arXiv:2608. 01582v1 Announce Type: cross Abstract: Symmetry is central to modern machine learning and physics: invariances and equivariances improve sample efficiency, robustness, and out-of-distribution generalization, while symmetry principles guide scientific modeling.
By Shida Liu, Abhishek Gupta, Sumit Sinha, L. Mahadevan
arXiv:2512. 20043v3 Announce Type: replace Abstract: Symmetry is fundamental to understanding physical systems and can improve performance and sample efficiency in machine learning.
By Yuxuan Chen, Jung Yeon Park, Floor Eijkelboom, Jianke Yang, Jan-Willem van de Meent, Lawson L. S. Wong, Robin Walters
The paper introduces a diagnostic tool that measures how neural emulators of partial differential equations capture physical symmetries by evaluating the overlap of loss gradients along symmetry-related states. This metric probes the local geometry of the learned loss landscape and goes beyond traditional equivariance tests by directly assessing learning dynamics. Applied to autoregressive fluid flow emulators, the study shows that orbit-wise gradient coherence enables generalization over symmetry transformations and reveals when training selects a symmetry-compatible basin.
By James Amarel, Robyn Miller, Nicolas Hengartner, Benjamin Migliori, Emily Casleton, Alexei Skurikhin, Earl Lawrence, Gerd J. Kunde
The paper introduces LatentLieODE, a neural ODE framework that learns linear Lie symmetries and first integrals from time‑series data such as videos. It uses an autoencoder to obtain a low‑dimensional latent space, fits linear infinitesimal generators to a Lie‑bracket residual, and trains a latent ODE to reconstruct observations. The method successfully identifies symmetries and conserved quantities in six benchmark systems, achieving high correlation with ground‑truth invariants and recovering a non‑abelian σ(3) algebra on the sphere.
By Matt L. Wiemman, Peter Melchior
arXiv:2608. 08091v1 Announce Type: cross Abstract: Dynamical systems model trajectory data generated by fixed underlying dynamics, with applications ranging from biology to physics.
By Behrooz Tahmasebi, Melanie Weber
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.
By Eduardo Santos-Escriche, Valerie Engelmayer, Ya-Wei Eileen Lin, Stefanie Jegelka