arXiv:2606. 14187v1 Announce Type: new Abstract: Large-scale neural network training increasingly relies on matrix-aware optimizers that exploit the structure of weight parameters beyond element-wise adaptation.
arXiv:2607. 13246v1 Announce Type: cross Abstract: 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.
The paper investigates why the orthogonal optimiser Muon outperforms Adam in large language model pretraining by analysing the spectral properties of Transformer loss landscapes. It finds that Muon’s momentum buffers exhibit an anisotropic spectral profile with a volatile head and a tolerant bulk, enabling larger effective step sizes. Building on this insight, the authors propose Spectral‑Aware Muon (SAMuon) and a lightweight variant, which adjust the bulk scaling while keeping the head unchanged, achieving 13–24 % fewer training tokens than Muon without extra FLOPs.
arXiv:2606. 25971v1 Announce Type: new Abstract: Modern neural network training relies on optimizers such as Adam and Muon which act on each weight matrix as a single object.
arXiv:2609.36692v1 Announce Type: cross Abstract: Matrix optimizers have emerged as a promising direction, with Muon standing out as a prominent design. Revisiting Muon through its full-Gram represen...
arXiv:2606. 27153v1 Announce Type: cross Abstract: Matrix-orthogonalization-based optimizers, exemplified by Muon, have demonstrated strong convergence behavior across a wide range of modern deep learning workloads.
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.
arXiv:2606. 16454v1 Announce Type: cross Abstract: Low-Rank Adaptation (LoRA) enables efficient adaptation of large pre-trained models to downstream tasks by parameterizing weight updates with low-rank matrices.
arXiv:2607. 17620v1 Announce Type: new Abstract: Low-rank adaptation (LoRA) makes finetuning large language models cheaper by adding to each weight matrix a trainable low-rank update parameterized as the product of two matrices.
The paper investigates the often-overlooked scale vectors in large language models, showing that despite their tiny size they are crucial for pre‑training performance. The authors provide theoretical insights that scale vectors mainly aid optimization rather than expressivity, and they analyze how weight decay affects different normalization layers. Building on these findings, they propose lightweight improvements—branch‑specific heterogeneity, better placement, and magnitude‑direction reparameterization—that consistently reduce loss across a range of model sizes and training settings.
Musec introduces MomentUm SpEctral Clipping, an optimizer-level, architecture‑agnostic technique that replaces Muon’s spectral flattening with selective spectral clipping to stabilize training. By clipping singular values above a threshold while preserving the momentum’s spectral structure, Musec addresses loss spikes and unbounded weight growth without requiring architecture‑specific changes. Soft Musec, an efficient implementation using smooth spectral saturation via coupled Newton‑Schulz iterations, offers convergence guarantees in nonconvex nonsmooth stochastic optimization and empirically improves stability across diverse learning rates and model sizes.
The paper introduces Newton-Schulz Attention (NS-Attn.), a parameter‑free transformation that applies a finite Newton‑Schulz polynomial step to the output of each attention head in Vision Transformers. By normalizing each head’s feature‑by‑token matrix with its Frobenius norm, applying the NS step, and restoring the norm, the method aims to reduce spectral concentration and increase effective rank before merging heads. Experiments on ViT and Swin models over CIFAR‑10 and CIFAR‑100 show consistent accuracy gains of 0.25–0.83 percentage points, though with added inference latency.
arXiv:2604. 09967v2 Announce Type: replace-cross Abstract: Muon has emerged as a promising optimizer for large-scale foundation model pre-training by exploiting the matrix structure of neural network updates through iterative orthogonalization.