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arXiv · 2605.23061

Anytime Training with Schedule-Free Spectral Optimization

Anuj Apte·Pranav Deshpande·Niraj Kumar·Shouvanik Chakrabarti·Junhyung Lyle Kim
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Abstract

Standard neural network training relies on learning-rate schedules tied to a fixed horizon, leading to strong path dependence and costly re-tuning as data availability changes. Schedule-Free (SF) methods address this by removing explicit schedules, yet SF-AdamW, the current state-of-the-art anytime optimizer, consistently underperforms well-tuned AdamW baselines. We propose SF-NorMuon, a schedule-free spectral optimizer that closes this gap: with a single hyperparameter configuration, SF-NorMuon matches or exceeds tuned AdamW on 125M and 772M parameter language models across $1$--$8\times$ Chinchilla horizons. On the theoretical side, we prove a stationarity guarantee for schedule-free spectral dynamics and identify weight decay at the fast iterate as essential for long-horizon stability. SF-NorMuon enables practitioners to obtain high-quality checkpoints at any point during training without committing to a horizon in advance. By closing the performance gap with tuned baselines, SF-NorMuon makes horizon-free optimization more practical, taking a step towards truly open-ended, continual learning.

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BibTeXRIS

Anuj Apte, Pranav Deshpande, Niraj Kumar, Shouvanik Chakrabarti, Junhyung Lyle Kim. 2026-05-21. Anytime Training with Schedule-Free Spectral Optimization. https://arxiv.org/abs/2605.23061

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