Author

Fang-Hui Liu

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#machine learning Preprint Sep 2026

From Spectra to Joint Schedules in LLM Pre-training: 3+3(+2) Scaling-Law Regimes

Power-law learning curves are often treated as fixed properties of a model and its data, although learning-rate and batch-size schedules can change the observed loss. We study this dependence in noisy online SGD with linear random features. Conditional on the representation, an exact Volterra equation separates two res...

Yi-Chen Wang, Fang-Hui Liu, Yu-Dong Chen · 0 citations

#machine learning Preprint Sep 2026

Muon Sublates the Edge of Stability in LLM Pretraining

Results support a split EoS picture for Muon: a stochastic loss-neutral edge survives, but it is not accompanied by a universal temporal-direction signature, and directions remain far from coherent reversal while training continues to improve.

Yan-Zhe Chen, Qifang Zhao, Xiao-Xiao Xu et al. · 0 citations