Daily Papers

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Coarse-graining (CG) accelerates molecular simulations of protein dynamics by simulating sets of atoms as singular beads. Backmapping is the opposite operation of bringing lost atomistic details back from the CG representation. While machine learning (ML) has produced accurate and efficient CG simulations of proteins, fast and reliable backmapping remains a challenge. Rule-based methods produce poor all-atom geometries, needing computationally costly refinement through additional simulations. Recently proposed ML approaches outperform traditional baselines but are not transferable between proteins and sometimes generate unphysical atom placements with steric clashes and implausible torsion angles. This work addresses both issues to build a fast, transferable, and reliable generative backmapping tool for CG protein representations. We achieve generalization and reliability through a combined set of innovations: representation based on internal coordinates; an equivariant encoder/prior; a custom loss function that helps ensure local structure, global structure, and physical constraints; and expert curation of high-quality out-of-equilibrium protein data for training. Our results pave the way for out-of-the-box backmapping of coarse-grained simulations for arbitrary proteins.

The task of locating first order saddle points on high-dimensional surfaces describing the variation of energy as a function of atomic coordinates is an essential step for identifying the mechanism and estimating the rate of thermally activated events within the harmonic approximation of transition state theory. When combined directly with electronic structure calculations, the number of energy and atomic force evaluations needed for convergence is a primary issue. Here, we describe an efficient implementation of Gaussian process regression (GPR) acceleration of the minimum mode following method where a dimer is used to estimate the lowest eigenmode of the Hessian. A surrogate energy surface is constructed and updated after each electronic structure calculation. The method is applied to a test set of 500 molecular reactions previously generated by Hermez and coworkers [J. Chem. Theory Comput. 18, 6974 (2022)]. An order of magnitude reduction in the number of electronic structure calculations needed to reach the saddle point configurations is obtained by using the GPR compared to the dimer method. Despite the wide range in stiffness of the molecular degrees of freedom, the calculations are carried out using Cartesian coordinates and are found to require similar number of electronic structure calculations as an elaborate internal coordinate method implemented in the Sella software package. The present implementation of the GPR surrogate model in C++ is efficient enough for the wall time of the saddle point searches to be reduced in 3 out of 4 cases even though the calculations are carried out at a low Hartree-Fock level.

In pose estimation for seen objects, a prevalent pipeline involves using neural networks to predict dense 3D coordinates of the object surface on 2D images, which are then used to establish dense 2D-3D correspondences. However, current methods primarily focus on more efficient encoding techniques to improve the precision of predicted 3D coordinates on the object's front surface, overlooking the potential benefits of incorporating the back surface and interior of the object. To better utilize the full surface and interior of the object, this study predicts 3D coordinates of both the object's front and back surfaces and densely samples 3D coordinates between them. This process creates ultra-dense 2D-3D correspondences, effectively enhancing pose estimation accuracy based on the Perspective-n-Point (PnP) algorithm. Additionally, we propose Hierarchical Continuous Coordinate Encoding (HCCE) to provide a more accurate and efficient representation of front and back surface coordinates. Experimental results show that, compared to existing state-of-the-art (SOTA) methods on the BOP website, the proposed approach outperforms across seven classic BOP core datasets. Code is available at https://github.com/WangYuLin-SEU/HCCEPose.

From a single image, visual cues can help deduce intrinsic and extrinsic camera parameters like the focal length and the gravity direction. This single-image calibration can benefit various downstream applications like image editing and 3D mapping. Current approaches to this problem are based on either classical geometry with lines and vanishing points or on deep neural networks trained end-to-end. The learned approaches are more robust but struggle to generalize to new environments and are less accurate than their classical counterparts. We hypothesize that they lack the constraints that 3D geometry provides. In this work, we introduce GeoCalib, a deep neural network that leverages universal rules of 3D geometry through an optimization process. GeoCalib is trained end-to-end to estimate camera parameters and learns to find useful visual cues from the data. Experiments on various benchmarks show that GeoCalib is more robust and more accurate than existing classical and learned approaches. Its internal optimization estimates uncertainties, which help flag failure cases and benefit downstream applications like visual localization. The code and trained models are publicly available at https://github.com/cvg/GeoCalib.

Boundary point detection aims to outline the external contour structure of clusters and enhance the inter-cluster discrimination, thus bolstering the performance of the downstream classification and clustering tasks. However, existing boundary point detectors are sensitive to density heterogeneity or cannot identify boundary points in concave structures and high-dimensional manifolds. In this work, we propose a robust and efficient boundary point detection method based on Local Direction Dispersion (LoDD). The core of boundary point detection lies in measuring the difference between boundary points and internal points. It is a common observation that an internal point is surrounded by its neighbors in all directions, while the neighbors of a boundary point tend to be distributed only in a certain directional range. By considering this observation, we adopt density-independent K-Nearest Neighbors (KNN) method to determine neighboring points and design a centrality metric LoDD using the eigenvalues of the covariance matrix to depict the distribution uniformity of KNN. We also develop a grid-structure assumption of data distribution to determine the parameters adaptively. The effectiveness of LoDD is demonstrated on synthetic datasets, real-world benchmarks, and application of training set split for deep learning model and hole detection on point cloud data. The datasets and toolkit are available at: https://github.com/ZPGuiGroupWhu/lodd.

Robust locomotion control depends on accurate state estimations. However, the sensors of most legged robots can only provide partial and noisy observations, making the estimation particularly challenging, especially for external states like terrain frictions and elevation maps. Inspired by the classical Internal Model Control principle, we consider these external states as disturbances and introduce Hybrid Internal Model (HIM) to estimate them according to the response of the robot. The response, which we refer to as the hybrid internal embedding, contains the robot's explicit velocity and implicit stability representation, corresponding to two primary goals for locomotion tasks: explicitly tracking velocity and implicitly maintaining stability. We use contrastive learning to optimize the embedding to be close to the robot's successor state, in which the response is naturally embedded. HIM has several appealing benefits: It only needs the robot's proprioceptions, i.e., those from joint encoders and IMU as observations. It innovatively maintains consistent observations between simulation reference and reality that avoids information loss in mimicking learning. It exploits batch-level information that is more robust to noises and keeps better sample efficiency. It only requires 1 hour of training on an RTX 4090 to enable a quadruped robot to traverse any terrain under any disturbances. A wealth of real-world experiments demonstrates its agility, even in high-difficulty tasks and cases never occurred during the training process, revealing remarkable open-world generalizability.

Reconstructing 3D shapes from planar cross-sections is a challenge inspired by downstream applications like medical imaging and geographic informatics. The input is an in/out indicator function fully defined on a sparse collection of planes in space, and the output is an interpolation of the indicator function to the entire volume. Previous works addressing this sparse and ill-posed problem either produce low quality results, or rely on additional priors such as target topology, appearance information, or input normal directions. In this paper, we present OReX, a method for 3D shape reconstruction from slices alone, featuring a Neural Field as the interpolation prior. A modest neural network is trained on the input planes to return an inside/outside estimate for a given 3D coordinate, yielding a powerful prior that induces smoothness and self-similarities. The main challenge for this approach is high-frequency details, as the neural prior is overly smoothing. To alleviate this, we offer an iterative estimation architecture and a hierarchical input sampling scheme that encourage coarse-to-fine training, allowing the training process to focus on high frequencies at later stages. In addition, we identify and analyze a ripple-like effect stemming from the mesh extraction step. We mitigate it by regularizing the spatial gradients of the indicator function around input in/out boundaries during network training, tackling the problem at the root. Through extensive qualitative and quantitative experimentation, we demonstrate our method is robust, accurate, and scales well with the size of the input. We report state-of-the-art results compared to previous approaches and recent potential solutions, and demonstrate the benefit of our individual contributions through analysis and ablation studies.