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arXiv · 2602.22553

Computing Kurdyka-\L{}ojasiewicz exponents via composition and symmetry

Cédric Josz·Wenqing Ouyang
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Abstract

We devise calculus rules for the Kurdyka-\L{}ojasiewicz 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.

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Cédric Josz, Wenqing Ouyang. 2026-02-26. Computing Kurdyka-\L{}ojasiewicz exponents via composition and symmetry. https://arxiv.org/abs/2602.22553

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