Elbow-Based MoE Routing: A Training-Free Inference Time Plugin for Expert Selection

Abstract

Mixture-of-Experts (MoE) models enable model scaling while maintaining low inference-time compute by activating only a subset of experts per token. However, conventional routing relies on a fixed top-k selection, forcing the model to spend the same compute regardless of how many experts are relevant. We introduce elbow-based routing, a training-free inference-time modification that dynamically adjusts the number of experts on a per-token basis. Our method examines the sorted router probability distribution and identifies an elbow point that separates high- and low-probability experts. We find that most router distributions exhibit clear inflection points suitable for this strategy, and we show both theoretically and empirically that elbow-based routing preserves expert load balance. Experiments on a state-of-the-art MoE model demonstrate an average latency reduction of 5.3% while maintaining accuracy across six benchmarks.