ID Balancing: Stable Training of Extremely Sparse MoE via PID-Based Load Control

Peng Jin, Zihan Qiu, Zekun Wang, Bo Zheng, Yang Xu +6

Scaling Large Language Models (LLMs) via Mixture-of-Experts (MoE) enables massive parameter growth with nearly constant per-token computation. However, further scaling the parameter count requires increasingly sparse routing, where expert load imbalance becomes more severe. This imbalance reduces parameter utilization and training efficiency, and can undermine training stability, becoming a bottleneck to reliable scaling. In this work, we unify two representative auxiliary-loss-free methods as incomplete Proportional-Integral-Derivative (PID) controllers: DeepSeek's loss-free method acts as a fixed-step integral controller, while Kimi K3's Quantile Balancing functions as a generalized proportional controller. Building on this control perspective, we propose ID Balancing, an Integral-Derivative controller. It scales its integral term with load error and activates its derivative term only when imbalance worsens, enabling stronger corrections for large or worsening errors and smaller updates near balance. Evaluated across Top-$10$, Top-$5$, and Top-$3$ routing over $768$ experts, ID Balancing reduces worst-case backbone MaxVio and training-average backbone MinVio by over $50\%$ and…