Implicit Bias of SGD for Diagonal Linear Networks: a Provable Benefit of Stochasticity
Prof. Nicolas Flammarion, Tenure-track assistant professor in computer science at EPFL – Swiss Federal Institute of Technology Lausanne
Wednesday, Oct 27, 2021, 10:00am-11:00pm (CEST)
Understanding the implicit bias of training algorithms is of crucial importance in order to explain the success of overparametrised neural networks. In this talk, we study the dynamics of stochastic gradient descent over diagonal linear networks through its continuous time version, namely stochastic gradient flow. We explicitly characterise the solution chosen by the stochastic flow and prove that it always enjoys better generalisation properties than that of gradient flow. Quite surprisingly, we show that the convergence speed of the training loss controls the magnitude of the biasing effect: the slower the convergence, the better the bias.
Our findings highlight the fact that structured noise can induce better generalisation and they help to explain the greater performances observed in practice of stochastic gradient descent over gradient descent.
Nicolas Flammarion is a tenure-track assistant professor in computer science at EPFL. Prior to that, he was a postdoctoral fellow at UC Berkeley, hosted by Michael I. Jordan. He received his PhD in 2017 from Ecole Normale Superieure in Paris, where he was advised by Alexandre d’Aspremont and Francis Bach.
His research focuses primarily on learning problems at the interface of machine learning, statistics and optimization.