Mixture of Many Zero-Compute Experts: A High-Rate Quantization Theory Perspective
This provides theoretical insights into MoE models for regression, but it is incremental as it builds on existing quantization theory without broad practical impact.
The paper tackles the problem of understanding mixture-of-experts (MoE) models for regression by applying high-rate quantization theory, showing that with many zero-compute experts, it formulates test error minimization and an error tradeoff dependent on expert count.
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 to 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.