Symmetry & Critical Points
Not on the map. Why?
Abstract (arXiv)
Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry important implications for our ability to efficiently minimize invariant nonconvex functions, in particular those associated with neural networks.
Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 14 of its 70 references that are in the map. First posted on arXiv 26 Aug 2024.
Builds on
14 of 70 references.
References · 14
- 2016Entropy-SGD: Biasing Gradient Descent Into Wide Valleyscited by 357
- 2016Eigenvalues of the Hessian in Deep Learning: Singularity and Beyondcited by 156
- 2019Dynamics of stochastic gradient descent for two-layer neural networks in the teacher-student setupcited by 112
- 2022On the Effective Number of Linear Regions in Shallow Univariate ReLU Networks: Convergence Guarantees and Implicit Biascited by 21
- 2020Analytic Characterization of the Hessian in Shallow ReLU Models: A Tale of Symmetrycited by 17
- 2021Analytic Study of Families of Spurious Minima in Two-Layer ReLU Neural Networks: A Tale of Symmetry IIcited by 16
- 2021Symmetry Breaking in Symmetric Tensor Decompositioncited by 10
- 2019On the Principle of Least Symmetry Breaking in Shallow ReLU Modelscited by 9
- 2020Symmetry & critical points for a model shallow neural networkcited by 9
- 2022Annihilation of Spurious Minima in Two-Layer ReLU Networkscited by 9
- 2023Should Under-parameterized Student Networks Copy or Average Teacher Weights?cited by 8
- 2021Equivariant bifurcation, quadratic equivariants, and symmetry breaking for the standard representation of Sncited by 5
2 more
- 2023Symmetry & Critical Points for Symmetric Tensor Decomposition Problemscited by 3
- 2023Hidden Minima in Two-Layer ReLU Networkscited by 2
Built on by
Citing papers per year: 2025: 1; 2026: 1.
2 papers.