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

arXiv: https://arxiv.org/abs/2505.10860 · HTML: https://mlsanity.com/paper/2505.10860/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in MoE large language models, one of 12 directions in Mixture-of-experts.
- First posted on arXiv 16 May 2025.

## Placed in

- Mixture-of-experts / [MoE large language models](https://mlsanity.com/moe/moe-large-language-models/)

## Built on by (most cited first, 5 of 5)

- [Rethinking Multinomial Logistic Mixture of Experts with Sigmoid Gating Function](https://mlsanity.com/paper/2602.01466/) (2026)
- [OmniMoE: An Efficient MoE by Orchestrating Atomic Experts at Scale](https://mlsanity.com/paper/2602.05711/) (2026)
- [Towards a Statistical Understanding of Mixture-of-Experts](https://mlsanity.com/paper/2609.03501/) (2026)
- [Unifying Semantic Priors and High-Frequency Traces: Enhancing V-JEPA with Mixture-of-Experts for Robust Synthetic Image Forensics](https://mlsanity.com/paper/2609.16778/) (2026)
- [Score the Update, Not the Token: Descent-Aligned Routing for Combinatorial LoRA Experts](https://mlsanity.com/paper/2610.00493/) (2026)

## Abstract (arXiv)

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.