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

arXiv: https://arxiv.org/abs/2403.17404 · HTML: https://mlsanity.com/paper/2403.17404/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts.
- Builds on 8 of its 15 references that are in the map.
- First posted on arXiv 26 Mar 2024.

## Placed in

- Mixture-of-experts / [MoE theory and gating functions](https://mlsanity.com/moe/moe-theory-and-gating-functions/)

## Builds on (most cited first, 8 of 8)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [Spectrally-normalized margin bounds for neural networks](https://mlsanity.com/paper/1706.08498/) (2017)
- [Learning Factored Representations in a Deep Mixture of Experts](https://mlsanity.com/paper/1312.4314/) (2013)
- [Towards Understanding Mixture of Experts in Deep Learning](https://mlsanity.com/paper/2208.02813/) (2022)
- [Demystifying Softmax Gating Function in Gaussian Mixture of Experts](https://mlsanity.com/paper/2305.03288/) (2023)
- [Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Experts](https://mlsanity.com/paper/2309.13850/) (2023)
- [A General Theory for Softmax Gating Multinomial Logistic Mixture of Experts](https://mlsanity.com/paper/2310.14188/) (2023)
- [Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Experts](https://mlsanity.com/paper/2305.07572/) (2023)

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

- [LIBMoE: A Library for comprehensive benchmarking Mixture of Experts in Large Language Models](https://mlsanity.com/paper/2411.00918/) (2024)
- [Learning Graph Foundation Models on Riemannian Graph-of-Graphs](https://mlsanity.com/paper/2605.09993/) (2026)
- [Horseshoe Mixtures-of-Experts (HS-MoE)](https://mlsanity.com/paper/2601.09043/) (2026)
- [DBES: A Systematic Benchmark and Metric Suite for Evaluating Expert Specialization in Large-Scale MoEs](https://mlsanity.com/paper/2605.18498/) (2026)
- [Sparsity Saves Compute, Not Samples: Oracle Inequalities for Dense and Sparse Mixture of Experts](https://mlsanity.com/paper/2610.15039/) (2026)

## Abstract (arXiv)

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 textithow sparsity contributes to the MoE's generalization, offering insights from the perspective of classical learning theory.