# Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling

arXiv: https://arxiv.org/abs/2604.12806 · HTML: https://mlsanity.com/paper/2604.12806/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 14 Apr 2026.

## Builds on (most cited first, 9 of 9)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [Factorised Neural Relational Inference for Multi-Interaction Systems](https://mlsanity.com/paper/1905.08721/) (2019)
- [Interpretable Machine Learning in Physics: A Review](https://mlsanity.com/paper/2503.23616/) (2025)
- [Automated discovery of interpretable gravitational-wave population models](https://mlsanity.com/paper/2207.12409/) (2022)
- [Learning Heterogeneous Interaction Strengths by Trajectory Prediction with Graph Neural Network](https://mlsanity.com/paper/2208.13179/) (2022)
- [Attention for Causal Relationship Discovery from Biological Neural Dynamics](https://mlsanity.com/paper/2311.06928/) (2023)
- [Deep learning reveals hidden interactions in complex systems](https://mlsanity.com/paper/2001.02539/) (2020)
- [SINDyG: Sparse Identification of Nonlinear Dynamical Systems from Graph-Structured Data, with Applications to Stuart-Landau Oscillator Networks](https://mlsanity.com/paper/2409.04463/) (2024)

## Abstract (arXiv)

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 COSINE (Co-Optimization of Symbolic Interactions and Network Edges), 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.