arXiv:2603. 28921v3 Announce Type: replace-cross Abstract: The critical damping condition of the damped harmonic oscillator model of SGD with momentum (Qian, 1999) yields a momentum schedule with no tuned hyperparameters: mu(t) = 1 - 2*sqrt(alpha(t)).
By Ivan Pasichnyk
arXiv:2607. 22927v1 Announce Type: new Abstract: Weights and biases are normally optimized as separate parameter tensors, yet they do not represent separate functions when the input to an affine layer has nonzero mean.
By Zhang Gongyue, Sheng Yixuan, Liu donghan, Wang Zhiyong, Ren Weihong, Liu honghai
AF‑Muon is an AdamW‑free extension of the Muon optimizer that retains Muon’s matrix update for hidden weights while applying a support‑aware finite‑cap linear minimization oracle to tied vocabulary tables and an RMS‑normalized update for one‑dimensional auxiliary parameters. This design eliminates second‑moment state, reducing optimizer‑state memory by about 20% compared to Hybrid Muon. Across nine tied‑token settings—including decoder‑only language models, T5‑style encoder‑decoders, and ImageGPT‑style variants—AF‑Muon consistently improves mean validation loss and perplexity over both Hybrid Muon and a SCION‑style Sign endpoint, with robust gains confirmed by long‑horizon runs and hyperparameter studies.
By Arash Lagzian, Paniz Halvachi, Junming Zhang, Zhouhan Lin, Dianbo Liu
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.
By Xiaodong Wu, Wenyi Yu, Chao Zhang, Philip Woodland
The paper introduces the Drift Contract, a spectral update geometry for local learning that improves depth robustness and hyperparameter stability. By applying momentum orthogonalization with spectral step scaling to per‑layer updates, the authors achieve consistent performance across a wide range of widths and depths on CIFAR‑10 MLPs, outperforming local Adam and providing a per‑layer, input‑conditioned drift bound. The study also shows that the spectral geometry itself, rather than step‑size rules, drives the observed depth robustness, while a negative result indicates that the stability benefit is limited to non‑normalized layers.
By Fabien Polly
arXiv:2607. 19331v1 Announce Type: cross Abstract: Reinforcement learning with verifiable rewards (RLVR) is rapidly advancing the reasoning capabilities of language models, yet the optimization layer that converts reward feedback into weight-space updates remains poorly understood.
By Hanqing Zhu, Wenyan Cong, Zhizhou Sha, Sagnik Mukherjee, Xinyuan Song, David Gonz\'alez-Mart\'inez, Xiaoxia Wu, Yuandong Tian, Shiwei Liu, David Z. Pan, Zhangyang "Atlas" Wang