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arXiv · 2606.01509

ProbMoE: Differentiable Probabilistic Routing for Mixture-of-Experts

Heng Zhao·Zilei Shao·Guy Van den Broeck·Zhe Zeng
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Abstract

Mixture-of-Experts (MoE) models scale by activating only a small subset of experts per token. However, training such models remains challenging because top-$k$ routing is discrete and non-differentiable, requiring gradient estimators for expert selection whose design remains a central open problem. We introduce ProbMoE, a probabilistic routing framework that models expert selection as a distribution over cardinality-constrained expert subsets and formulates routing as probabilistic inference in this discrete subset space. We first propose ProbMoE Exact-$k$ routing, which samples $k$-expert subsets in the forward pass, and the backward pass uses gradients through each expert's exact marginal probability as a tractable surrogate for the true gradient. ProbMoE naturally generalizes to a dynamic-$k$ routing setting, where both training and inference constrain the routing cardinality to the same predefined range, allowing adaptive expert allocation per token. Across benchmarks and model backbones, ProbMoE Exact-$k$ achieves strong performance compared to competitive baselines, with improved expert utilization and routing diversity; ProbMoE Dynamic-$k$ achieves comparable performance with fewer activated experts.

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Heng Zhao, Zilei Shao, Guy Van den Broeck, Zhe Zeng. 2026-06-01. ProbMoE: Differentiable Probabilistic Routing for Mixture-of-Experts. https://arxiv.org/abs/2606.01509

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