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Abstract - Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR
Muon is a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforce spectral gradient orthogonalization by driving all singular values of the momentum matrix toward 1. While this uniform spectral whitening enhances exploration and outperforms AdamW in LLM pretraining, we show it could lead to fundamental limitations beyond pretraining in two regimes: (i) cross-modality vision-language-action (VLA) training, where inherently low-rank action-module gradients cause amplification of noisy tail directions, and (ii) reinforcement learning with verifiable rewards (RLVR), where low-SNR gradients and the need to preserve per-head specialization from prior training make whitening unstable. To address these challenges, we propose Pion, a drop-in replacement for Muon that preserves its computational efficiency while replacing uniform spectral whitening with a two-stage Promotion+Suppression mechanism, which we call the high-pass NS iteration. This design induces a sharp spectral high-pass effect, anchoring dominant singular values at 1 while suppressing noisy tail components toward 0, with controllable filter strength. To preserve pretrained per-head heterogeneity, Pion also supports a per-head mode that applies updates independently across attention heads via a simple reshape, at no extra cost. In VLA training on LIBERO and LIBERO-Plus, Pion consistently outperforms both baselines across l_1-regression (VLA-Adapter) and flow-matching (VLANeXt) architectures, e.g., reaching 100% success rate on LIBERO Object after 1,500 training steps with VLA-Adapter, vs. 97.0% for Muon and only 32.2% for AdamW. The advantage of Pion further extends to a real Franka Research 3 robot with a pi_0.5 backbone under the DROID setup on three grasp-and-place tasks. In RLVR post-training on Qwen3-1.7B/4B with GRPO and GMPO, Pion also outperforms AdamW on MATH and GSM8K while Muon collapses to zero.
超越预训练:重新审视Muon优化器在视觉-语言-动作模型和带验证奖励强化学习中的频谱失效问题及高通滤波解决方案 /
Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR
1️⃣ 一句话总结
本文发现Muon优化器在预训练中有效的均匀频谱白化策略,在处理视觉-语言-动作模型中的低秩梯度以及带验证奖励的强化学习中的低信噪比梯度时会导致性能崩溃,为此提出了Pion优化器,通过一种高通滤波机制保留主要梯度方向同时抑制噪声尾巴,并在机器人操作和数学推理任务中显著优于Muon和AdamW。