The paper investigates whether adaptive control of equivariance relaxation is necessary for neural networks to capture symmetry-breaking structure in data. By adding a residual path to a strictly equivariant model and limiting their interaction, the authors observe that the residual can either collapse or survive, a phenomenon they term asymmetry tunneling. They analyze this behavior across five benchmarks using four diagnostics and conclude that adaptive control of equivariance relaxation is not required to model symmetry-breaking patterns.
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.
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
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...
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.
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.
arXiv:2608.24700v1 Announce Type: new Abstract: When a network has learned a function with a known symmetry, can that symmetry be moved through the parametrisation---is there a motion in parameter sp...
arXiv:2610.17269v1 Announce Type: cross Abstract: Learning symmetries through data augmentation offers an alternative to architectural equivariance, but does not guarantee that a network respects tho...
arXiv:2607. 08561v1 Announce Type: new Abstract: A series of results from the NeuroAI over the past fifteen years have raised core questions both about how to compare Deep Neural Network (DNN) models to the brain, and about how much convergent evolution to expect between artificial networks and real brain networks.
arXiv:2606. 26273v1 Announce Type: new Abstract: Symmetries are important for many deep learning tasks, ranging from applications in the sciences to medical imaging.
arXiv:2505. 19619v3 Announce Type: replace Abstract: Deep generative models have recently garnered significant attention across various fields, from physics to chemistry, where sampling from unnormalized Boltzmann-like distributions represents a fundamental challenge.
arXiv:2602.23405v3 Announce Type: replace-cross Abstract: Varying the number of neurons while preserving function is difficult because neural networks' dense connectivity creates strong computational...