Spectral symmetry fingerprints in equivariant representations
Read the original on arXiv Machine Learning →The Flow has not summarised this story yet — read it at arXiv Machine Learning.
The Flow has not summarised this story yet — read it at arXiv Machine Learning.
Symmetry governs the organization of physical structures, while symmetry breaking reveals their transformations. In geometric deep learning, symmetry imposes rank constraints on equivariant representa...
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:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
arXiv:2608.31045v1 Announce Type: new Abstract: Rotational symmetry is one of the most important structural principles in machine learning on 3D data. In applications ranging from physics and materia...
arXiv:2608. 05336v1 Announce Type: cross Abstract: Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships.
The paper investigates why Hessian spectra of trained deep learning models consistently show a bulk of eigenvalues near zero and a few isolated outliers. It proposes that these patterns arise from a hidden, highly symmetric reference configuration; when the model is perturbed (e.g., by architecture, data, or metric changes), the symmetry is broken, producing the observed cluster hierarchy. The authors analyze this mechanism in three‑layer ReLU networks and extend it to convolutional, graph, transformer models, the NTK, and related matrices such as layerwise Hessians and the Gauss‑Newton matrix.