arxivcs.LGmath.ST2026-06-26
Replica Symmetry Breaking and Algorithmic Thresholds in Empirical Risk Minimization under Multi-Index Model
Andrea Montanari, Kangjie Zhou
Modern machine learning models are trained by optimizing high-dimensional non-convex empirical risk functions. Such cost functions can have a multitude of local optima and yet, gradient-based optimization appears to converge to near-global optima. Within a simple supervised learn…