Homotopy Relaxation Training Algorithms for Infinite-Width Two-Layer ReLU Neural Networks

TL;DR

This paper introduces the Homotopy Relaxation Training Algorithm (HRTA) for infinite-width two-layer ReLU neural networks, which accelerates training by smoothly connecting activation functions and relaxing parameters, leading to improved convergence.

Contribution

The paper proposes a novel HRTA that combines homotopy activation functions and parameter relaxation, significantly improving training convergence in NTK regime for wide neural networks.

Findings

Enhanced convergence rates demonstrated in theory

Experimental validation on large-width networks

Potential applicability to other activation functions

Abstract

In this paper, we present a novel training approach called the Homotopy Relaxation Training Algorithm (HRTA), aimed at accelerating the training process in contrast to traditional methods. Our algorithm incorporates two key mechanisms: one involves building a homotopy activation function that seamlessly connects the linear activation function with the ReLU activation function; the other technique entails relaxing the homotopy parameter to enhance the training refinement process. We have conducted an in-depth analysis of this novel method within the context of the neural tangent kernel (NTK), revealing significantly improved convergence rates. Our experimental results, especially when considering networks with larger widths, validate the theoretical conclusions. This proposed HRTA exhibits the potential for other activation functions and deep neural networks.