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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

Muon is increasingly used for language-model pretraining, yet its large-step dynamics are not captured by the classical edge-of-stability (EoS) picture of gradient descent (GD). In GD, loss neutrality, equal-magnitude update reversal, and marginal stability meet at a single learning-rate-dependent edge. We show that Mu...

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

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