Discovering Important Experts for Mixture-of-Experts Models Pruning Through a Theoretical Perspective

Mixture-of-Experts (MoE) architectures enable efficient scaling of large language models but face prohibitive memory demands due to massive parameterization. Existing pruning methods rely on heuristic metrics or impractical enumeration of expert subsets, leading to suboptimal performance or scalability. In this paper, we propose Shapley-MoE, an efficient pruning method for MoE models inspired by cooperative game theory. By quantifying each expert’s contribution via Shapley value, our method identifies important experts without exhaustive combination evaluations. To overcome the NP-hard complexity of exact Shapley computation, we introduce a Monte Carlo sampling strategy for efficient approximation that reduces complexity to quadratic time. However, vanilla Monte Carlo sampling still faces issues of insufficient estimation accuracy and low sampling efficiency. To address these issues, we further propose two novel methods to improve sampling accuracy and efficiency: (1) Early Truncation, which early terminates unstable sampling steps caused by overly small expert subsets, and (2) Router-Guided Importance Sampling, which prioritize sampling important expert subsets using gating activation probabilities. Both theoretical and experimental analyses show that both methods can accelerate Shapley value estimation and improve accuracy. Extensive empirical evaluations demonstrate that our pruned MoE models outperform existing expert pruning methods. Notably, when applied to the Qwen2-57B-A14B model, our method reduces the number of experts by 25% with only a 0.92 increase in perplexity and over 96.4% of the average zero-shot accuracy is maintained.