Expert Routing for Communication-Efficient MoE via Finite Expert Banks
This work investigates the information-theoretic efficiency of routing mechanisms in sparse Mixture-of-Experts (MoE) architectures, aiming to balance model accuracy with communication and computational resource utilization. The gating router is modeled as a stochastic channel, and a discrete mutual information estimator is proposed under a finite expert pool. Empirical posterior distributions \( q(W|S) \) are leveraged to compute \( I(X;T) \) and \( I(S;W) \), with the latter shown to exhibit a monotonic relationship with the generalization gap. The Blahut–Arimoto algorithm is employed to trace the accuracy–rate trade-off curve. Experiments demonstrate that the proposed mutual information estimator effectively tracks the generalization gap and significantly outperforms both the Xu–Raginsky bound and the uniform joint bound, offering a practical analytical tool for resource-aware MoE systems.