On DeepSeekMoE: Statistical Benefits of Shared Experts and Normalized Sigmoid Gating

TL;DR

This paper provides a theoretical and empirical analysis of DeepSeekMoE, highlighting the statistical benefits of shared experts and normalized sigmoid gating in large language models, and examining their impact on model efficiency and routing behavior.

Contribution

It offers the first comprehensive theoretical justification for shared expert strategies and normalized sigmoid gating in DeepSeekMoE, supported by empirical validation.

Findings

Shared expert strategy improves sample efficiency.

Normalized sigmoid gating enhances expert utilization.

Empirical results confirm theoretical predictions.

Abstract

Mixture of experts (MoE) methods are a key component in most large language model architectures, including the recent series of DeepSeek models. Compared to other MoE implementations, DeepSeekMoE stands out because of two unique features: the deployment of a shared expert strategy and of the normalized sigmoid gating mechanism. Despite the prominent role of DeepSeekMoE in the success of the DeepSeek series of models, there have been only a few attempts to justify theoretically the value of the shared expert strategy, while its normalized sigmoid gating has remained unexplored. To bridge this gap, we undertake a comprehensive theoretical study of these two features of DeepSeekMoE from a statistical perspective. We perform a convergence analysis of the expert estimation task to highlight the gains in sample efficiency for both the shared expert strategy and the normalized sigmoid gating, offering useful insights into the design of expert and gating structures. To verify empirically our theoretical findings, we carry out several experiments on both synthetic data and real-world datasets for (vision) language modeling tasks. Finally, we conduct an extensive empirical analysis of the router behaviors, ranging from router saturation, router change rate, to expert utilization.