# Randomized coordinate gradient descent almost surely escapes strict saddle points

arXiv: https://arxiv.org/abs/2508.07535 · HTML: https://mlsanity.com/paper/2508.07535/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Aug 2025.

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

- [Escaping Saddle Points via Curvature-Calibrated Perturbations: A Complete Analysis with Explicit Constants and Empirical Validation](https://mlsanity.com/paper/2508.16540/) (2025)

## Abstract (arXiv)

We analyze the behavior of randomized coordinate gradient descent for nonconvex optimization, proving that under standard assumptions, the iterates almost surely escape strict saddle points. By formulating the method as a nonlinear random dynamical system and characterizing neighborhoods of critical points, we establish this result through the center-stable manifold theorem.