arXiv Machine Learning
Rotational Equivariance in Machine Learning: A Comprehensive Tutorial
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arXiv AI
Jun 30
Representation Learning for Equivariant Inference with Guarantees
arXiv:2505. 19809v3 Announce Type: replace-cross Abstract: In many real-world applications of regression, conditional probability estimation, and uncertainty quantification, exploiting symmetries rooted in physics or geometry can dramatically improve generalization and sample efficiency.
Hugging Face Trending Papers
Jul 1
Group-Equivariant Poincaré Convolutional Networks
While recent advancements like the Poincaré ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold. Furthermore, standard hyperbolic networks treat spatial transformations of the same object as distinct hierarchical concepts, leading to redundant parameter usage and vanishing signals.
arXiv AI
Jul 2
Group-Equivariant Poincar\'e Convolutional Networks
arXiv:2607. 00556v1 Announce Type: cross Abstract: While recent advancements like the Poincar\'e ResNet have demonstrated the potential of learning visual representations directly in hyperbolic space, their optimisation remains hampered by the computationally intensive nature of Riemannian gradients and the strict boundaries of the manifold.
arXiv Machine Learning
Aug 3
Moment kernels: a simple and scalable approach for equivariance to rotations and reflections in deep convolutional networks
arXiv:2505. 21736v2 Announce Type: replace-cross Abstract: Translation equivariance is a central reason convolutional neural networks have been successful in computer vision.
arXiv AI
Jun 3
EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs
arXiv:2606. 03260v1 Announce Type: cross Abstract: Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems.
arXiv Machine Learning
Oct 8
How Do Transformers Learn to Represent Symmetries?
The paper investigates how a vanilla Transformer learns symmetries from finite data augmentation on point cloud datasets. It finds an ordering of learnability: non-angle-preserving symmetries are easiest, followed by angle-preserving symmetries, and finally base angle-preserving subgroups such as translation, rotation, and scale. The study also examines the Transformer's extrapolation behavior, performs a structural analysis of trained models to uncover interpretable mechanisms for invariance, and extends these findings to equivariant functions, suggesting that the identified mechanisms can serve as building blocks for learned equivariance.