Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR

Hugging Face Daily Papers Papers
optimizer vision-language-action reinforcement-learning spectral-whitening arxiv machine-learning

Summary

This paper introduces Pion, a new optimizer that replaces Muon's spectral whitening with a high-pass NS iteration to stabilize training in low-rank and low-SNR regimes, achieving improved performance in VLA and RLVR tasks.

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.
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Paper page - Rethinking Muon Beyond Pretraining: Spectral Failures and High-Pass Remedies for VLA and RLVR

Source: https://huggingface.co/papers/2605.19282

Abstract

Muon’s spectral whitening approach in LLM pretraining is replaced by Pion, which uses a high-pass NS iteration to stabilize training in low-rank and low-SNR regimes while maintaining computational efficiency and supporting per-head updates.

Muonis a matrix-aware optimizer that leverages Newton-Schulz (NS) iterations to enforcespectral gradient orthogonalizationby driving allsingular valuesof 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 forMuonthat 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 sharpspectral high-pass effect, anchoring dominantsingular valuesat 1 while suppressing noisy tail components toward 0, with controllable filter strength. To preserve pretrained per-head heterogeneity, Pion also supports aper-head modethat applies updates independently acrossattention headsvia 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 withVLA-Adapter, vs. 97.0% forMuonand 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 theDROID setupon three grasp-and-place tasks. In RLVR post-training on Qwen3-1.7B/4B withGRPOandGMPO, Pion also outperforms AdamW on MATH and GSM8K whileMuoncollapses to zero.

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