arXiv:2605. 02701v2 Announce Type: replace-cross Abstract: We propose a robust gradient estimator based on per-sample gradient clipping and analyze its properties both theoretically and empirically.
By Davide Nobile, Philipp Grohs
arXiv:2505.20817v3 Announce Type: replace-cross
Abstract: Gradient clipping is widely used in language-model training to control heavy-tailed gradient noise and can improve convergence guarantees ove...
By Taha El Bakkali El Kadi, Savelii Chezhegov, Aleksandr Beznosikov, Samuel Horv\'ath, Eduard Gorbunov
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.
By Zhuanghua Liu, Menglian Wang, Luo Luo
arXiv:2610.32465v1 Announce Type: new
Abstract: Adversarial sharpness penalty per iteration of a base optimizer, known as sharpness-aware minimization (SAM), is an accepted technique to improve gener...
By Geetika, Shivani Singh Chauhan, Gauranshi Gupta, Anant Jain, Kaushik Kalyanaraman, Bapi Chatterjee
arXiv:2610.19761v1 Announce Type: new
Abstract: Soft spectral clipping (SSC) reduces gradient singular values, but its effect depends on the gradient scale and clipping threshold. We introduce CAST (...
By Jiacheng Li, Jianchao Tan, Kefeng Zhang, Yuchen Xie, Xunliang Cai
The paper establishes the first optimal last‑iterate convergence rates, in high probability, for Clipped‑SGD when the gradient noise is heavy‑tailed. It addresses the gap left by earlier results that required strong noise assumptions, such as exponentially decaying tails. By proving these rates, the authors provide theoretical support for the practical effectiveness of gradient clipping in stochastic convex optimization.
By Zijian Liu