Generalization Error Analysis for Sparse Mixture-of-Experts: A Preliminary Study
This addresses a theoretical gap for researchers in machine learning, but it is incremental as it builds on existing MoE frameworks without introducing new methods.
The paper tackles the lack of theoretical understanding in Sparse Mixture-of-Experts (Sparse MoE) by analyzing its generalization error in relation to factors like data samples, number of experts, sparsity, and routing complexity, providing insights into how sparsity affects generalization from a learning theory perspective.
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.