Gradient Flow Through Diagram Expansions: Learning Regimes and Explicit Solutions
arXiv:2602.04548v1 Announce Type: cross Abstract: We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution, with coefficients encoded by diagrams akin to Feynman diagrams. We show that this expansion has a well-defined large-size limit that can be used to reveal different learning phases and, in some cases, to obtain explicit solutions of […]