Related papers: A Practical Guide for Incorporating Symmetry in Di…

Embodied agents operate in a structured world, often solving tasks with spatial, temporal, and permutation symmetries. Most algorithms for planning and model-based reinforcement learning (MBRL) do not take this rich geometric structure into…

Equivariant representation learning aims to capture variations induced by input transformations in the representation space, whereas invariant representation learning encodes semantic information by disregarding such transformations. Recent…

Flow matching models have emerged as a strong alternative to diffusion models, but existing inversion and editing methods designed for diffusion are often ineffective or inapplicable to them. The straight-line, non-crossing trajectories of…

Recently, a variety of new equivariant neural network model architectures have been proposed that generalize better over rotational and reflectional symmetries than standard models. These models are relevant to robotics because many…

Diffusion models are central to generative modeling and have been adapted to graphs by diffusing adjacency matrix representations. The challenge of having up to $n!$ such representations for graphs with $n$ nodes is only partially mitigated…

Diffusion models has emerged as a powerful framework for tasks like image controllable generation and dense prediction. However, existing models often struggle to capture underlying semantics (e.g., edges, textures, shapes) and effectively…

3D policy learning promises superior generalization and cross-embodiment transfer, but progress has been hindered by training instabilities and severe overfitting, precluding the adoption of powerful 3D perception models. In this work, we…

Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…

With a view to statistical inference for discretely observed diffusion models, we propose simple methods of simulating diffusion bridges, approximately and exactly. Diffusion bridge simulation plays a fundamental role in likelihood and…

In autonomous driving, deep learning enabled motion prediction is a popular topic. A critical gap in traditional motion prediction methodologies lies in ensuring equivariance under Euclidean geometric transformations and maintaining…

Successful coordination in Dec-POMDPs requires agents to adopt robust strategies and interpretable styles of play for their partner. A common failure mode is symmetry breaking, when agents arbitrarily converge on one out of many equivalent…

Accurately estimating camera motion from image sequences poses a significant challenge in computer vision and robotics. Many computer vision methods first compute the essential matrix associated with a motion and then extract orientation…

Diffusion-based policies have shown impressive performance in robotic manipulation tasks while struggling with out-of-domain distributions. Recent efforts attempted to enhance generalization by improving the visual feature encoding for…

Bifurcation phenomena in nonlinear dynamical systems often lead to multiple coexisting stable solutions, particularly in the presence of symmetry breaking. Deterministic machine learning models are unable to capture this multiplicity,…

Equivariance to symmetries has proven to be a powerful inductive bias in deep learning research. Recent works on mesh processing have concentrated on various kinds of natural symmetries, including translations, rotations, scaling, node…

The goal of point cloud assembly is to reconstruct a complete 3D shape by aligning multiple point cloud pieces. This work presents a novel equivariant solver for assembly tasks based on flow matching models. We first theoretically show that…

Achieving invariance to nuisance transformations is a fundamental challenge in the construction of robust and reliable vision systems. Existing approaches to invariance scale exponentially with the dimension of the family of…

Partial differential equation (PDE) models and their associated variational energy formulations are often rotationally invariant by design. This ensures that a rotation of the input results in a corresponding rotation of the output, which…

Wavelet scattering networks, which are convolutional neural networks (CNNs) with fixed filters and weights, are promising tools for image analysis. Imposing symmetry on image statistics can improve human interpretability, aid in…

Pooling multiple neuroimaging datasets across institutions often enables improvements in statistical power when evaluating associations (e.g., between risk factors and disease outcomes) that may otherwise be too weak to detect. When there…