3 papers
math.OC2026
A non-autonomous center-stable set theorem for saddle avoidance in optimization
Andreea-Alexandra Muşat, Nicolas Boumal
Optimization algorithms are unlikely to converge to strict saddle points. Proofs to that effect rely on the Center-Stable Manifold Theorem (CSMT), casting algorithms as dynamical s…
math.OC2026
Insights on Muon from Simple Quadratics
Antoine Gonon, Andreea-Alexandra Muşat, Nicolas Boumal
Muon updates weight matrices along (approximate) polar factors of the gradients and has shown strong empirical performance in large-scale training. Existing attempts at explaining…
math.OC2025
Gradient descent avoids strict saddles with a simple line-search method too
Andreea-Alexandra Muşat, Andreea-Alexandra Musat, Nicolas Boumal
It is known that gradient descent (GD) on a cost function generically avoids strict saddle points when using a small, constant step size. However, no such guarantee existed f…