"juntas" [Blum and Langley, 1997]), that is functions that depend only on a small number

We explain the discrepancy by reproducing the Kaplan et al. scaling law on two datasets (OpenWebText2 and RefinedWeb)

Neural Information Processing Systems http://nips.cc/

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.

Is Integer Arithmetic Enoughfor Deep Learning Training?

Wefurthermore derive, with mathematical proof and extensive numerical evidence, the scalinglawexponents inallofthese phases, inparticular computing theoptimal modelparameter-count as a function of floating point operation budget.