Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling

2026-04-14

AI Summary

This work addresses the challenge of jointly inferring latent interaction structures and interpretable dynamical equations from dynamic observational data by introducing the COSINE framework. COSINE uniquely integrates large language models with differentiable symbolic regression, enabling joint optimization of graph structure learning and symbolic dynamics. This co-optimization dynamically adapts the symbolic hypothesis space, facilitating the simultaneous discovery of unknown network topologies and governing evolution equations. Experiments on both synthetic systems and real-world large-scale epidemiological data demonstrate that COSINE accurately recovers underlying interaction graphs and produces concise, physically plausible dynamical expressions, substantially enhancing model interpretability and generalization capability.

Technology Category

• Machine Learning: Neuro-Symbolic Learning
• Cognitive Modeling & Cognitive Systems: Symbolic Representations
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• relational inference
• symbolic dynamics
• interpretable modeling
• interaction structure
• many-body systems

Innovation

• symbolic dynamics
• interaction graph discovery
• large language model
• differentiable optimization
• interpretable AI