Position: Understanding LLMs Requires More Than Statistical Generalization
<|reference_start|>Position: Understanding LLMs Requires More Than Statistical Generalization: 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.<|reference_end|>
@article{reizinger2024position:,
    title={Position: Understanding LLMs Requires More Than Statistical
  Generalization},
    author={Patrik Reizinger, Szilvia Ujv'ary, Anna M'esz'aros, Anna Kerekes,
  Wieland Brendel, Ferenc Husz'ar},
    journal={arXiv preprint arXiv:2405.01964},
    year={2024},
    archivePrefix={arXiv},
    eprint={2405.01964},
    primaryClass={stat.ML cs.LG}
}