Compute-Optimal LLMs Provably Generalize Better With Scale

Fuente: arXiv
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Main Authors: Finzi, Marc, Kapoor, Sanyam, Granziol, Diego, Gu, Anming, De Sa, Christopher, Kolter, J. Zico, Wilson, Andrew Gordon
Format: Preprint
Published: 2025
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author Finzi, Marc
Kapoor, Sanyam
Granziol, Diego
Gu, Anming
De Sa, Christopher
Kolter, J. Zico
Wilson, Andrew Gordon
author_facet Finzi, Marc
Kapoor, Sanyam
Granziol, Diego
Gu, Anming
De Sa, Christopher
Kolter, J. Zico
Wilson, Andrew Gordon
contents Why do larger language models generalize better? To investigate this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla scaling laws. We introduce a novel, fully empirical Freedman-type martingale concentration inequality that tightens existing bounds by accounting for the variance of the loss function. This generalization bound can be decomposed into three interpretable components: the number of parameters per token, the loss variance, and the quantization error at a fixed bitrate. As compute-optimal language models are scaled up, the number of parameters per data point remains constant; however, both the loss variance and the quantization error decrease, implying that larger models should have smaller generalization gaps. We examine why larger models tend to be more quantizable from an information theoretic perspective, showing that the rate at which they can integrate new information grows more slowly than their capacity on the compute-optimal frontier. From these findings we produce a scaling law for the generalization gap, with bounds that become predictably stronger with scale.
format Preprint
id arxiv_https___arxiv_org_abs_2504_15208
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Compute-Optimal LLMs Provably Generalize Better With Scale
Finzi, Marc
Kapoor, Sanyam
Granziol, Diego
Gu, Anming
De Sa, Christopher
Kolter, J. Zico
Wilson, Andrew Gordon
Machine Learning
Artificial Intelligence
Why do larger language models generalize better? To investigate this question, we develop generalization bounds on the pretraining objective of large language models (LLMs) in the compute-optimal regime, as described by the Chinchilla scaling laws. We introduce a novel, fully empirical Freedman-type martingale concentration inequality that tightens existing bounds by accounting for the variance of the loss function. This generalization bound can be decomposed into three interpretable components: the number of parameters per token, the loss variance, and the quantization error at a fixed bitrate. As compute-optimal language models are scaled up, the number of parameters per data point remains constant; however, both the loss variance and the quantization error decrease, implying that larger models should have smaller generalization gaps. We examine why larger models tend to be more quantizable from an information theoretic perspective, showing that the rate at which they can integrate new information grows more slowly than their capacity on the compute-optimal frontier. From these findings we produce a scaling law for the generalization gap, with bounds that become predictably stronger with scale.
title Compute-Optimal LLMs Provably Generalize Better With Scale
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2504.15208