Uncertainty-Aware Routing for Principled Alignment with MoE Dynamics

AbstractMixture-of-Experts (MoE) is a cornerstone for scaling LLMs, yet its training dynamics remain poorly understood, often leading to sub-optimal specialization. Moving beyond static routing, we present a systematic study of the MoE lifecycle using Helmholtz Free Energyand Router Entropy. We identify a universal Three-Stage Phase Transition—Exploration, Symmetry Breaking, and Stabilization—marked by an Energy Climb and Plateau. This reflects Frustrated Exploration, caused by structural interference between specialization drives and uniformity constraints. To address this, we propose Uncertainty-Aware Routing (UAR), which aligns routing with the model’s epistemic state via: (1) Evidence-Triggered Expansion, increasing active experts for high-energy tokens, and (2) Epistemic Masking, applying load-balancing only in high-uncertainty regimes to shield mature experts. Experiments confirm UAR reduces perplexity and improves expert distinctiveness, offering a principled path toward thermodynamically aligned computation.