TrasMuon: Trust-Region Adaptive Scaling for Orthogonalized Momentum Optimizers

Peng Cheng, Jiucheng Zang, Qingnan Li, Liheng Ma, Yufei Cui, Yingxue Zhang, Boxing Chen, Ming Jian, Wen Tong

Keywords: Optimizer, Muon

Abstract: Muon-style optimizers leverage Newton-Schulz (NS) iterations to orthogonalize updates, yielding update geometries that often outperform Adam-series methods. However, this orthogonalization discards magnitude information, rendering training sensitive to step-size hyperparameters and vulnerable to high-energy bursts. To mitigate this, we introduce TrasMuon (**T**rust **R**egion **A**daptive **S**caling **Muon**). TrasMuon preserves the near-isometric geometry of Muon while stabilizing magnitudes through (i) global RMS calibration and (ii) energy-based trust-region clipping. We demonstrate that while reintroducing adaptive scaling improves optimization efficiency, it typically exacerbates instability due to high-energy outliers. TrasMuon addresses this by defining a trust region based on relative energy ratios, confining updates to a stable zone. Empirical experiments on vision and language models demonstrate that TrasMuon converges faster than baselines. Furthermore, experiments without warmup stages confirm TrasMuon’s superior stability and robustness.

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Challenge: This submission is an entry to the science of DL improvement challenge.

Submission Number: 65