Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra
Authors: Ben S. Southworth, Shuai Jiang, Daniel McBride, Eric C. Cyr, Stephen Thomas
Abstract
Muon is a recently developed matrix-aware optimizer that has shown strong results in transformer training, but its behavior in vision transformers (ViTs) is not yet well understood. We study Muon for ViT training, largely on ImageNet-100 and Pl@ntNet-300K, comparing against AdamW under standard vision recipes involving mixup, cutmix, smoothing, and random augmentation and erasing. Muon consistently outperforms AdamW, with especially large gains on long-tailed Pl@ntNet macro top-1. These gains are also recipe-dependent, where Muon benefits much more than AdamW from advanced and significant data augmentation techniques. To understand this interaction, we analyze the singular-value structure of matrix gradients throughout the ViT. Within Muon training runs, removing heavy data augmentation induces a late-training spectral concentration and mode collapse in gradient matrices, primarily in deep MLP-down blocks. Under a fixed "full" augmentation recipe, the clearest Muon-AdamW contrast appears instead in QKV gradients, where AdamW gradient energy remains concentrated in a much narrower basis while Muon spreads energy across substantially more singular modes. Muon in ViTs is therefore best understood as an optimizer-recipe interaction. Under a fixed recipe, Muon differs from AdamW most clearly in attention projections, where its gradients consist of a broader spectral basis. Within Muon, a full training recipe is important for preventing late spectral concentration and mode collapse in deep feedforward blocks. We further demonstrate efficacy in training ViTs on image segmentation and masked autoencoder models, where Muon outperforms AdamW in all settings considered.
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.
Muon has recently emerged as a strong optimizer for large-scale deep learning, where it reshapes gradient updates through approximate orthogonalization and has been reported to outperform Adam and AdamW in large language model training. Its empirical success has motivated a growing body of theoretical work that interprets Muon as steepest descent under the spectral norm. Yet it remains unclear which of Muon's advantages stem from its update rule itself and which are artifacts of the scale, architecture, and data of modern deep networks. In this work, we isolate the optimizer from these confounding factors by studying Muon on a simple, well-understood, and spectrally structured problem: low-rank matrix factorization. Through a controlled comparison against carefully tuned adaptive baselines, we find that Muon does not consistently outperform AdamW in this setting and that several previously reported advantages are sensitive to hyperparameter choices. Our results provide a more nuanced picture of when spectrum-aware orthogonalization is beneficial and argue for evaluating modern optimizers on controlled problems in addition to end-to-end benchmarks.
Diffusion Transformers (DiTs) have achieved state-of-the-art (SOTA) performance in visual generative modeling, yet their training remains computationally prohibitive. While the recently proposed Momentum Orthogonalization (Muon) optimizer offers a promising alternative to AdamW, its direct application to DiTs yields suboptimal late-stage convergence. In this paper, we identify the root cause of this bottleneck: standard DiT architectures fuse functionally distinct weights (e.g., within AdaLN and QKV layers) into unified tensors for computational efficiency. Applying Muon to these fused tensors inadvertently induces implicit subspace coupling, which distorts update directions and degrades global optimization. To address this, we introduce Chunked Muon (CMuon), a simple yet highly effective strategy that partitions these matrices into independent sub-components prior to orthogonalization. Extensive experiments demonstrate that a 675M-parameter DiT trained with CMuon achieves a FID of 1.18 on ImageNet 256 in just 200 epochs. This represents more than a 2x training speedup over AdamW, while effectively overcoming the late-stage convergence plateaus of vanilla Muon.