Generalization Error Analysis for Sparse Mixture-of-Experts: A Preliminary Study

TL;DR

This paper analyzes how sparsity in Sparse Mixture-of-Experts models affects their ability to generalize, providing theoretical insights into the factors influencing their performance.

Contribution

It offers the first theoretical analysis of generalization error in Sparse MoE, highlighting the role of sparsity and other factors from classical learning theory perspectives.

Findings

Sparsity improves generalization by reducing overfitting.

The number of experts and data samples significantly influence error bounds.

Routing and expert complexities are key factors in model performance.

Abstract

Mixture-of-Experts (MoE) represents an ensemble methodology that amalgamates predictions from several specialized sub-models (referred to as experts). This fusion is accomplished through a router mechanism, dynamically assigning weights to each expert's contribution based on the input data. Conventional MoE mechanisms select all available experts, incurring substantial computational costs. In contrast, Sparse Mixture-of-Experts (Sparse MoE) selectively engages only a limited number, or even just one expert, significantly reducing computation overhead while empirically preserving, and sometimes even enhancing, performance. Despite its wide-ranging applications and these advantageous characteristics, MoE's theoretical underpinnings have remained elusive. In this paper, we embark on an exploration of Sparse MoE's generalization error concerning various critical factors. Specifically, we investigate the impact of the number of data samples, the total number of experts, the sparsity in expert selection, the complexity of the routing mechanism, and the complexity of individual experts. Our analysis sheds light on \textit{how \textbf{sparsity} contributes to the MoE's generalization}, offering insights from the perspective of classical learning theory.