This repository contains the source code for reproducing the experiments in the following NeurIPS spotlight paper:
A. Bodard, P. Patrinos,
Escaping saddle points without Lipschitz smoothness: the power of nonlinear preconditioning,
NeurIPS 2025 (accepted).
Make sure that NumPy and Matplotlib are installed.
The factorization_visualization.py script reproduces the Nonlinear preconditioning for symmetric matrix factorization figure.
The octopus.py reproduces the Fast avoidance of saddle points figures.
For the implementation of the so-called octopus function, we used the implementation from https://github.com/rafflesintown/escape-saddle-points-2pt (see utils.py).