Global Convergence of SGD For Logistic Loss on Two Layer Neural Nets

arXiv:2309.09258v2 Announce Type: replace
Abstract: In this note, we demonstrate a first-of-its-kind provable convergence of SGD to the global minima of appropriately regularized logistic empirical risk of depth $2$ nets -- for arbitrary data and with any number of gates with adequately smooth and bounded activations like sigmoid and tanh. We also prove an exponentially fast convergence rate for continuous time SGD that also applies to smooth unbounded activations like SoftPlus. Our key idea is to show the existence of …

abstract arxiv convergence cs.lg data gates global kind layer loss math.oc neural nets risk sigmoid stat.ml type