Towards Greater Leverage: Scaling Laws for Efficient Mixture-of-Experts Language Models

TL;DR

This paper introduces a scaling law for Mixture-of-Experts models that predicts their efficiency based on configuration, validated by training a new model that matches larger dense models with less compute.

Contribution

The paper develops a unified scaling law for MoE models' efficiency leveraging empirical data from over 300 models, enabling better prediction of model capacity and resource use.

Findings

EL is driven by expert activation ratio and compute budget following power laws.

Expert granularity has a non-linear effect with an optimal range.

A pilot MoE model matched larger dense models' performance with less compute.

Abstract

Mixture-of-Experts (MoE) has become a dominant architecture for scaling Large Language Models (LLMs) efficiently by decoupling total parameters from computational cost. However, this decoupling creates a critical challenge: predicting the model capacity of a given MoE configurations (e.g., expert activation ratio and granularity) remains an unresolved problem. To address this gap, we introduce Efficiency Leverage (EL), a metric quantifying the computational advantage of an MoE model over a dense equivalent. We conduct a large-scale empirical study, training over 300 models up to 28B parameters, to systematically investigate the relationship between MoE architectural configurations and EL. Our findings reveal that EL is primarily driven by the expert activation ratio and the total compute budget, both following predictable power laws, while expert granularity acts as a non-linear modulator with a clear optimal range. We integrate these discoveries into a unified scaling law that accurately predicts the EL of an MoE architecture based on its configuration. To validate our derived scaling laws, we designed and trained Ling-mini-beta, a pilot model for Ling-2.0 series with only 0.85B active parameters, alongside a 6.1B dense model for comparison. When trained on an identical 1T high-quality token dataset, Ling-mini-beta matched the performance of the 6.1B dense model while consuming over 7x fewer computational resources, thereby confirming the accuracy of our scaling laws. This work provides a principled and empirically-grounded foundation for the scaling of efficient MoE models.