Computing Kurdyka-Łojasiewicz exponents via composition and symmetry
Abstract
We devise calculus rules for the Kurdyka-Łojasiewicz exponent using the rank theorem and Lie group actions. They apply to a wide class of composite and invariant functions, and are particularly suitable for handling nonisolated local minima. Notably, smoothness plays no role, eschewing gradient and Hessian computations. This provides a unified framework for establishing linear convergence of various algorithms in matrix factorization, $\ell_1$-matrix factorization, matrix sensing, and linear neural networks.
Fields of Study & Subjects
Optimization and Variational Analysis
Stochastic Gradient Optimization Techniques
Advanced Optimization Algorithms Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Preprint