Scaling laws in LLM training emerge from schedules, not fixed properties
Researchers have decoupled power-law scaling behavior in LLM pre-training from fixed model properties, showing instead that learning-rate and batch-size schedules fundamentally reshape loss curves. Using spectral analysis of noisy SGD, the work proves that scaling laws emerge conditionally from weighted spectral mass distributions rather than individual eigenvalue patterns. This finding reframes optimization as a joint scheduling problem where intrinsic time and batch dynamics interact to control convergence. The insight matters for practitioners tuning training regimes: observed scaling laws are not immutable constraints but artifacts of schedule design, opening new levers for efficiency gains during pre-training.
Modelwire context
ExplainerThe paper's core claim is that scaling laws aren't intrinsic to model architecture or data but emerge from how you schedule learning rate and batch size during training. This inverts the usual framing: instead of asking 'what scaling law does this model follow?', practitioners should ask 'what scaling law do I want to construct?'
This connects directly to ScAn-Bench (late September), which exposed hidden methodological assumptions baked into how labs derive scaling curves. Where ScAn-Bench asked which measurement techniques actually work, this paper goes deeper: it shows the curves themselves are artifacts of optimization schedule design, not ground truth. The finding also contextualizes the Looped MoE scaling work from the same week, which unified efficiency laws across architectural choices. If schedules reshape loss trajectories, then comparing scaling laws across different training regimes requires accounting for this schedule dependency, not just model architecture.
If teams report reproducing published scaling laws with different learning-rate schedules on the same model and data, that confirms the thesis. Conversely, if major labs begin publishing their full schedule specifications alongside scaling curves (rather than just final hyperparameters), that signals the field is taking schedule-dependence seriously as a confound.
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MentionsLLM · SGD · Volterra equation · spectral analysis
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Modelwire summarizes, we don’t republish. arXiv cs.LG originally reported this story as “From Spectra to Joint Schedules in LLM Pre-training: 3+3(+2) Scaling-Law Regimes”. The full content lives on arxiv.org. If you’re a publisher and want a different summarization policy for your work, see our takedown page.