Mixture-of-Experts under Finite-Rate Gating: Communication--Generalization Trade-offs

2026-02-16

AI Summary

This work investigates the trade-off between model expressivity and generalization performance in Mixture-of-Experts (MoE) architectures under communication constraints. For the first time, rate-distortion theory is introduced into MoE analysis by modeling the gating mechanism as a stochastic channel operating at a finite rate. By integrating mutual information-based generalization bounds with the rate-distortion function \(D(R_g)\), the study establishes a quantitative relationship between the gating communication rate and generalization error. A theoretical upper bound on generalization error is derived and validated through synthetic multi-expert model simulations, which demonstrate that reducing the gating rate, while limiting expressivity, can enhance generalization. Based on these insights, the paper proposes a capacity-aware design principle for MoE systems, offering theoretical guidance for efficient model construction in resource-constrained settings.

Technology Category

• Machine Learning: Mixture of Experts (MoE)
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

Abstract

Mixture-of-Experts (MoE) architectures decompose prediction tasks into specialized expert sub-networks selected by a gating mechanism. This letter adopts a communication-theoretic view of MoE gating, modeling the gate as a stochastic channel operating under a finite information rate. Within an information-theoretic learning framework, we specialize a mutual-information generalization bound and develop a rate-distortion characterization $D(R_g)$ of finite-rate gating, where $R_g:=I(X; T)$, yielding (under a standard empirical rate-distortion optimality condition) $\mathbb{E}[R(W)] \le D(R_g)+δ_m+\sqrt{(2/m)\, I(S; W)}$. The analysis yields capacity-aware limits for communication-constrained MoE systems, and numerical simulations on synthetic multi-expert models empirically confirm the predicted trade-offs between gating rate, expressivity, and generalization.

Problem

• Mixture-of-Experts
• finite-rate gating
• communication-generalization trade-off
• information-theoretic learning
• rate-distortion

Innovation

• Mixture-of-Experts
• finite-rate gating
• information-theoretic learning
• rate-distortion theory
• generalization bound