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arXiv · 2602.09001

DirMoE: Dirichlet-routed Mixture of Experts

Amirhossein Vahidi·Hesam Asadollahzadeh·Navid Akhavan Attar·Marie Moullet·Kevin Ly·Xingyi Yang·Mohammad Lotfollahi
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Abstract

Mixture-of-Experts (MoE) models have demonstrated exceptional performance in large-scale language models. Existing routers typically rely on non-differentiable Top-$k$+Softmax, limiting their performance and scalability. We argue that two distinct decisions, which experts to activate and how to distribute expert contributions among them, are conflated in standard Top-$k$+Softmax. We introduce Dirichlet-Routed MoE (DirMoE), a novel end-to-end differentiable routing mechanism built on a Dirichlet variational autoencoder framework. This design fundamentally disentangles the core routing problems: expert selection, modeled by a Bernoulli component, and expert contribution among chosen experts, handled by a Dirichlet component. The entire forward pass remains fully differentiable through the use of Gumbel-Sigmoid relaxation for the expert selection and implicit reparameterization for the Dirichlet distribution. Our training objective, a variational ELBO, includes a direct sparsity penalty that precisely controls the number of active experts in expectation, alongside a schedule for key hyperparameters that guides the model from an exploratory to a definitive routing state. Moreover, our DirMoE router matches or exceeds other methods while improving expert specialization.

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Amirhossein Vahidi, Hesam Asadollahzadeh, Navid Akhavan Attar, Marie Moullet, Kevin Ly, Xingyi Yang, Mohammad Lotfollahi. 2026-02-09. DirMoE: Dirichlet-routed Mixture of Experts. https://arxiv.org/abs/2602.09001

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