arXiv Machine Learning By Zitao Song, Cedar Site Bai, Zhe Zhang, Brian Bullins, David F. Gleich

Can Entry-Wise Clipping Give Spectral Control of Stochastic Gradients?

Read the original on arXiv Machine Learning →

arXiv:2605. 27733v2 Announce Type: replace Abstract: Training instabilities such as loss spikes are frequently the result of stochastic gradient noise.

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arXiv Machine Learning
Sep 11

Musec: MomentUm SpEctral Clipping for Stable Muon-type Training

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 Machine Learning
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On the Last-Iterate Convergence of Clipped Gradient Methods

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By Zijian Liu