# Muon in Vision Transformers: Optimizer-Recipe Interactions and Gradient Spectra

arXiv: https://arxiv.org/abs/2605.24770 · HTML: https://mlsanity.com/paper/2605.24770/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 31 of its 39 references that are in the map.
- First posted on arXiv 23 May 2026.

## Builds on (most cited first, 30 of 31)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [DINOv2: Learning Robust Visual Features without Supervision](https://mlsanity.com/paper/2304.07193/) (2023)
- [Masked Autoencoders Are Scalable Vision Learners](https://mlsanity.com/paper/2111.06377/) (2021)
- [mixup: Beyond Empirical Risk Minimization](https://mlsanity.com/paper/1710.09412/) (2017)
- [Fully Convolutional Networks for Semantic Segmentation](https://mlsanity.com/paper/1411.4038/) (2014)
- [Scaling Up Visual and Vision-Language Representation Learning With Noisy Text Supervision](https://mlsanity.com/paper/2102.05918/) (2021)
- [SegFormer: Simple and Efficient Design for Semantic Segmentation with Transformers](https://mlsanity.com/paper/2105.15203/) (2021)
- [CutMix: Regularization Strategy to Train Strong Classifiers with Localizable Features](https://mlsanity.com/paper/1905.04899/) (2019)
- [Xception: Deep Learning with Depthwise Separable Convolutions](https://mlsanity.com/paper/1610.02357/) (2016)
- [RandAugment: Practical automated data augmentation with a reduced search space](https://mlsanity.com/paper/1909.13719/) (2019)
- [DINOv3](https://mlsanity.com/paper/2508.10104/) (2025)
- [Random Erasing Data Augmentation](https://mlsanity.com/paper/1708.04896/) (2017)
- [Self-Supervised Learning from Images with a Joint-Embedding Predictive Architecture](https://mlsanity.com/paper/2301.08243/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [data2vec: A General Framework for Self-supervised Learning in Speech, Vision and Language](https://mlsanity.com/paper/2202.03555/) (2022)
- [LoveDA: A Remote Sensing Land-Cover Dataset for Domain Adaptive Semantic Segmentation](https://mlsanity.com/paper/2110.08733/) (2021)
- [Optimal whitening and decorrelation](https://mlsanity.com/paper/1512.00809/) (2015)
- [Muon Optimizes Under Spectral Norm Constraints](https://mlsanity.com/paper/2506.15054/) (2025)
- [Gluon: Making Muon & Scion Great Again! (Bridging Theory and Practice of LMO-based Optimizers for LLMs)](https://mlsanity.com/paper/2505.13416/) (2025)
- [PolarGrad: A Class of Matrix-Gradient Optimizers from a Unifying Preconditioning Perspective](https://mlsanity.com/paper/2505.21799/) (2025)
- [Muon Outperforms Adam in Tail-End Associative Memory Learning](https://mlsanity.com/paper/2509.26030/) (2025)
- [Convergence of Muon with Newton-Schulz](https://mlsanity.com/paper/2601.19156/) (2026)
- [To Use or not to Use Muon: How Simplicity Bias in Optimizers Matters](https://mlsanity.com/paper/2603.00742/) (2026)
- [SpecFormer: Guarding Vision Transformer Robustness via Maximum Singular Value Penalization](https://mlsanity.com/paper/2402.03317/) (2024)
- [FastPose-ViT: A Vision Transformer for Real-Time Spacecraft Pose Estimation](https://mlsanity.com/paper/2512.09792/) (2025)
- [Beyond Muon: MUD (MomentUm Decorrelation) for Faster Transformer Training](https://mlsanity.com/paper/2603.17970/) (2026)
- [Efficient Adaptation of Pre-trained Vision Transformer underpinned by Approximately Orthogonal Fine-Tuning Strategy](https://mlsanity.com/paper/2507.13260/) (2025)
- [Muon-Accelerated Attention Distillation for Real-Time Edge Synthesis via Optimized Latent Diffusion](https://mlsanity.com/paper/2504.08451/) (2025)

## Built on by (most cited first, 1 of 1)

- [The Drift Contract: Spectral Updates for Depth-Robust Local Learning](https://mlsanity.com/paper/2609.26811/) (2026)

## Abstract (arXiv)

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.