Sparsity Saves Compute, Not Samples: Oracle Inequalities for Dense and Sparse Mixture of Experts
Mixture-of-Experts (MoE) models combine specialized experts through an input-dependent routing mechanism, and their sparse variants underpin many modern large-scale systems. Yet the statistical cost of adaptive routing remains only partially understood. We study the estimation error of least-squares MoE estimators when both the experts and the gating network are Lipschitz in their parameters. We represent each MoE as a gate--expert pair in a Gated Hilbert Space, whose norm $\|\cdot\|_Δ$ separates the contributions of routing and expert discrepancies. Using its empirical representation, we derive an oracle inequality with a fast rate of order $\tilde{\mathcal O}\big((Kd_{\mathrm{pr},e}+d_{...
| Authors | Sagar Ghosh, Huy Nguyen, Alessandro Rinaldo |
|---|---|
| Primary category | cs.LG |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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