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This paper provides a statistical framework for understanding Mixture-of-Experts (MoE) architectures by analyzing the effects of routing, sparse activation, and shared experts on model performance. By deriving oracle risk bounds and separating various sources of error, the authors reveal how sparse Top-K routing can optimize localized aggregation while managing computational costs. The findings highlight the importance of input-dependent expert aggregation in maximizing expert specialization and computational efficiency, offering insights into the design of future MoE models.
Sparse Top-K routing can optimize expert specialization while controlling computational costs, reshaping our understanding of MoE architectures.
Mixture-of-experts (MoE) architectures increase model capacity by combining a collection of expert predictors through input-dependent routing, while often activating only a small subset of experts for each input. Despite their growing importance in modern large-scale models, the statistical roles of their design choices, especially routing, sparse activation, and shared experts, remain only partially understood, as existing theory has largely focused on parametric or correctly specified MoE models. In this paper, we view MoE as a form of localized aggregation and show how this localization reshapes the approximation-estimation-computation tradeoff. We derive oracle risk bounds for learning dense and sparse routing with evolving experts, separating approximation, expert-learning, and router-estimation errors, and characterize how sparse Top-K routing can retain the benefits of localized aggregation while controlling per-input computation. We also interpret gating through the geometry of input space, relating routing performance to regions of local expert advantage, and show how shared experts, as adopted in architectures such as DeepSeekMoE, can extract common predictive structure so that routed experts focus on residual local variation. Together, these results provide a unified statistical framework for understanding MoE through input-dependent expert aggregation, in which expert specialization and computational tradeoffs are governed by local predictive structure.
