A view of mini-batch SGD via generating functions: conditions of convergence, phase transitions, benefit from negative momenta. (arXiv:2206.11124v1 [cs.LG])

Web: http://arxiv.org/abs/2206.11124

Mini-batch SGD with momentum is a fundamental algorithm for learning large
predictive models. In this paper we develop a new analytic framework to analyze
mini-batch SGD for linear models at different momenta and sizes of batches. Our
key idea is to describe the loss value sequence in terms of its generating
function, which can be written in a compact form assuming a diagonal
approximation for the second moments of model weights. By analyzing this
generating function, we deduce various conclusions …

arxiv convergence lg negative