[2604.09175] Generalization and Scaling Laws for Mixture-of-Experts Transformers

Computer Science > Machine Learning arXiv:2604.09175 (cs) [Submitted on 10 Apr 2026] Title:Generalization and Scaling Laws for Mixture-of-Experts Transformers Authors:Mansour Zoubeirou a Mayaki View a PDF of the paper titled Generalization and Scaling Laws for Mixture-of-Experts Transformers, by Mansour Zoubeirou a Mayaki View PDF HTML (experimental) Abstract:We develop a theory of generalization and scaling for Mixture-of-Experts (MoE) Transformers that cleanly separates \emph{active} per-input capacity from routing combinatorics. By conditioning on fixed routing patterns and union-bounding across them, we derive a sup-norm covering-number bound whose metric entropy scales with the active parameter budget and incurs a MoE-specific routing overhead. Combined with a standard ERM analysis for squared loss, this yields a generalization bound under a $d$-dimensional manifold data model and $C^\beta$ targets, showing that approximation and estimation trade off as in dense networks once active parameters are accounted for appropriately. We further prove a constructive approximation theorem for MoE architectures, showing that, under the approximation construction, error can decrease either by scaling active capacity or by increasing the number of experts, depending on the dominant bottleneck. From these results we derive neural scaling laws for model size, data size, and compute-optimal tradeoffs. Overall, our results provide a transparent statistical reference point for reasonin...