On the geometry of flat minima
Optimization and Control
2026-02-06 v2
Abstract
What does it mean to be flat? We propose to define it by measuring the maximal variation around a point, or from a dual perspective, the distance to neighboring level sets. After developing some calculus rules, we show how flat minima, conservation laws, and symmetries are intertwined. Gradient flows of conserved quantities are of particular interest, due to their flattening properties.
Cite
@article{arxiv.2509.11386,
title = {On the geometry of flat minima},
author = {Cédric Josz},
journal= {arXiv preprint arXiv:2509.11386},
year = {2026}
}