Globally Convergent Multilevel Training of Deep Residual Networks

TL;DR

This paper introduces a globally convergent multilevel training method for deep residual networks, leveraging a novel recursive trust-region approach with adaptive mini-batch sizing and curvature information, inspired by dynamical system interpretations.

Contribution

The paper presents a new multilevel training algorithm for ResNets that combines trust-region methods with a dynamical systems perspective, enabling adaptive mini-batch sizing and curvature incorporation.

Findings

Demonstrates improved convergence properties in classification and regression tasks.

Shows the effectiveness of the multilevel trust-region approach compared to traditional methods.

Provides numerical evidence of enhanced training performance and stability.

Abstract

We propose a globally convergent multilevel training method for deep residual networks (ResNets). The devised method can be seen as a novel variant of the recursive multilevel trust-region (RMTR) method, which operates in hybrid (stochastic-deterministic) settings by adaptively adjusting mini-batch sizes during the training. The multilevel hierarchy and the transfer operators are constructed by exploiting a dynamical system's viewpoint, which interprets forward propagation through the ResNet as a forward Euler discretization of an initial value problem. In contrast to traditional training approaches, our novel RMTR method also incorporates curvature information on all levels of the multilevel hierarchy by means of the limited-memory SR1 method. The overall performance and the convergence properties of our multilevel training method are numerically investigated using examples from the field of classification and regression.