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Main Authors: Chen, Lizhang, Li, Jonathan, Wang, Qi, Liao, Runlong, Li, Shuozhe, Liang, Chen, Lao, Ni, Liu, Qiang
Format: Preprint
Published: 2026
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Online Access:https://arxiv.org/abs/2605.15403
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author Chen, Lizhang
Li, Jonathan
Wang, Qi
Liao, Runlong
Li, Shuozhe
Liang, Chen
Lao, Ni
Liu, Qiang
author_facet Chen, Lizhang
Li, Jonathan
Wang, Qi
Liao, Runlong
Li, Shuozhe
Liang, Chen
Lao, Ni
Liu, Qiang
contents Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $ϕ$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $ϕ$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.
format Preprint
id arxiv_https___arxiv_org_abs_2605_15403
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle $ϕ$-Balancing for Mixture-of-Experts Training
Chen, Lizhang
Li, Jonathan
Wang, Qi
Liao, Runlong
Li, Shuozhe
Liang, Chen
Lao, Ni
Liu, Qiang
Machine Learning
Optimization and Control
Mixture-of-Experts (MoE) models rely on balanced expert utilization to fully realize their scalability. However, existing load-balancing methods are largely heuristic and operate on noisy mini-batch assignment statistics, introducing bias relative to population-level objectives. We propose $ϕ$-balancing, a principled framework that directly targets population-level expert balance by minimizing a strictly convex, symmetric, and differentiable potential of the expected routing distribution. Using convex duality, we derive an equivalent min-max formulation and obtain a simple online algorithm via mirror descent, yielding an efficient EMA-based routing adjustment with negligible overhead. Across large-scale pretraining and downstream fine-tuning, $ϕ$-balancing consistently outperforms prior Switch-style and loss-free baselines, demonstrating more stable and effective expert utilization.
title $ϕ$-Balancing for Mixture-of-Experts Training
topic Machine Learning
Optimization and Control
url https://arxiv.org/abs/2605.15403