On the geometry of flat minima
arXiv:2509.11386
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.