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Deriving neural scaling laws from the statistics of natural language (arxiv.org)
3 points by sharma-arjun 16 days ago | hide | past | pdf | discuss on HN

In plain words: Two language stats — how fast word links fade with distance, and how fast next-word uncertainty shrinks with context — predict how fast a model's error falls with more training data. It matched measured drop rates on two different kinds of text with no adjustable numbers.

Abstract · Deriving Neural Scaling Laws from the statistics of natural language

Despite the fact that experimental neural scaling laws have substantially guided empirical progress in large-scale machine learning, no existing theory can quantitatively predict the exponents of these important laws for any modern LLM trained on any natural language dataset. We provide the first such theory in the case of data-limited scaling laws. We isolate two key statistical properties of language that alone can predict neural scaling exponents: (i) the decay of pairwise token correlations with time separation between token pairs, and (ii) the decay of the next-token conditional entropy with the length of the conditioning context. We further derive a simple formula in terms of these statistics that predicts data-limited neural scaling exponents from first principles without any free parameters or synthetic data models. Our theory exhibits a remarkable match with experimentally measured neural scaling laws obtained from training GPT-2 and LLaMA style models from scratch on two qualitatively different benchmarks, TinyStories and WikiText.

Francesco Cagnetta, Allan Raventós, Surya Ganguli, Matthieu Wyart
arXiv:2602.07488 · cs.LG, cs.AI, stat.ML · submitted Feb 7, 2026 · updated Jul 3, 2026
abstract · pdf · html · ICML 2026

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