arXiv:2511. 09432v2 Announce Type: replace Abstract: Machine learning (ML) models achieve remarkable performance but remain hard to interpret due to their scale and complexity.
By Ege Erdogan, Ana Lucic
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
By Ning Lin, Jiacheng Cen, Anyi Li, Wenbing Huang, Hao Sun
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
arXiv:2610.17424v1 Announce Type: cross
Abstract: Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks...
By Tomas Karella, Emily Shinkle, Alice Elisabeth Anastasia Allen, Pieter J. Swart, Nicholas Lubbers, Roxana Bujack
arXiv:2606. 04754v1 Announce Type: new Abstract: Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged.
By Vincent B\"urgin, Daniel Herbst, Ya-Wei Eileen Lin, Stefanie Jegelka
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