LLMs learn governing principles of dynamical systems, revealing an in-context neural scaling law
Toni J.b. Liu, Nicolas Boulle, Raphaël Sarfati, Christopher Earls
Abstract
We study LLMs’ ability to extrapolate the behavior of various dynamical systems, including stochastic, chaotic, continuous, and discrete systems, whose evolution is governed by principles of physical interest. Our results show that LLaMA-2, a language model trained on text, achieves accurate predictions of dynamical system time series without fine-tuning or prompt engineering. Moreover, the accuracy of the learned physical rules increases with the length of the input context window, revealing an in-context version of a neural scaling law. Along the way, we present a flexible and efficient algorithm for extracting probability density functions of multi-digit numbers directly from LLMs.
BibTeX
@inproceedings{liu-etal-2024-llms-learn,
title = "{LLM}s learn governing principles of dynamical systems, revealing an in-context neural scaling law",
author = {Liu, Toni J.b. and
Boulle, Nicolas and
Sarfati, Rapha{\"e}l and
Earls, Christopher},
editor = "Al-Onaizan, Yaser and
Bansal, Mohit and
Chen, Yun-Nung",
booktitle = "Proceedings of the 2024 Conference on Empirical Methods in Natural Language Processing",
month = nov,
year = "2024",
address = "Miami, Florida, USA",
publisher = "Association for Computational Linguistics",
url = "https://aclanthology.org/2024.emnlp-main.842/",
doi = "10.18653/v1/2024.emnlp-main.842",
pages = "15097--15117"
}