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

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.

Exploring how deep learning decodes anomalous diffusion via Grad-CAM

While deep learning has been successfully applied to the data-driven classification of anomalous diffusion mechanisms, how the algorithm achieves the feat still remains a mystery. In this study, we use a well-known technique aimed at achieving explainable AI, namely the Gradient-weighted Class Activation Map (Grad-CAM), to investigate how deep learning (implemented by ResNets) recognizes the distinctive features of a particular anomalous diffusion model from the raw trajectory data. Our results show that Grad-CAM reveals the portions of the trajectory that hold crucial information about the underlying mechanism of anomalous diffusion, which can be utilized to enhance the robustness of the trained classifier against the measurement noise. Moreover, we observe that deep learning distills unique statistical characteristics of different diffusion mechanisms at various spatiotemporal scales, with larger-scale (smaller-scale) features identified at higher (lower) layers.

From Empirical Observations to Universality: Dynamics of Deep Learning with Inputs Built on Gaussian mixture

This study broadens the scope of theoretical frameworks in deep learning by delving into the dynamics of neural networks with inputs that demonstrate the structural characteristics to Gaussian Mixture (GM). We analyzed how the dynamics of neural networks under GM-structured inputs diverge from the predictions of conventional theories based on simple Gaussian structures. A revelation of our work is the observed convergence of neural network dynamics towards conventional theory even with standardized GM inputs, highlighting an unexpected universality. We found that standardization, especially in conjunction with certain nonlinear functions, plays a critical role in this phenomena. Consequently, despite the complex and varied nature of GM distributions, we demonstrate that neural networks exhibit asymptotic behaviors in line with predictions under simple Gaussian frameworks.