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

Kavli Affiliate: Jia Liu

| First 5 Authors: Changxin Tian, Changxin Tian, , ,

| Summary:

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.

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