Unlocking Tokens as Data Points for Generalization Bounds on Larger Language Models

TL;DR

This paper introduces a novel approach using martingale properties to derive non-vacuous generalization bounds for large language models, leveraging token-based data to improve bounds for models like LLaMA2-70B.

Contribution

It presents a new method that exploits token properties to obtain meaningful generalization bounds for large, high-quality language models, surpassing previous compression-based approaches.

Findings

Achieved non-vacuous bounds for LLaMA2-70B.

Bound tightness benefits from token-based data rather than document count.

Demonstrated bounds for models generating high-quality text.

Abstract

Large language models (LLMs) with billions of parameters excel at predicting the next token in a sequence. Recent work computes non-vacuous compression-based generalization bounds for LLMs, but these bounds are vacuous for large models at the billion-parameter scale. Moreover, these bounds are obtained through restrictive compression techniques, bounding compressed models that generate low-quality text. Additionally, the tightness of these existing bounds depends on the number of IID documents in a training set rather than the much larger number of non-IID constituent tokens, leaving untapped potential for tighter bounds. In this work, we instead use properties of martingales to derive generalization bounds that benefit from the vast number of tokens in LLM training sets. Since a dataset contains far more tokens than documents, our generalization bounds not only tolerate but actually benefit from far less restrictive compression schemes. With Monarch matrices, Kronecker factorizations, and post-training quantization, we achieve non-vacuous generalization bounds for LLMs as large as LLaMA2-70B. Unlike previous approaches, our work achieves the first non-vacuous bounds for models that are deployed in practice and generate high-quality text.