Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling
Xiaoxiao Liang, Juyuan Zhang, Liming Pan, Linyuan Lü
TLDR
COSINE is a new framework that uses an LLM to guide symbolic dynamics modeling, jointly discovering interaction graphs and interpretable equations.
Key contributions
- Proposes COSINE, a differentiable framework for joint discovery of interaction graphs and sparse symbolic dynamics.
- Integrates an outer-loop LLM to adaptively prune and expand the symbolic hypothesis space.
- Overcomes limitations of fixed symbolic libraries and black-box neural approaches for relational inference.
- Achieves robust structural recovery and compact, mechanism-aligned dynamical expressions on real-world data.
Why it matters
This work addresses a key challenge in many-body systems by providing a method to infer both interaction structures and their governing equations. By leveraging LLMs, it offers a more interpretable alternative to black-box neural models, crucial for understanding complex dynamics.
Original Abstract
Inferring latent interaction structures from observed dynamics is a fundamental inverse problem in many-body interacting systems. Most neural approaches rely on black-box surrogates over trainable graphs, achieving accuracy at the expense of mechanistic interpretability. Symbolic regression offers explicit dynamical equations and stronger inductive biases, but typically assumes known topology and a fixed function library. We propose \textbf{COSINE} (\textbf{C}o-\textbf{O}ptimization of \textbf{S}ymbolic \textbf{I}nteractions and \textbf{N}etwork \textbf{E}dges), a differentiable framework that jointly discovers interaction graphs and sparse symbolic dynamics. To overcome the limitations of fixed symbolic libraries, COSINE further incorporates an outer-loop large language model that adaptively prunes and expands the hypothesis space using feedback from the inner optimization loop. Experiments on synthetic systems and large-scale real-world epidemic data demonstrate robust structural recovery and compact, mechanism-aligned dynamical expressions. Code: https://anonymous.4open.science/r/COSINE-6D43.
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