[Paper Review] Globally Consistent Algorithms for Mixture of Experts.

Ashok Vardhan Makkuva, Sreeram Kannan+1 more|arXiv (Cornell University)|Feb 21, 2018

Tensor decomposition and applications49 references2 citations

TL;DR

This paper presents the first globally consistent algorithm for learning the parameters of a Mixture-of-Experts (MoE) model with provable guarantees, combining the EM algorithm with tensor-based moment techniques. It achieves exact parameter recovery for a wide class of non-linearities, outperforming standard baselines on both synthetic and real-world data.

ABSTRACT

Mixture-of-Experts (MoE) is a widely popular neural network architecture and is a basic building block of highly successful modern neural networks, for example, Gated Recurrent Units (GRU) and Attention networks. However, despite the empirical success, finding an efficient and provably consistent algorithm to learn the parameters remains a long standing open problem for more than two decades. In this paper, we introduce the first algorithm that learns the true parameters of a MoE model for a wide class of non-linearities with global consistency guarantees. Our algorithm relies on a novel combination of the EM algorithm and the tensor method of moment techniques. We empirically validate our algorithm on both the synthetic and real data sets in a variety of settings, and show superior performance to standard baselines.

Motivation & Objective

• To address the long-standing open problem of finding an efficient, provably consistent algorithm for learning Mixture-of-Experts (MoE) models.
• To extend parameter learning guarantees to non-linear MoE models beyond linear cases.
• To develop a method that ensures global convergence to the true parameters under mild assumptions.
• To empirically validate the algorithm across diverse synthetic and real-world settings.

Proposed method

• The algorithm combines the Expectation-Maximization (EM) framework with higher-order moment techniques based on tensor decompositions.
• It leverages the structure of the MoE model to extract identifiable moments using tensor methods.
• The method exploits the non-linearity of the experts to construct a system of equations that uniquely identifies the true parameters.
• A novel initialization strategy based on tensor power iteration ensures convergence to the global optimum.
• The algorithm is designed to be robust to noise and applicable to a wide class of non-linear activation functions.

Experimental results

Research questions

• RQ1 Can a globally consistent algorithm be developed for MoE models with non-linearities?
• RQ2 Can the EM algorithm be combined with tensor methods to achieve provable parameter recovery in MoE?
• RQ3 Does the proposed method outperform standard baselines in both synthetic and real-world settings?
• RQ4 What are the conditions under which the algorithm guarantees convergence to the true parameters?

Key findings

• The proposed algorithm achieves global consistency in learning the true parameters of MoE models with a wide class of non-linearities.
• It provides the first provable guarantees for parameter recovery in MoE models, resolving a two-decade open problem.
• Empirical results show superior performance compared to standard baselines on both synthetic and real datasets.
• The method is robust to noise and effective across diverse architectural and data settings.