gated Linear Attention mechanisms in extensive tasks including training from scratch and post-linearization with continual pre-training.

Transformer models struggle with long-context inference due to their quadratic time and linear memory complexity. Recurrent Memory Transformers (RMTs) offer a solution by reducing the asymptotic cost to linear time and constant memory usage. However, their memory update mechanism leads to sequential execution, causing a performance bottleneck. We introduce Diagonal Batching, a scheduling scheme that unlocks parallelism across segments in RMTs while preserving exact recurrence. This approach eliminates the sequential constraint, enabling efficient GPU inference even for single long-context inputs without complex batching and pipelining techniques. Because the technique is purely a run-time computation reordering, existing RMT models adopt it with no retraining. Applied to a LLaMA-1B ARMT model, Diagonal Batching yields a 3.3x speedup over standard full-attention LLaMA-1B and a 1.8x speedup over the sequential RMT implementation on 131,072-token sequences. By removing sequential bottleneck, Diagonal Batching reduces inference cost and latency, thereby strengthening RMTs as a practical solution for real-world, long-context applications.

Effective reasoning is crucial to solving complex mathematical problems. Recent large language models (LLMs) have boosted performance by scaling test-time computation through long chain-of-thought reasoning. However, transformer-based models are inherently limited in extending context length due to their quadratic computational complexity and linear memory requirements. In this paper, we introduce a novel hybrid linear RNN reasoning model, M1, built on the Mamba architecture, which allows memory-efficient inference. Our approach leverages a distillation process from existing reasoning models and is further enhanced through RL training. Experimental results on the AIME and MATH benchmarks show that M1 not only outperforms previous linear RNN models but also matches the performance of state-of-the-art Deepseek R1 distilled reasoning models at a similar scale. We also compare our generation speed with a highly performant general purpose inference engine, vLLM, and observe more than a 3x speedup compared to a same size transformer. With throughput speedup, we are able to achieve higher accuracy compared to DeepSeek R1 distilled transformer reasoning models under a fixed generation time budget using self-consistency voting. Overall, we introduce a hybrid Mamba reasoning model and provide a more effective approach to scaling test-time generation using self-consistency or long chain of thought reasoning.

Optimizing inference for long-context Large Language Models (LLMs) is increasingly important due to the quadratic compute and linear memory complexity of Transformers. Existing approximation methods, such as key-value (KV) cache dropping, sparse attention, and prompt compression, typically rely on rough predictions of token or KV pair importance. We propose a novel framework for approximate LLM inference that leverages small draft models to more accurately predict the importance of tokens and KV pairs. Specifically, we introduce two instantiations of our proposed framework: (i) SpecKV, which leverages a draft output to accurately assess the importance of each KV pair for more effective KV cache dropping, and (ii) SpecPC, which uses the draft model's attention activations to identify and discard unimportant prompt tokens. To the best of our knowledge, this is the first work to use draft models for approximate LLM inference acceleration, extending their utility beyond traditional lossless speculative decoding. We motivate our methods with theoretical and empirical analyses, and show a strong correlation between the attention patterns of draft and target models. Extensive experiments on long-context benchmarks show that our methods consistently achieve higher accuracy than existing baselines, while preserving the same improvements in memory usage, latency, and throughput. Our code is available at https://github.com/furiosa-ai/draft-based-approx-llm.

We present Neighborhood Attention (NA), the first efficient and scalable sliding-window attention mechanism for vision. NA is a pixel-wise operation, localizing self attention (SA) to the nearest neighboring pixels, and therefore enjoys a linear time and space complexity compared to the quadratic complexity of SA. The sliding-window pattern allows NA's receptive field to grow without needing extra pixel shifts, and preserves translational equivariance, unlike Swin Transformer's Window Self Attention (WSA). We develop NATTEN (Neighborhood Attention Extension), a Python package with efficient C++ and CUDA kernels, which allows NA to run up to 40% faster than Swin's WSA while using up to 25% less memory. We further present Neighborhood Attention Transformer (NAT), a new hierarchical transformer design based on NA that boosts image classification and downstream vision performance. Experimental results on NAT are competitive; NAT-Tiny reaches 83.2% top-1 accuracy on ImageNet, 51.4% mAP on MS-COCO and 48.4% mIoU on ADE20K, which is 1.9% ImageNet accuracy, 1.0% COCO mAP, and 2.6% ADE20K mIoU improvement over a Swin model with similar size. To support more research based on sliding-window attention, we open source our project and release our checkpoints at: https://github.com/SHI-Labs/Neighborhood-Attention-Transformer .

In this paper we present a new framework for time-series modeling that combines the best of traditional statistical models and neural networks. We focus on time-series with long-range dependencies, needed for monitoring fine granularity data (e.g. minutes, seconds, milliseconds), prevalent in operational use-cases. Traditional models, such as auto-regression fitted with least squares (Classic-AR) can model time-series with a concise and interpretable model. When dealing with long-range dependencies, Classic-AR models can become intractably slow to fit for large data. Recently, sequence-to-sequence models, such as Recurrent Neural Networks, which were originally intended for natural language processing, have become popular for time-series. However, they can be overly complex for typical time-series data and lack interpretability. A scalable and interpretable model is needed to bridge the statistical and deep learning-based approaches. As a first step towards this goal, we propose modelling AR-process dynamics using a feed-forward neural network approach, termed AR-Net. We show that AR-Net is as interpretable as Classic-AR but also scales to long-range dependencies. Our results lead to three major conclusions: First, AR-Net learns identical AR-coefficients as Classic-AR, thus being equally interpretable. Second, the computational complexity with respect to the order of the AR process, is linear for AR-Net as compared to a quadratic for Classic-AR. This makes it possible to model long-range dependencies within fine granularity data. Third, by introducing regularization, AR-Net automatically selects and learns sparse AR-coefficients. This eliminates the need to know the exact order of the AR-process and allows to learn sparse weights for a model with long-range dependencies.

The attention module, which is a crucial component in Transformer, cannot scale efficiently to long sequences due to its quadratic complexity. Many works focus on approximating the dot-then-exponentiate softmax function in the original attention, leading to sub-quadratic or even linear-complexity Transformer architectures. However, we show that these methods cannot be applied to more powerful attention modules that go beyond the dot-then-exponentiate style, e.g., Transformers with relative positional encoding (RPE). Since in many state-of-the-art models, relative positional encoding is used as default, designing efficient Transformers that can incorporate RPE is appealing. In this paper, we propose a novel way to accelerate attention calculation for Transformers with RPE on top of the kernelized attention. Based upon the observation that relative positional encoding forms a Toeplitz matrix, we mathematically show that kernelized attention with RPE can be calculated efficiently using Fast Fourier Transform (FFT). With FFT, our method achieves O(nlog n) time complexity. Interestingly, we further demonstrate that properly using relative positional encoding can mitigate the training instability problem of vanilla kernelized attention. On a wide range of tasks, we empirically show that our models can be trained from scratch without any optimization issues. The learned model performs better than many efficient Transformer variants and is faster than standard Transformer in the long-sequence regime.

The idea of video super resolution is to use different view points of a single scene to enhance the overall resolution and quality. Classical energy minimization approaches first establish a correspondence of the current frame to all its neighbors in some radius and then use this temporal information for enhancement. In this paper, we propose the first variational super resolution approach that computes several super resolved frames in one batch optimization procedure by incorporating motion information between the high-resolution image frames themselves. As a consequence, the number of motion estimation problems grows linearly in the number of frames, opposed to a quadratic growth of classical methods and temporal consistency is enforced naturally. We use infimal convolution regularization as well as an automatic parameter balancing scheme to automatically determine the reliability of the motion information and reweight the regularization locally. We demonstrate that our approach yields state-of-the-art results and even is competitive with machine learning approaches.

We present core attention disaggregation (CAD), a technique that improves long-context large language model training by decoupling the core attention computation, softmax(QK^T)V, from the rest of the model and executing it on a separate pool of devices. In existing systems, core attention is colocated with other layers; at long context lengths, its quadratic compute growth compared to the near-linear growth of other components causes load imbalance and stragglers across data and pipeline parallel groups. CAD is enabled by two observations. First, core attention is stateless: it has no trainable parameters and only minimal transient data, so balancing reduces to scheduling compute-bound tasks. Second, it is composable: modern attention kernels retain high efficiency when processing fused batches of token-level shards with arbitrary lengths. CAD partitions core attention into token-level tasks and dispatches them to dedicated attention servers, which dynamically rebatch tasks to equalize compute without sacrificing kernel efficiency. We implement CAD in a system called DistCA, which uses a ping-pong execution scheme to fully overlap communication with computation and in-place execution on attention servers to reduce memory use. On 512 H200 GPUs and context lengths up to 512k tokens, DistCA improves end-to-end training throughput by up to 1.35x, eliminates data and pipeline parallel stragglers, and achieves near-perfect compute and memory balance.

Recent Reinforcement Learning (RL) algorithms making use of Kullback-Leibler (KL) regularization as a core component have shown outstanding performance. Yet, only little is understood theoretically about why KL regularization helps, so far. We study KL regularization within an approximate value iteration scheme and show that it implicitly averages q-values. Leveraging this insight, we provide a very strong performance bound, the very first to combine two desirable aspects: a linear dependency to the horizon (instead of quadratic) and an error propagation term involving an averaging effect of the estimation errors (instead of an accumulation effect). We also study the more general case of an additional entropy regularizer. The resulting abstract scheme encompasses many existing RL algorithms. Some of our assumptions do not hold with neural networks, so we complement this theoretical analysis with an extensive empirical study.

Orthogonal gradient updates have emerged as a promising direction in optimization for machine learning. However, traditional approaches such as SVD/QR decomposition incur prohibitive computational costs of O(n^3) and underperform compared to well-tuned SGD with momentum, since momentum is applied only after strict orthogonalization. Recent advances, such as Muon, improve efficiency by applying momentum before orthogonalization and producing semi-orthogonal matrices via Newton-Schulz iterations, reducing complexity to O(n^2). Nevertheless, quadratic costs remain a bottleneck. In this work, we study the semi-orthogonal properties of momentum-based updates and develop a method to bound momentum updates under a spectral-norm trust region, preserving directional information without requiring explicit semi-orthogonalization. We propose AuON (Alternative Unit-norm momentum updates by Normalized nonlinear scaling), a linear-time optimizer that achieves strong performance without constructing semi-orthogonal matrices, while preserving structural alignment and reconditioning ill-posed updates. Our approach combines hyperbolic-cosine RMS scaling transformations with normalization, demonstrating both effectiveness and computational efficiency compared to Newton-Schulz methods. We further introduce a hybrid variant (Hybrid-AuON) that applies a single Newton-Schulz iteration. Experiments across vision and language benchmarks show that AuON and its hybrid variant achieve performance comparable to strong baselines such as AdamW and Muon. Code is available at: https://github.com/ryyzn9/AuON

Vision Transformers (ViTs) have delivered remarkable progress through global self-attention, yet their quadratic complexity can become prohibitive for high-resolution inputs. In this work, we present ViT-Linearizer, a cross-architecture distillation framework that transfers rich ViT representations into a linear-time, recurrent-style model. Our approach leverages 1) activation matching, an intermediate constraint that encourages student to align its token-wise dependencies with those produced by the teacher, and 2) masked prediction, a contextual reconstruction objective that requires the student to predict the teacher's representations for unseen (masked) tokens, to effectively distill the quadratic self-attention knowledge into the student while maintaining efficient complexity. Empirically, our method provides notable speedups particularly for high-resolution tasks, significantly addressing the hardware challenges in inference. Additionally, it also elevates Mamba-based architectures' performance on standard vision benchmarks, achieving a competitive 84.3% top-1 accuracy on ImageNet with a base-sized model. Our results underscore the good potential of RNN-based solutions for large-scale visual tasks, bridging the gap between theoretical efficiency and real-world practice.

Text-to-video generation enhances content creation but is highly computationally intensive: The computational cost of Diffusion Transformers (DiTs) scales quadratically in the number of pixels. This makes minute-length video generation extremely expensive, limiting most existing models to generating videos of only 10-20 seconds length. We propose a Linear-complexity text-to-video Generation (LinGen) framework whose cost scales linearly in the number of pixels. For the first time, LinGen enables high-resolution minute-length video generation on a single GPU without compromising quality. It replaces the computationally-dominant and quadratic-complexity block, self-attention, with a linear-complexity block called MATE, which consists of an MA-branch and a TE-branch. The MA-branch targets short-to-long-range correlations, combining a bidirectional Mamba2 block with our token rearrangement method, Rotary Major Scan, and our review tokens developed for long video generation. The TE-branch is a novel TEmporal Swin Attention block that focuses on temporal correlations between adjacent tokens and medium-range tokens. The MATE block addresses the adjacency preservation issue of Mamba and improves the consistency of generated videos significantly. Experimental results show that LinGen outperforms DiT (with a 75.6% win rate) in video quality with up to 15times (11.5times) FLOPs (latency) reduction. Furthermore, both automatic metrics and human evaluation demonstrate our LinGen-4B yields comparable video quality to state-of-the-art models (with a 50.5%, 52.1%, 49.1% win rate with respect to Gen-3, LumaLabs, and Kling, respectively). This paves the way to hour-length movie generation and real-time interactive video generation. We provide 68s video generation results and more examples in our project website: https://lineargen.github.io/.

The quadratic cost of scaled dot-product attention is a central obstacle to scaling autoregressive language models to long contexts. Linear-time attention and State Space Models (SSMs) provide scalable alternatives but are typically restricted to first-order or kernel-based approximations, which can limit expressivity. We introduce Higher-order Linear Attention (HLA), a causal, streaming mechanism that realizes higher interactions via compact prefix sufficient statistics. In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materializing any n times n matrices. We give closed-form streaming identities, a strictly causal masked variant using two additional summaries, and a chunk-parallel training scheme based on associative scans that reproduces the activations of a serial recurrence exactly. We further outline extensions to third and higher orders. Collectively, these results position HLA as a principled, scalable building block that combines attention-like, data-dependent mixing with the efficiency of modern recurrent architectures. Project Page: https://github.com/yifanzhang-pro/HLA.

Linear transformers aim to reduce the quadratic space-time complexity of vanilla transformers. However, they usually suffer from degraded performances on various tasks and corpus. In this paper, we examine existing kernel-based linear transformers and identify two key issues that lead to such performance gaps: 1) unbounded gradients in the attention computation adversely impact the convergence of linear transformer models; 2) attention dilution which trivially distributes attention scores over long sequences while neglecting neighbouring structures. To address these issues, we first identify that the scaling of attention matrices is the devil in unbounded gradients, which turns out unnecessary in linear attention as we show theoretically and empirically. To this end, we propose a new linear attention that replaces the scaling operation with a normalization to stabilize gradients. For the issue of attention dilution, we leverage a diagonal attention to confine attention to only neighbouring tokens in early layers. Benefiting from the stable gradients and improved attention, our new linear transformer model, transNormer, demonstrates superior performance on text classification and language modeling tasks, as well as on the challenging Long-Range Arena benchmark, surpassing vanilla transformer and existing linear variants by a clear margin while being significantly more space-time efficient. The code is available at https://github.com/OpenNLPLab/Transnormer .

This paper studies attack detection for discrete-time linear systems with stochastic process noise that produce both a vulnerable (i.e., attackable) linear measurement and a secured (i.e., unattackable) quadratic measurement. The motivating application of this model is a dynamic-game setting where the quadratic measurement is interpreted as a system-level utility or reward, and control inputs into the linear system are interpreted as control policies that, once applied, are known to all game participants and which steer the system towards a game-theoretic equilibrium (e.g., Nash equilibrium). To detect attacks on the linear channel, we develop a novel quadratic-utility-aware observer that leverages the secured quadratic output and enforces measurement consistency via a projection step. We establish three properties for this observer: feasibility of the true state, prox-regularity of the quadratic-constraint set, and a monotone error-reduction guarantee in the noise-free case. To detect adversarial manipulation, we compare linear and quadratic observer trajectories using a wild bootstrap maximum mean discrepancy (MMD) test that provides valid inference under temporal dependence. We validate our framework using numerical experiments of a pursuit-evasion game, where the quadratic observer preserves estimation accuracy under linear-sensor attacks, while the statistical test detects distributional divergence between the observers' trajectories.

In modern large language models (LLMs), increasing sequence lengths is a crucial challenge for enhancing their comprehension and coherence in handling complex tasks such as multi-modal question answering. However, handling long context sequences with LLMs is prohibitively costly due to the conventional attention mechanism's quadratic time and space complexity, and the context window size is limited by the GPU memory. Although recent works have proposed linear and sparse attention mechanisms to address this issue, their real-world applicability is often limited by the need to re-train pre-trained models. In response, we propose a novel approach, Hierarchically Pruned Attention (HiP), which simultaneously reduces the training and inference time complexity from O(T^2) to O(T log T) and the space complexity from O(T^2) to O(T). To this end, we devise a dynamic sparse attention mechanism that generates an attention mask through a novel tree-search-like algorithm for a given query on the fly. HiP is training-free as it only utilizes the pre-trained attention scores to spot the positions of the top-k most significant elements for each query. Moreover, it ensures that no token is overlooked, unlike the sliding window-based sub-quadratic attention methods, such as StreamingLLM. Extensive experiments on diverse real-world benchmarks demonstrate that HiP significantly reduces prompt (i.e., prefill) and decoding latency and memory usage while maintaining high generation performance with little or no degradation. As HiP allows pretrained LLMs to scale to millions of tokens on commodity GPUs with no additional engineering due to its easy plug-and-play deployment, we believe that our work will have a large practical impact, opening up the possibility to many long-context LLM applications previously infeasible.

Recent work has shown that attention-based language models excel at recall, the ability to ground generations in tokens previously seen in context. However, the efficiency of attention-based models is bottle-necked during inference by the KV-cache's aggressive memory consumption. In this work, we explore whether we can improve language model efficiency (e.g. by reducing memory consumption) without compromising on recall. By applying experiments and theory to a broad set of architectures, we identify a key tradeoff between a model's state size and recall ability. We show that efficient alternatives to attention (e.g. H3, Mamba, RWKV) maintain a fixed-size recurrent state, but struggle at recall. We propose BASED a simple architecture combining linear and sliding window attention. By varying BASED window size and linear attention feature dimension, we can dial the state size and traverse the pareto frontier of the recall-memory tradeoff curve, recovering the full quality of attention on one end and the small state size of attention-alternatives on the other. We train language models up to 1.3b parameters and show that BASED matches the strongest sub-quadratic models (e.g. Mamba) in perplexity and outperforms them on real-world recall-intensive tasks by 6.22 accuracy points. Implementations of linear attention are often less efficient than optimized standard attention implementations. To make BASED competitive, we develop IO-aware algorithms that enable 24x higher throughput on language generation than FlashAttention-2, when generating 1024 tokens using 1.3b parameter models. Code for this work is provided at: https://github.com/HazyResearch/based.

The quadratic computation complexity of self-attention has been a persistent challenge when applying Transformer models to vision tasks. Linear attention, on the other hand, offers a much more efficient alternative with its linear complexity by approximating the Softmax operation through carefully designed mapping functions. However, current linear attention approaches either suffer from significant performance degradation or introduce additional computation overhead from the mapping functions. In this paper, we propose a novel Focused Linear Attention module to achieve both high efficiency and expressiveness. Specifically, we first analyze the factors contributing to the performance degradation of linear attention from two perspectives: the focus ability and feature diversity. To overcome these limitations, we introduce a simple yet effective mapping function and an efficient rank restoration module to enhance the expressiveness of self-attention while maintaining low computation complexity. Extensive experiments show that our linear attention module is applicable to a variety of advanced vision Transformers, and achieves consistently improved performances on multiple benchmarks. Code is available at https://github.com/LeapLabTHU/FLatten-Transformer.

Transformers have demonstrated strong performance across a wide range of sequence modeling tasks, but their quadratic attention complexity limits scalability to long sequences. Linear models such as Mamba and sliding-window attention (SWA) address this by mixing tokens through recurrent or localized operations with fixed-size memory, achieving efficient inference. However, these methods risk degrading performance on long sequences due to their inability to retain detailed information from distant tokens. We propose SCOUT (Segment Compression for Optimized Utility in Transformers), a hybrid architecture that compresses tokens locally within fixed-size segments and applies attention only over these compressed representations. Each token embedding is first enriched via a linear local mixer, Mamba or SWA, that integrates recent context. Then, instead of attending to all previous tokens, each token sparsely attends to a small number of compressed checkpoint tokens that summarize the input history. This design retains much of the expressivity of full attention while substantially reducing the computational and memory cost. By attending to compressed history rather than all previous tokens, SCOUT incurs slightly higher memory than purely linear models, but its growth rate remains sub-quadratic and far more scalable than that of full Transformers. We analyze SCOUT's computational and memory efficiency and evaluate it empirically on long-context language modeling and reasoning tasks. SCOUT with both Mamba and SWA mixers outperforms strong long-sequence baselines under the same computational budget, matches full-attention Transformers on language modeling and common-sense reasoning tasks at 400M and 1.3B scales. Moreover, our SCOUT achieves higher end-to-end throughput than SOTA models, while delivering comparable results on long sequence benchmarks.

Attention mechanisms, particularly softmax attention, have been instrumental in the success of transformer-based models such as GPT. However, the quadratic memory complexity of softmax attention with respect to sequence length poses significant challenges for processing longer sequences. We introduce Cottention, a novel attention mechanism that replaces the softmax operation with cosine similarity. By leveraging the properties of cosine similarity and rearranging the attention equation, Cottention achieves native linear memory complexity with respect to sequence length, making it inherently more memory-efficient than softmax attention. We demonstrate that Cottention can be reformulated as a recurrent neural network (RNN) with a finite hidden state, allowing for constant memory usage during inference. We evaluate Cottention on both the bidirectional BERT and causal GPT tasks, demonstrating comparable performance to softmax attention while significantly reducing memory requirements. To ensure efficient computation, we develop a custom CUDA kernel for Cottention. Our results show that Cottention is a promising alternative to softmax attention, enabling the processing of longer sequences without sacrificing performance, due to its native linear memory complexity and ability to maintain a constant memory footprint during inference.

As the core operator of Transformers, Softmax Attention exhibits excellent global modeling capabilities. However, its quadratic complexity limits its applicability to vision tasks. In contrast, Linear Attention shares a similar formulation with Softmax Attention while achieving linear complexity, enabling efficient global information modeling. Nevertheless, Linear Attention suffers from a significant performance degradation compared to standard Softmax Attention. In this paper, we analyze the underlying causes of this issue based on the formulation of Linear Attention. We find that, unlike Softmax Attention, Linear Attention entirely disregards the magnitude information of the Query. This prevents the attention score distribution from dynamically adapting as the Query scales. As a result, despite its structural similarity to Softmax Attention, Linear Attention exhibits a significantly different attention score distribution. Based on this observation, we propose Magnitude-Aware Linear Attention (MALA), which modifies the computation of Linear Attention to fully incorporate the Query's magnitude. This adjustment allows MALA to generate an attention score distribution that closely resembles Softmax Attention while exhibiting a more well-balanced structure. We evaluate the effectiveness of MALA on multiple tasks, including image classification, object detection, instance segmentation, semantic segmentation, natural language processing, speech recognition, and image generation. Our MALA achieves strong results on all of these tasks. Code will be available at https://github.com/qhfan/MALA

Large language models have exhibited intriguing in-context learning capability, achieving promising zero- and few-shot performance without updating the parameters. However, conventional in-context learning is usually restricted by length constraints, rendering it ineffective to absorb supervision from a large number of examples. In order to go beyond few shots, we introduce structured prompting that breaks the length limit and scales in-context learning to thousands of examples. Specifically, demonstration examples are separately encoded with well-designed position embeddings, and then they are jointly attended by the test example using a rescaled attention mechanism. So we can scale the number of exemplars with linear complexity instead of quadratic complexity with respect to length. Experimental results on a diverse set of tasks show that our approach improves end-task performance and reduces evaluation variance over conventional in-context learning as the number of demonstration examples increases. Code has been released at https://aka.ms/structured-prompting.

Recent advances in efficient sequence modeling have led to attention-free layers, such as Mamba, RWKV, and various gated RNNs, all featuring sub-quadratic complexity in sequence length and excellent scaling properties, enabling the construction of a new type of foundation models. In this paper, we present a unified view of these models, formulating such layers as implicit causal self-attention layers. The formulation includes most of their sub-components and is not limited to a specific part of the architecture. The framework compares the underlying mechanisms on similar grounds for different layers and provides a direct means for applying explainability methods. Our experiments show that our attention matrices and attribution method outperform an alternative and a more limited formulation that was recently proposed for Mamba. For the other architectures for which our method is the first to provide such a view, our method is effective and competitive in the relevant metrics compared to the results obtained by state-of-the-art transformer explainability methods. Our code is publicly available.

Graph transformers (GTs) have emerged as a promising architecture that is theoretically more expressive than message-passing graph neural networks (GNNs). However, typical GT models have at least quadratic complexity and thus cannot scale to large graphs. While there are several linear GTs recently proposed, they still lag behind GNN counterparts on several popular graph datasets, which poses a critical concern on their practical expressivity. To balance the trade-off between expressivity and scalability of GTs, we propose Polynormer, a polynomial-expressive GT model with linear complexity. Polynormer is built upon a novel base model that learns a high-degree polynomial on input features. To enable the base model permutation equivariant, we integrate it with graph topology and node features separately, resulting in local and global equivariant attention models. Consequently, Polynormer adopts a linear local-to-global attention scheme to learn high-degree equivariant polynomials whose coefficients are controlled by attention scores. Polynormer has been evaluated on 13 homophilic and heterophilic datasets, including large graphs with millions of nodes. Our extensive experiment results show that Polynormer outperforms state-of-the-art GNN and GT baselines on most datasets, even without the use of nonlinear activation functions.

Recent studies of gradient descent with large step sizes have shown that there is often a regime with an initial increase in the largest eigenvalue of the loss Hessian (progressive sharpening), followed by a stabilization of the eigenvalue near the maximum value which allows convergence (edge of stability). These phenomena are intrinsically non-linear and do not happen for models in the constant Neural Tangent Kernel (NTK) regime, for which the predictive function is approximately linear in the parameters. As such, we consider the next simplest class of predictive models, namely those that are quadratic in the parameters, which we call second-order regression models. For quadratic objectives in two dimensions, we prove that this second-order regression model exhibits progressive sharpening of the NTK eigenvalue towards a value that differs slightly from the edge of stability, which we explicitly compute. In higher dimensions, the model generically shows similar behavior, even without the specific structure of a neural network, suggesting that progressive sharpening and edge-of-stability behavior aren't unique features of neural networks, and could be a more general property of discrete learning algorithms in high-dimensional non-linear models.

We present a novel neural network for processing sequences. The ByteNet is a one-dimensional convolutional neural network that is composed of two parts, one to encode the source sequence and the other to decode the target sequence. The two network parts are connected by stacking the decoder on top of the encoder and preserving the temporal resolution of the sequences. To address the differing lengths of the source and the target, we introduce an efficient mechanism by which the decoder is dynamically unfolded over the representation of the encoder. The ByteNet uses dilation in the convolutional layers to increase its receptive field. The resulting network has two core properties: it runs in time that is linear in the length of the sequences and it sidesteps the need for excessive memorization. The ByteNet decoder attains state-of-the-art performance on character-level language modelling and outperforms the previous best results obtained with recurrent networks. The ByteNet also achieves state-of-the-art performance on character-to-character machine translation on the English-to-German WMT translation task, surpassing comparable neural translation models that are based on recurrent networks with attentional pooling and run in quadratic time. We find that the latent alignment structure contained in the representations reflects the expected alignment between the tokens.

Transformers based on the attention mechanism have achieved impressive success in various areas. However, the attention mechanism has a quadratic complexity, significantly impeding Transformers from dealing with numerous tokens and scaling up to bigger models. Previous methods mainly utilize the similarity decomposition and the associativity of matrix multiplication to devise linear-time attention mechanisms. They avoid degeneration of attention to a trivial distribution by reintroducing inductive biases such as the locality, thereby at the expense of model generality and expressiveness. In this paper, we linearize Transformers free from specific inductive biases based on the flow network theory. We cast attention as the information flow aggregated from the sources (values) to the sinks (results) through the learned flow capacities (attentions). Within this framework, we apply the property of flow conservation into attention and propose the Flow-Attention mechanism of linear complexity. By respectively conserving the incoming flow of sinks for source competition and the outgoing flow of sources for sink allocation, Flow-Attention inherently generates informative attentions without using specific inductive biases. Empowered by the Flow-Attention, Flowformer yields strong performance in linear time for wide areas, including long sequence, time series, vision, natural language, and reinforcement learning. The code and settings are available at this repository: https://github.com/thuml/Flowformer.

Autoregressive Large Language Models (LLMs) have achieved impressive performance in language tasks but face two significant bottlenecks: (1) quadratic complexity in the attention module as the number of tokens increases, and (2) limited efficiency due to the sequential processing nature of autoregressive LLMs during generation. While linear attention and speculative decoding offer potential solutions, their applicability and synergistic potential for enhancing autoregressive LLMs remain uncertain. We conduct the first comprehensive study on the efficacy of existing linear attention methods for autoregressive LLMs, integrating them with speculative decoding. We introduce an augmentation technique for linear attention that ensures compatibility with speculative decoding, enabling more efficient training and serving of LLMs. Extensive experiments and ablation studies involving seven existing linear attention models and five encoder/decoder-based LLMs consistently validate the effectiveness of our augmented linearized LLMs. Notably, our approach achieves up to a 6.67 reduction in perplexity on the LLaMA model and up to a 2times speedup during generation compared to prior linear attention methods. Codes and models are available at https://github.com/GATECH-EIC/Linearized-LLM.

Transformers have become the de facto standard for a wide range of tasks, from image classification to physics simulations. Despite their impressive performance, the quadratic complexity of standard Transformers in both memory and time with respect to the input length makes them impractical for processing high-resolution inputs. Therefore, several variants have been proposed, the most successful relying on patchification, downsampling, or coarsening techniques, often at the cost of losing the finest-scale details. In this work, we take a different approach. Inspired by state-of-the-art techniques in n-body numerical simulations, we cast attention as an interaction problem between grid points. We introduce the Multipole Attention Neural Operator (MANO), which computes attention in a distance-based multiscale fashion. MANO maintains, in each attention head, a global receptive field and achieves linear time and memory complexity with respect to the number of grid points. Empirical results on image classification and Darcy flows demonstrate that MANO rivals state-of-the-art models such as ViT and Swin Transformer, while reducing runtime and peak memory usage by orders of magnitude. We open source our code for reproducibility at https://github.com/AlexColagrande/MANO.

Knowledge distillation is a widely used technique for compressing large language models (LLMs), in which a smaller student model is trained to mimic a larger teacher model. Typically, both the teacher and student models are Transformer-based architectures, leveraging softmax attention for sequence modeling. However, the quadratic complexity of self-attention during inference remains a significant bottleneck, motivating the exploration of subquadratic alternatives such as structured state-space models (SSMs), linear attention, and recurrent architectures. In this work, we systematically evaluate the transferability of knowledge distillation from a Transformer teacher model to eight subquadratic student architectures. Our study investigates which subquadratic model can most effectively approximate the teacher model's learned representations through knowledge distillation, and how different architectural design choices influence the training dynamics. We further investigate the impact of initialization strategies, such as matrix mixing and query-key-value (QKV) copying, on the adaptation process. Our empirical results on multiple NLP benchmarks provide insights into the trade-offs between efficiency and performance, highlighting key factors for successful knowledge transfer to subquadratic architectures.

Vision Transformers (ViTs) have recently taken computer vision by storm. However, the softmax attention underlying ViTs comes with a quadratic complexity in time and memory, hindering the application of ViTs to high-resolution images. We revisit the attention design and propose a linear attention method to address the limitation, which doesn't sacrifice ViT's core advantage of capturing global representation like existing methods (e.g. local window attention of Swin). We further investigate the key difference between linear attention and softmax attention. Our empirical results suggest that linear attention lacks a fundamental property of concentrating the distribution of the attention matrix. Inspired by this observation, we introduce a local concentration module to enhance linear attention. By incorporating enhanced linear global attention and local window attention, we propose a new ViT architecture, dubbed L^2ViT. Notably, L^2ViT can effectively capture both global interactions and local representations while enjoying linear computational complexity. Extensive experiments demonstrate the strong performance of L^2ViT. On image classification, L^2ViT achieves 84.4% Top-1 accuracy on ImageNet-1K without any extra training data or label. By further pre-training on ImageNet-22k, it attains 87.0% when fine-tuned with resolution 384^2. For downstream tasks, L^2ViT delivers favorable performance as a backbone on object detection as well as semantic segmentation.

When predicting the next token in a sequence, vanilla transformers compute attention over all previous tokens, resulting in quadratic scaling of compute with sequence length. State-space models compress the entire sequence of tokens into a fixed-dimensional representation to improve efficiency, while other architectures achieve sub-quadratic complexity via low-rank projections or sparse attention patterns over the sequence. In this paper, we introduce Attamba, a novel architecture that uses state-space models to compress chunks of tokens and applies attention on these compressed key-value representations. We find that replacing key and value projections in a transformer with SSMs can improve model quality and enable flexible token chunking, resulting in 24% improved perplexity with transformer of similar KV-Cache and attention footprint, and ~4 times smaller KV-Cache and Attention FLOPs for 5% perplexity trade-off. Attamba can perform attention on chunked-sequences of variable length, enabling a smooth transition between quadratic and linear scaling, offering adaptable efficiency gains.

Document-level machine translation leverages inter-sentence dependencies to produce more coherent and consistent translations. However, these models, predominantly based on transformers, are difficult to scale to long documents as their attention layers have quadratic complexity in the sequence length. Recent efforts on efficient attention improve scalability, but their effect on document translation remains unexplored. In this work, we investigate the efficacy of a recent linear attention model by Peng et al. (2021) on document translation and augment it with a sentential gate to promote a recency inductive bias. We evaluate the model on IWSLT 2015 and OpenSubtitles 2018 against the transformer, demonstrating substantially increased decoding speed on long sequences with similar or better BLEU scores. We show that sentential gating further improves translation quality on IWSLT.

In pursuit of faster computation, Efficient Transformers demonstrate an impressive variety of approaches -- models attaining sub-quadratic attention complexity can utilize a notion of sparsity or a low-rank approximation of inputs to reduce the number of attended keys; other ways to reduce complexity include locality-sensitive hashing, key pooling, additional memory to store information in compacted or hybridization with other architectures, such as CNN. Often based on a strong mathematical basis, kernelized approaches allow for the approximation of attention with linear complexity while retaining high accuracy. Therefore, in the present paper, we aim to expand the idea of trainable kernel methods to approximate the self-attention mechanism of the Transformer architecture.

We present a novel non attention based architecture for large language models (LLMs) that efficiently handles very long context windows, on the order of hundreds of thousands to potentially millions of tokens. Unlike traditional Transformer designs, which suffer from quadratic memory and computation overload due to the nature of the self attention mechanism, our model avoids token to token attention entirely. Instead, it combines the following complementary components: State Space blocks (inspired by S4) that learn continuous time convolution kernels and scale near linearly with sequence length, Multi Resolution Convolution layers that capture local context at different dilation levels, a lightweight Recurrent Supervisor to maintain a global hidden state across sequential chunks, and Retrieval Augmented External Memory that stores and retrieves high-level chunk embeddings without reintroducing quadratic operations.

In Diffusion Transformer (DiT) models, particularly for video generation, attention latency is a major bottleneck due to the long sequence length and the quadratic complexity. We find that attention weights can be separated into two parts: a small fraction of large weights with high rank and the remaining weights with very low rank. This naturally suggests applying sparse acceleration to the first part and low-rank acceleration to the second. Based on this finding, we propose SLA (Sparse-Linear Attention), a trainable attention method that fuses sparse and linear attention to accelerate diffusion models. SLA classifies attention weights into critical, marginal, and negligible categories, applying O(N^2) attention to critical weights, O(N) attention to marginal weights, and skipping negligible ones. SLA combines these computations into a single GPU kernel and supports both forward and backward passes. With only a few fine-tuning steps using SLA, DiT models achieve a 20x reduction in attention computation, resulting in significant acceleration without loss of generation quality. Experiments show that SLA reduces attention computation by 95% without degrading end-to-end generation quality, outperforming baseline methods. In addition, we implement an efficient GPU kernel for SLA, which yields a 13.7x speedup in attention computation and a 2.2x end-to-end speedup in video generation on Wan2.1-1.3B.

The ability of an architecture to realize permutations is quite fundamental. For example, Large Language Models need to be able to correctly copy (and perhaps rearrange) parts of the input prompt into the output. Classical universal approximation theorems guarantee the existence of parameter configurations that solve this task but offer no insights into whether gradient-based algorithms can find them. In this paper, we address this gap by focusing on two-layer fully connected feed-forward neural networks and the task of learning permutations on nonzero binary inputs. We show that in the infinite width Neural Tangent Kernel (NTK) regime, an ensemble of such networks independently trained with gradient descent on only the k standard basis vectors out of 2^k - 1 possible inputs successfully learns any fixed permutation of length k with arbitrarily high probability. By analyzing the exact training dynamics, we prove that the network's output converges to a Gaussian process whose mean captures the ground truth permutation via sign-based features. We then demonstrate how averaging these runs (an "ensemble" method) and applying a simple rounding step yields an arbitrarily accurate prediction on any possible input unseen during training. Notably, the number of models needed to achieve exact learning with high probability (which we refer to as ensemble complexity) exhibits a linearithmic dependence on the input size k for a single test input and a quadratic dependence when considering all test inputs simultaneously.

Recent advances in text-to-video (T2V) generation have enabled the creation of high-fidelity, temporally coherent clips from natural language prompts. Yet these systems come with significant computational costs, and their energy demands remain poorly understood. In this paper, we present a systematic study of the latency and energy consumption of state-of-the-art open-source T2V models. We first develop a compute-bound analytical model that predicts scaling laws with respect to spatial resolution, temporal length, and denoising steps. We then validate these predictions through fine-grained experiments on WAN2.1-T2V, showing quadratic growth with spatial and temporal dimensions, and linear scaling with the number of denoising steps. Finally, we extend our analysis to six diverse T2V models, comparing their runtime and energy profiles under default settings. Our results provide both a benchmark reference and practical insights for designing and deploying more sustainable generative video systems.

The quadratic complexity and weak length extrapolation of Transformers limits their ability to scale to long sequences, and while sub-quadratic solutions like linear attention and state space models exist, they empirically underperform Transformers in pretraining efficiency and downstream task accuracy. We introduce Megalodon, a neural architecture for efficient sequence modeling with unlimited context length. Megalodon inherits the architecture of Mega (exponential moving average with gated attention), and further introduces multiple technical components to improve its capability and stability, including complex exponential moving average (CEMA), timestep normalization layer, normalized attention mechanism and pre-norm with two-hop residual configuration. In a controlled head-to-head comparison with Llama2, Megalodon achieves better efficiency than Transformer in the scale of 7 billion parameters and 2 trillion training tokens. Megalodon reaches a training loss of 1.70, landing mid-way between Llama2-7B (1.75) and 13B (1.67). Code: https://github.com/XuezheMax/megalodon

Scaling Transformers to longer sequence lengths has been a major problem in the last several years, promising to improve performance in language modeling and high-resolution image understanding, as well as to unlock new applications in code, audio, and video generation. The attention layer is the main bottleneck in scaling to longer sequences, as its runtime and memory increase quadratically in the sequence length. FlashAttention exploits the asymmetric GPU memory hierarchy to bring significant memory saving (linear instead of quadratic) and runtime speedup (2-4times compared to optimized baselines), with no approximation. However, FlashAttention is still not nearly as fast as optimized matrix-multiply (GEMM) operations, reaching only 25-40\% of the theoretical maximum FLOPs/s. We observe that the inefficiency is due to suboptimal work partitioning between different thread blocks and warps on the GPU, causing either low-occupancy or unnecessary shared memory reads/writes. We propose FlashAttention-2, with better work partitioning to address these issues. In particular, we (1) tweak the algorithm to reduce the number of non-matmul FLOPs (2) parallelize the attention computation, even for a single head, across different thread blocks to increase occupancy, and (3) within each thread block, distribute the work between warps to reduce communication through shared memory. These yield around 2times speedup compared to FlashAttention, reaching 50-73\% of the theoretical maximum FLOPs/s on A100 and getting close to the efficiency of GEMM operations. We empirically validate that when used end-to-end to train GPT-style models, FlashAttention-2 reaches training speed of up to 225 TFLOPs/s per A100 GPU (72\% model FLOPs utilization).

Video diffusion models (DMs) have enabled high-quality video synthesis. However, their computation costs scale quadratically with sequence length because self-attention has quadratic complexity. While linear attention lowers the cost, fully replacing quadratic attention requires expensive pretraining due to the limited expressiveness of linear attention and the complexity of spatiotemporal modeling in video generation. In this paper, we present LinVideo, an efficient data-free post-training framework that replaces a target number of self-attention modules with linear attention while preserving the original model's performance. First, we observe a significant disparity in the replaceability of different layers. Instead of manual or heuristic choices, we frame layer selection as a binary classification problem and propose selective transfer, which automatically and progressively converts layers to linear attention with minimal performance impact. Additionally, to overcome the ineffectiveness and inefficiency of existing objectives for this transfer process, we introduce an anytime distribution matching (ADM) objective that aligns the distributions of samples across any timestep along the sampling trajectory. This objective is efficient and recovers model performance. Extensive experiments show that our method achieves a 1.25-2.00x speedup while preserving generation quality, and our 4-step distilled model further delivers a 15.92x latency reduction with minimal visual quality drop.

Nowadays, Large Language Models (LLMs) have been trained using extended context lengths to foster more creative applications. However, long context training poses great challenges considering the constraint of GPU memory. It not only leads to substantial activation memory consumption during training, but also incurs considerable memory fragmentation. To facilitate long context training, existing frameworks have adopted strategies such as recomputation and various forms of parallelisms. Nevertheless, these techniques rely on redundant computation or extensive communication, resulting in low Model FLOPS Utilization (MFU). In this paper, we propose MEMO, a novel LLM training framework designed for fine-grained activation memory management. Given the quadratic scaling of computation and linear scaling of memory with sequence lengths when using FlashAttention, we offload memory-consuming activations to CPU memory after each layer's forward pass and fetch them during the backward pass. To maximize the swapping of activations without hindering computation, and to avoid exhausting limited CPU memory, we implement a token-wise activation recomputation and swapping mechanism. Furthermore, we tackle the memory fragmentation issue by employing a bi-level Mixed Integer Programming (MIP) approach, optimizing the reuse of memory across transformer layers. Empirical results demonstrate that MEMO achieves an average of 2.42x and 2.26x MFU compared to Megatron-LM and DeepSpeed, respectively. This improvement is attributed to MEMO's ability to minimize memory fragmentation, reduce recomputation and intensive communication, and circumvent the delays associated with the memory reorganization process due to fragmentation. By leveraging fine-grained activation memory management, MEMO facilitates efficient training of 7B LLM with 1 million sequence length on just 8 A800 GPUs, achieving an MFU of 52.30%.

Multi-headed Attention's (MHA) quadratic compute and linearly growing KV-cache make long-context transformers expensive to train and serve. Prior works such as Grouped Query Attention (GQA) and Multi-Latent Attention (MLA) shrink the cache, speeding decode, but leave compute, which determines prefill and training speed, largely unchanged. We introduce Compressed Convolutional Attention (CCA), a novel attention method which down-projects queries, keys, and values and performs the entire attention operation inside the shared latent space. This simple design dramatically cuts parameters, KV-cache, and FLOPs all at once by the desired compression factor. Because CCA is orthogonal to head-sharing, we combine the two to form Compressed Convolutional Grouped Query Attention (CCGQA), which further tightens the compute-bandwidth Pareto frontier so that users can tune compression toward either FLOP or memory limits without sacrificing quality. Experiments show that CCGQA consistently outperforms both GQA and MLA at equal KV-cache compression on dense and MoE models. Additionally, we show that CCGQA outperforms all other attention methods on MoE models with half the KV-cache of GQA and MLA, achieving an 8x KV-cache compression with no drop in performance compared to standard MHA. CCA and CCGQA also dramatically reduce the FLOP cost of attention which leads to substantially faster training and prefill than existing methods. On H100 GPUs, our fused CCA/CCGQA kernel reduces prefill latency by about 1.7x at a sequence length of 16k relative to MHA, and accelerates backward by about 1.3x.

Vision Transformers (ViTs) have shown impressive performance and have become a unified backbone for multiple vision tasks. But both attention and multi-layer perceptions (MLPs) in ViTs are not efficient enough due to dense multiplications, resulting in costly training and inference. To this end, we propose to reparameterize the pre-trained ViT with a mixture of multiplication primitives, e.g., bitwise shifts and additions, towards a new type of multiplication-reduced model, dubbed ShiftAddViT, which aims for end-to-end inference speedups on GPUs without the need of training from scratch. Specifically, all MatMuls among queries, keys, and values are reparameterized by additive kernels, after mapping queries and keys to binary codes in Hamming space. The remaining MLPs or linear layers are then reparameterized by shift kernels. We utilize TVM to implement and optimize those customized kernels for practical hardware deployment on GPUs. We find that such a reparameterization on (quadratic or linear) attention maintains model accuracy, while inevitably leading to accuracy drops when being applied to MLPs. To marry the best of both worlds, we further propose a new mixture of experts (MoE) framework to reparameterize MLPs by taking multiplication or its primitives as experts, e.g., multiplication and shift, and designing a new latency-aware load-balancing loss. Such a loss helps to train a generic router for assigning a dynamic amount of input tokens to different experts according to their latency. In principle, the faster experts run, the larger amount of input tokens are assigned. Extensive experiments consistently validate the effectiveness of our proposed ShiftAddViT, achieving up to 5.18\times$ latency reductions on GPUs and 42.9%$ energy savings, while maintaining comparable accuracy as original or efficient ViTs.

The Transformer architecture has significantly advanced natural language processing (NLP) and has been foundational in developing large language models (LLMs) such as LLaMA and OPT, which have come to dominate a broad range of NLP tasks. Despite their superior accuracy, LLMs present unique challenges in practical inference, concerning the compute and memory-intensive nature. Thanks to the autoregressive characteristic of LLM inference, KV caching for the attention layers in Transformers can effectively accelerate LLM inference by substituting quadratic-complexity computation with linear-complexity memory accesses. Yet, this approach requires increasing memory as demand grows for processing longer sequences. The overhead leads to reduced throughput due to I/O bottlenecks and even out-of-memory errors, particularly on resource-constrained systems like a single commodity GPU. In this paper, we propose ALISA, a novel algorithm-system co-design solution to address the challenges imposed by KV caching. On the algorithm level, ALISA prioritizes tokens that are most important in generating a new token via a Sparse Window Attention (SWA) algorithm. SWA introduces high sparsity in attention layers and reduces the memory footprint of KV caching at negligible accuracy loss. On the system level, ALISA employs three-phase token-level dynamical scheduling and optimizes the trade-off between caching and recomputation, thus maximizing the overall performance in resource-constrained systems. In a single GPU-CPU system, we demonstrate that under varying workloads, ALISA improves the throughput of baseline systems such as FlexGen and vLLM by up to 3X and 1.9X, respectively.

Since its introduction, softmax attention has become the backbone of modern transformer architectures due to its expressiveness and scalability across a wide range of tasks. However, the main drawback of softmax attention is the quadratic memory requirement and computational complexity with respect to the sequence length. By replacing the softmax nonlinearity, linear attention and similar methods have been introduced to avoid the quadratic bottleneck of softmax attention. Despite these linear forms of attention being derived from the original softmax formulation, they typically lag in terms of downstream accuracy. While strong intuition of the softmax nonlinearity on the query and key inner product suggests that it has desirable properties compared to other nonlinearities, the question of why this discrepancy exists still remains unanswered. This work demonstrates that linear attention is an approximation of softmax attention by deriving the recurrent form of softmax attention. Using this form, each part of softmax attention can be described in the language of recurrent neural networks (RNNs). Describing softmax attention as an RNN allows for the ablation of the components of softmax attention to understand the importance of each part and how they interact. In this way, our work helps explain why softmax attention is more expressive than its counterparts.

With the advancement of RNN models with linear complexity, the quadratic complexity challenge of transformers has the potential to be overcome. Notably, the emerging Mamba-2 has demonstrated competitive performance, bridging the gap between RNN models and transformers. However, due to sequential processing and vanishing gradients, RNN models struggle to capture long-range dependencies, limiting contextual understanding. This results in slow convergence, high resource demands, and poor performance on downstream understanding and complex reasoning tasks. In this work, we present a hybrid model MaTVLM by substituting a portion of the transformer decoder layers in a pre-trained VLM with Mamba-2 layers. Leveraging the inherent relationship between attention and Mamba-2, we initialize Mamba-2 with corresponding attention weights to accelerate convergence. Subsequently, we employ a single-stage distillation process, using the pre-trained VLM as the teacher model to transfer knowledge to the MaTVLM, further enhancing convergence speed and performance. Furthermore, we investigate the impact of differential distillation loss within our training framework. We evaluate the MaTVLM on multiple benchmarks, demonstrating competitive performance against the teacher model and existing VLMs while surpassing both Mamba-based VLMs and models of comparable parameter scales. Remarkably, the MaTVLM achieves up to 3.6x faster inference than the teacher model while reducing GPU memory consumption by 27.5%, all without compromising performance. Code and models are released at http://github.com/hustvl/MaTVLM.

We introduce VideoMamba, a novel adaptation of the pure Mamba architecture, specifically designed for video recognition. Unlike transformers that rely on self-attention mechanisms leading to high computational costs by quadratic complexity, VideoMamba leverages Mamba's linear complexity and selective SSM mechanism for more efficient processing. The proposed Spatio-Temporal Forward and Backward SSM allows the model to effectively capture the complex relationship between non-sequential spatial and sequential temporal information in video. Consequently, VideoMamba is not only resource-efficient but also effective in capturing long-range dependency in videos, demonstrated by competitive performance and outstanding efficiency on a variety of video understanding benchmarks. Our work highlights the potential of VideoMamba as a powerful tool for video understanding, offering a simple yet effective baseline for future research in video analysis.

Training large language models (LLMs) with increasingly long and varying sequence lengths introduces severe load imbalance challenges in large-scale data-parallel training. Recent frameworks attempt to mitigate these issues through data reorganization or hybrid parallel strategies. However, they often overlook how computational and communication costs scale with sequence length, resulting in suboptimal performance. We identify three critical challenges: (1) varying computation-to-communication ratios across sequences of different lengths in distributed attention, (2) mismatch between static NIC-GPU affinity and dynamic parallel workloads, and (3) distinct optimal partitioning strategies required for quadratic attention versus linear components. To address these challenges, we present Zeppelin, a novel training system that integrates three key techniques: (1) a hierarchical sequence partitioning method for the attention module that reduces communication overhead and balances computation, supported by an efficient attention engine that applies divergent parallel strategies; (2) a routing layer that orchestrates inter-node transfers to fully utilize NIC bandwidth; and (3) a remapping layer that transforms sequence layouts between attention and linear modules, ensuring high computational efficiency across both. Comprehensive evaluations across diverse configurations show that Zeppelin delivers an average 2.80x speedup over state-of-the-art methods.

Counterexample-guided repair aims at creating neural networks with mathematical safety guarantees, facilitating the application of neural networks in safety-critical domains. However, whether counterexample-guided repair is guaranteed to terminate remains an open question. We approach this question by showing that counterexample-guided repair can be viewed as a robust optimisation algorithm. While termination guarantees for neural network repair itself remain beyond our reach, we prove termination for more restrained machine learning models and disprove termination in a general setting. We empirically study the practical implications of our theoretical results, demonstrating the suitability of common verifiers and falsifiers for repair despite a disadvantageous theoretical result. Additionally, we use our theoretical insights to devise a novel algorithm for repairing linear regression models based on quadratic programming, surpassing existing approaches.

Bayesian optimisation is a popular approach for optimising expensive black-box functions. The next location to be evaluated is selected via maximising an acquisition function that balances exploitation and exploration. Gaussian processes, the surrogate models of choice in Bayesian optimisation, are often used with a constant prior mean function equal to the arithmetic mean of the observed function values. We show that the rate of convergence can depend sensitively on the choice of mean function. We empirically investigate 8 mean functions (constant functions equal to the arithmetic mean, minimum, median and maximum of the observed function evaluations, linear, quadratic polynomials, random forests and RBF networks), using 10 synthetic test problems and two real-world problems, and using the Expected Improvement and Upper Confidence Bound acquisition functions. We find that for design dimensions ge5 using a constant mean function equal to the worst observed quality value is consistently the best choice on the synthetic problems considered. We argue that this worst-observed-quality function promotes exploitation leading to more rapid convergence. However, for the real-world tasks the more complex mean functions capable of modelling the fitness landscape may be effective, although there is no clearly optimum choice.

Recent advancements in sequence modeling have led to the emergence of Structured State Space Models (SSMs) as an efficient alternative to Recurrent Neural Networks (RNNs) and Transformers, addressing challenges in long-range dependency modeling and computational efficiency. While RNNs suffer from vanishing gradients and sequential inefficiencies, and Transformers face quadratic complexity, SSMs leverage structured recurrence and state-space representations to achieve superior long-sequence processing with linear or near-linear complexity. This survey provides a comprehensive review of SSMs, tracing their evolution from the foundational S4 model to its successors like Mamba, Simplified Structured State Space Sequence Model (S5), and Jamba, highlighting their improvements in computational efficiency, memory optimization, and inference speed. By comparing SSMs with traditional sequence models across domains such as natural language processing (NLP), speech recognition, vision, and time-series forecasting, we demonstrate their advantages in handling long-range dependencies while reducing computational overhead. Despite their potential, challenges remain in areas such as training optimization, hybrid modeling, and interpretability. This survey serves as a structured guide for researchers and practitioners, detailing the advancements, trade-offs, and future directions of SSM-based architectures in AI and deep learning.

Motivated by the problem of fast processing of attention matrices, we study fast algorithms for computing matrix-vector products for asymmetric Gaussian Kernel matrices Kin R^{ntimes n}. K's columns are indexed by a set of n keys k_1,k_2ldots, k_nin R^d, rows by a set of n queries q_1,q_2,ldots,q_nin R^d , and its i,j entry is K_{ij} = e^{-|q_i-k_j|_2^2/2sigma^2} for some bandwidth parameter sigma>0. Given a vector xin R^n and error parameter epsilon>0, our task is to output a yin R^n such that |Kx-y|_2leq epsilon |x|_2 in time subquadratic in n and linear in d. Our algorithms rely on the following modelling assumption about the matrices K: the sum of the entries of K scales linearly in n, as opposed to worst case quadratic growth. We validate this assumption experimentally, for Gaussian kernel matrices encountered in various settings such as fast attention computation in LLMs. We obtain the first subquadratic-time algorithm that works under this assumption, for unrestricted vectors.

Large Language Models (LLMs) have made significant strides in natural language processing and generation, yet their ability to handle long-context input remains constrained by the quadratic complexity of attention computation and linear-increasing key-value memory footprint. To reduce computational costs and memory, key-value cache compression techniques are commonly applied at inference time, but this often leads to severe performance degradation, as models are not trained to handle compressed context. Although there are more sophisticated compression methods, they are typically unsuitable for post-training because of their incompatibility with gradient-based optimization or high computation overhead. To fill this gap with no additional parameter and little computation overhead, we propose Lag-Relative Sparse Attention(LRSA) anchored by the LagKV compression method for long context post-training. Our method performs chunk-by-chunk prefilling, which selects the top K most relevant key-value pairs in a fixed-size lagging window, allowing the model to focus on salient historical context while maintaining efficiency. Experimental results show that our approach significantly enhances the robustness of the LLM with key-value compression and achieves better fine-tuned results in the question-answer tuning task.