Smooth Scaling Laws Hide Stepwise Token Learning

2026-06-29

AI Summary

Although the overall loss of language models follows a smooth power-law scaling, the token-level learning dynamics remain poorly understood. This work proposes a token-level analysis framework that fits the loss trajectory of each contextualized token with a sigmoid function, revealing that learning predominantly occurs through discrete phase transitions. For the first time on large-scale real-world pretraining data, the study demonstrates that the temporal spectrum of token learning governs the shape of scaling laws and leverages this insight to design a training data reweighting strategy. Based on over one hundred pretraining experiments, the method successfully reconstructs the derivative of validation loss, achieving an 11% faster decline in validation loss compared to standard training.

Abstract

Language model loss follows remarkably regular scaling laws over model and data size, yet it remains unclear why the aggregate loss should exhibit a power-law form. Existing explanations often attribute this regularity to a heavy-tailed spectrum of pattern difficulty in natural language, but this view has not been directly validated at token-level granularity in large-scale real-data training. We present a token-level framework that decomposes scaling laws into localized learning events of individual contextualized tokens. By fitting token loss trajectories with sigmoids, we show that token learning is concentrated in localized transitions, giving rise to a learning-time spectrum that dominates the scaling-law shape. Across more than one hundred pre-training runs on large and diverse real-language corpora with modern LLM architectures, scaling up to 6B parameters and 300B training tokens, the measured learning-time spectrum quantitatively reconstructs the validation loss derivative along the training-step $T$, data-scale $D$, and model-scale $M$ axes. We further show that the same signal is actionable: by reshaping the training distribution according to when tokens become learnable, we alter the optimization trajectory and achieve 11\% faster validation-loss reduction. These results provide direct empirical evidence that scaling laws are governed primarily by the distribution of token-level learning times, and that this distribution can be used not only to explain scaling behavior but also to improve training performance.

Problem

• scaling laws
• token-level learning
• language models
• loss trajectory
• learning-time spectrum

Innovation

• scaling laws
• token-level learning
• learning-time spectrum
• sigmoid fitting
• training distribution reshaping