# Computing Kurdyka-Lojasiewicz exponents via composition and symmetry

arXiv: https://arxiv.org/abs/2602.22553 · HTML: https://mlsanity.com/paper/2602.22553/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Feb 2026.

## Built on by (most cited first, 1 of 1)

- [Connecting Score Matching, Maximum Likelihood, and Expectation-Maximization in Mixed Linear Regression](https://mlsanity.com/paper/2609.05688/) (2026)

## Abstract (arXiv)

We devise calculus rules for the Kurdyka-Lojasiewicz 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, ℓ1-matrix factorization, matrix sensing, and linear neural networks.