Position: Understanding LLMs Requires More Than Statistical Generalization

TL;DR

This paper argues that understanding large language models (LLMs) requires more than statistical generalization, emphasizing the importance of model non-identifiability and its implications for various LLM capabilities.

Contribution

It introduces the concept that non-identifiability in probabilistic models explains several LLM behaviors, supported by mathematical examples and empirical case studies.

Findings

Non-identifiability explains zero-shot rule extrapolation.

In-context learning is approximately non-identifiable.

Fine-tunability also exhibits non-identifiability issues.

Abstract

The last decade has seen blossoming research in deep learning theory attempting to answer, "Why does deep learning generalize?" A powerful shift in perspective precipitated this progress: the study of overparametrized models in the interpolation regime. In this paper, we argue that another perspective shift is due, since some of the desirable qualities of LLMs are not a consequence of good statistical generalization and require a separate theoretical explanation. Our core argument relies on the observation that AR probabilistic models are inherently non-identifiable: models zero or near-zero KL divergence apart -- thus, equivalent test loss -- can exhibit markedly different behaviors. We support our position with mathematical examples and empirical observations, illustrating why non-identifiability has practical relevance through three case studies: (1) the non-identifiability of zero-shot rule extrapolation; (2) the approximate non-identifiability of in-context learning; and (3) the non-identifiability of fine-tunability. We review promising research directions focusing on LLM-relevant generalization measures, transferability, and inductive biases.