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Symmetry & Critical Points

2024/08/26 by Yossi Arjevani, Arjevani, Yossi
Computer Science · Mathematics · #Advanced Optimization Algorithms Research #FOS: Computer and information sciences #FOS: Mathematics #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Stochastic Gradient Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2408.14445

openalex publication_date 2024/08/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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