Preconditioned Stochastic Gradient Langevin Dynamics for Deep Neural Networks

TL;DR

This paper introduces a preconditioned SGLD method that adapts to the local geometry of deep neural network parameter spaces, improving convergence and predictive performance.

Contribution

It combines adaptive preconditioning with SGLD, providing theoretical convergence guarantees and demonstrating state-of-the-art results on various neural network models.

Findings

Preconditioned SGLD achieves faster convergence.

The method improves predictive accuracy on neural networks.

Theoretical analysis confirms asymptotic convergence.

Abstract

Effective training of deep neural networks suffers from two main issues. The first is that the parameter spaces of these models exhibit pathological curvature. Recent methods address this problem by using adaptive preconditioning for Stochastic Gradient Descent (SGD). These methods improve convergence by adapting to the local geometry of parameter space. A second issue is overfitting, which is typically addressed by early stopping. However, recent work has demonstrated that Bayesian model averaging mitigates this problem. The posterior can be sampled by using Stochastic Gradient Langevin Dynamics (SGLD). However, the rapidly changing curvature renders default SGLD methods inefficient. Here, we propose combining adaptive preconditioners with SGLD. In support of this idea, we give theoretical properties on asymptotic convergence and predictive risk. We also provide empirical results for Logistic Regression, Feedforward Neural Nets, and Convolutional Neural Nets, demonstrating that our preconditioned SGLD method gives state-of-the-art performance on these models.