mlsanityData to 14 Oct 2026

Mixture of Many Zero-Compute Experts: A High-Rate Quantization Theory Perspective

arXiv 2510.03151 ↗First posted 3 Oct 2025cs.LGcited by 0

On the map: Mixture-of-experts → MoE theory and gating functions

Abstract (arXiv)

This paper uses classical high-rate quantization theory to provide new insights into mixture-of-experts (MoE) models for regression tasks. Our MoE is defined by a segmentation of the input space to regions, each with a single-parameter expert that acts as a constant predictor with zero-compute at inference. Motivated by high-rate quantization theory assumptions, we assume that the number of experts is sufficiently large to make their input-space regions very small. This lets us study the approximation error of our MoE model class: (i) for one-dimensional inputs, we formulate the test error and its minimizing segmentation and experts; (ii) for multidimensional inputs, we formulate an upper bound for the test error and study its minimization. Moreover, we consider the learning of the expert parameters from a training dataset, given an input-space segmentation, and formulate their statistical learning properties. This leads us to theoretically and empirically show how the tradeoff between approximation and estimation errors in MoE learning depends on the number of experts.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in MoE theory and gating functions, one of 12 directions in Mixture-of-experts. Builds on 13 of its 29 references that are in the map. First posted on arXiv 3 Oct 2025.

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13 of 29 references.

Closest ancestors · 6

Same direction, newest first

  1. 2024Sparse Mixture-of-Experts for Compositional Generalization: Empirical Evidence and Theoretical Foundations of Optimal Sparsity17 Oct
  2. 2024Sigmoid Gating is More Sample Efficient than Softmax Gating in Mixture of Experts22 May
  3. 2024On Least Square Estimation in Softmax Gating Mixture of Experts5 Feb
  4. 2023Statistical Perspective of Top-K Sparse Softmax Gating Mixture of Experts25 Sep
  5. 2023Towards Convergence Rates for Parameter Estimation in Gaussian-gated Mixture of Experts12 May
  6. 2023Demystifying Softmax Gating Function in Gaussian Mixture of Experts5 May

Other references · 7

  1. 2017Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layercited by 3,509
  2. 2021Switch Transformers: Scaling to Trillion Parameter Models with Simple and Efficient Sparsitycited by 3,073
  3. 2024DeepSeek-V2: A Strong, Economical, and Efficient Mixture-of-Experts Language Modelcited by 1,135
  4. 2021Scaling Vision with Sparse Mixture of Expertscited by 747
  5. 2022A Review of Sparse Expert Models in Deep Learningcited by 148
  6. 2024MoE++: Accelerating Mixture-of-Experts Methods with Zero-Computation Expertscited by 56
  7. 2024Mixture of Parrots: Experts improve memorization more than reasoningcited by 21

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  1. 2024Generalization Error Analysis for Sparse Mixture-of-Experts: A Preliminary Study
  2. 2024QuantMoE-Bench: Examining Post-Training Quantization for Mixture-of-Experts
  3. 2026Efficient Quantization of Mixture-of-Experts with Theoretical Generalization Guarantees
  4. 2023Revisiting Single-gated Mixtures of Experts
  5. 2019Regularized Estimation and Feature Selection in Mixtures of Generalized Linear Experts
  6. 2026AlphaQ: Calibration-Free Bit Allocation for Mixture-of-Experts Quantization
  7. 2024Learning Mixtures of Experts with EM: A Mirror Descent Perspective
  8. 2026The qs Inequality: Quantifying the Double Penalty of Mixture-of-Experts at Inference