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<p>In this work, we study the asymptotic behavior of mixture of experts (MoE) trained via gradient flow on supervised learning problems. Our main result establishes the propagation of chaos for a MoE as the number of experts diverges. We demonstrate that the corresponding empirical measure of their parameters is close to a probability measure that solves a nonlinear continuity equation, and we provide an explicit convergence rate that depends solely on the number of experts and on the dimensionality of the parameter space. We apply our results to a MoE generated by a quantum neural network.</p>

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Mean-field limit from general mixtures of experts to quantum neural networks

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月27日

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  • Anderson Melchor Hernandez,
  • Davide Pastorello,
  • Giacomo De Palma

摘要

In this work, we study the asymptotic behavior of mixture of experts (MoE) trained via gradient flow on supervised learning problems. Our main result establishes the propagation of chaos for a MoE as the number of experts diverges. We demonstrate that the corresponding empirical measure of their parameters is close to a probability measure that solves a nonlinear continuity equation, and we provide an explicit convergence rate that depends solely on the number of experts and on the dimensionality of the parameter space. We apply our results to a MoE generated by a quantum neural network.