Uncovering Emergent Physics Representations Learned In-Context by Large Language Models

TL;DR

This paper investigates how large language models learn and encode physical concepts during in-context learning, revealing that they develop representations aligned with physical variables like energy through analyzing their internal activations.

Contribution

It introduces a mechanistic analysis of LLMs' physics reasoning, showing that meaningful physical concepts are encoded during in-context learning using sparse autoencoders.

Findings

LLMs improve physics-based dynamics forecasting with longer contexts

Sparse autoencoders reveal features correlating with physical variables like energy

Physical concepts are encoded within LLMs during in-context learning

Abstract

Large language models (LLMs) exhibit impressive in-context learning (ICL) abilities, enabling them to solve wide range of tasks via textual prompts alone. As these capabilities advance, the range of applicable domains continues to expand significantly. However, identifying the precise mechanisms or internal structures within LLMs that allow successful ICL across diverse, distinct classes of tasks remains elusive. Physics-based tasks offer a promising testbed for probing this challenge. Unlike synthetic sequences such as basic arithmetic or symbolic equations, physical systems provide experimentally controllable, real-world data based on structured dynamics grounded in fundamental principles. This makes them particularly suitable for studying the emergent reasoning behaviors of LLMs in a realistic yet tractable setting. Here, we mechanistically investigate the ICL ability of LLMs, especially focusing on their ability to reason about physics. Using a dynamics forecasting task in physical systems as a proxy, we evaluate whether LLMs can learn physics in context. We first show that the performance of dynamics forecasting in context improves with longer input contexts. To uncover how such capability emerges in LLMs, we analyze the model's residual stream activations using sparse autoencoders (SAEs). Our experiments reveal that the features captured by SAEs correlate with key physical variables, such as energy. These findings demonstrate that meaningful physical concepts are encoded within LLMs during in-context learning. In sum, our work provides a novel case study that broadens our understanding of how LLMs learn in context.