Langevin Dynamics with Continuous Tempering for Training Deep Neural Networks

TL;DR

This paper introduces a two-phase training method for deep neural networks using Langevin dynamics with continuous tempering, improving exploration of the energy landscape and resulting in better generalization.

Contribution

It proposes a novel two-phase training approach combining Bayesian sampling with stochastic optimization, utilizing continuous tempering in Langevin dynamics for enhanced neural network training.

Findings

Achieved better generalization performance across various neural network architectures.

Overcame early trapping in local minima with the proposed tempering strategy.

Theoretical analysis supports the effectiveness of the method.

Abstract

Minimizing non-convex and high-dimensional objective functions is challenging, especially when training modern deep neural networks. In this paper, a novel approach is proposed which divides the training process into two consecutive phases to obtain better generalization performance: Bayesian sampling and stochastic optimization. The first phase is to explore the energy landscape and to capture the "fat" modes; and the second one is to fine-tune the parameter learned from the first phase. In the Bayesian learning phase, we apply continuous tempering and stochastic approximation into the Langevin dynamics to create an efficient and effective sampler, in which the temperature is adjusted automatically according to the designed "temperature dynamics". These strategies can overcome the challenge of early trapping into bad local minima and have achieved remarkable improvements in various types of neural networks as shown in our theoretical analysis and empirical experiments.