arXiv Machine Learning
Jul 7
A Complete Symmetry Classification of Shallow ReLU Networks
arXiv:2604. 14037v2 Announce Type: replace Abstract: Parameter space is not function space for neural network architectures.
Parameter-Level Attribution of Symmetry in Trained Networks Though Parameter-Wise Functional Sensitivity
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Hugging Face Trending Papers
Aug 12
Reducing Symmetry Increase in Equivariant Neural Networks
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 Machine Learning
Aug 13
Reducing Symmetry Increase in Equivariant Neural Networks
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
arXiv Machine Learning
Jun 4
Beyond Structural Symmetries: Linear Mode Connectivity via Neuron Identifiability
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.
arXiv Machine Learning
Jul 7
Observable- and Positional-Encoding-Dependent Symmetry Readout from Neural Network Weights
arXiv:2607. 03108v1 Announce Type: new Abstract: Post-hoc analysis of trained neural network weights often seeks to recover geometric structure directly from the parameters.
arXiv Machine Learning
2d ago
Parameter symmetries determine representational geometry in overparameterized nonlinear networks
arXiv:2609.39078v1 Announce Type: new Abstract: Representations are routinely used across machine learning, psychology, and neuroscience to draw inferences about the computations of biological and ar...
arXiv AI
Jun 18
A Link between Shock-wave Theory and Symmetry-reduced Stochastic Gradient Descent for Artificial Neural Networks
arXiv:2606. 18303v1 Announce Type: cross Abstract: We develop a mathematically explicit link between shock-wave theory and the symmetry-quotiented learning dynamics of stochastic gradient descent, drawing on differential geometry, Lie group theory, and fluid mechanics.
arXiv Machine Learning
Jul 10
Explaining Near-Zero Hessian Eigenvalues Through Approximate Symmetries in Neural Networks
arXiv:2607. 07845v1 Announce Type: new Abstract: The Hessian of the training loss governs the local geometry of the loss landscape, yet despite existing explanations for its largest eigenvalues, the origin of the vast multitude of vanishingly small eigenvalues remains elusive.
arXiv Machine Learning
Aug 27
Loss Landscape Geometry of Partial Differential Equation Emulators: Or, Symmetry Learning via Gradient Alignment
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 Machine Learning
Jul 30
Automorphism-Induced Non-Canonicity in Top-k Explanations of Graph Neural Networks
arXiv:2607. 26344v1 Announce Type: new Abstract: A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit.
arXiv Machine Learning
Jun 10
Conservation Laws from Data Symmetry in Neural Networks
arXiv:2606. 10913v1 Announce Type: new Abstract: We explore whether intrinsic symmetries of the training data lead to conserved quantities during gradient-flow training of neural networks.
arXiv AI
Sep 1
Equivariant Sheaf Neural Networks: Learning Geometric Transport on Graphs
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...