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Symmetry & Critical Points

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arxiv 2408.14445 v1 pith:6L7HHLRL submitted 2024-08-26 cs.LG cs.NAmath.NAmath.OCstat.ML

Yossi Arjevani This is my paper · ORCID
classification cs.LGcs.NAmath.NAmath.OCstat.ML
keywords criticalinvariantpointssymmetricsymmetrythoseabilityadjacent
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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.

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Cited by 1 Pith paper

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  1. A Spin Glass Characterization of Neural Networks

    cond-mat.dis-nn 2025-08 unverdicted novelty 6.0 of 10

    A Hopfield-type spin glass constructed from a feedforward network yields replica overlap statistics that serve as a per-instance descriptor of the network's generalization, capacity, and robustness.

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