L2R: Low-Rank and Lipschitz-Controlled Routing for Mixture-of-Experts

Mixture-of-Experts (MoE) models scale neural networks by conditionally activating a small subset of experts, where the router plays a central role in determining expert specialization and overall model performance. However, many modern MoE systems still adopt linear routers in raw high-dimensional representation spaces, where representation mismatch, angular concentration, and scale-sensitive scoring can jointly undermine routing discriminability and stable expert specialization. In this work, we propose Low-rank & Lipschitz-controlled Routing (L2R), a unified routing framework that reshapes both the routing space and scoring geometry. L2R performs expert assignment in a shared low-rank latent routing space and introduces Saturated Inner-Product Scoring (SIPS) to explicitly control the Lipschitz behavior of routing functions, yielding smoother and more stable routing geometry. In addition, L2R incorporates a parameter-efficient multi-anchor routing mechanism to enhance expert expressiveness. Experiments on an OLMoE-based language MoE model and a ViT-based ImageNet setting show improved overall performance in both domains; OLMoE diagnostics further show improved routing geometry and expert discrimination.