Learning is Forgetting: LLM Training As Lossy Compression

TL;DR

This paper proposes viewing large language models as lossy compressors, linking their information retention to performance and providing an information-theoretic framework for understanding their learning process.

Contribution

It introduces an information-theoretic perspective on LLM training, demonstrating how compression relates to model performance and interpretability.

Findings

Pre-training results approach the Information Bottleneck bound.

Different models compress differently based on data and training recipes.

Optimal compression correlates with downstream benchmark performance.

Abstract

Despite the increasing prevalence of large language models (LLMs), we still have a limited understanding of how their representational spaces are structured. This limits our ability to interpret how and what they learn or relate them to learning in humans. We argue LLMs are best seen as an instance of lossy compression, where over training they learn by retaining only information in their training data relevant to their objective(s). We show pre-training results in models that are optimally compressed for next-sequence prediction, approaching the Information Bottleneck bound on compression. Across an array of open weights models, each compresses differently, likely due to differences in the data and training recipes used. However even across different families of LLMs the optimality of a model's compression, and the information present in it, can predict downstream performance on across a wide array of benchmarks, letting us directly link representational structure to actionable insights about model performance. In the general case the work presented here offers a unified Information-Theoretic framing for how these models learn that is deployable at scale.