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Interpretable Relational Inference with LLM-Guided Symbolic Dynamics Modeling

NeurIPS 2026 · Probabilistic and scientific modeling › Dynamical systems · approach: Switching and law-discovery dynamics · 0 citations (OpenAlex)

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Proposes COSINE, a differentiable framework that jointly infers latent interaction graphs and sparse symbolic message/update dynamics over LLM-evolved basis libraries, evaluated on six synthetic systems and COVID-19 mobility data.

Problem

Relational inference of latent interaction graphs from observed dynamics, where black-box neural methods lack interpretability and symbolic regression requires known topology and a fixed function library.

Approach

Co-optimize a Gumbel-Softmax latent graph and sparse linear combinations of message and update basis functions in an inner loop, while an outer-loop LLM prunes and augments the basis library using inner-loop validation loss as an acceptance gate (best-so-far).

Key results

• COSINE reaches AUC 99.63 on MM ER-50 versus 96.25 for NRI and 98.31 for GDP.
• On Kuramoto BA-50 COSINE achieves AUC 99.85, versus 69.70 for NRI and 90.13 for GDP.
• Ablation with LLM scale: 8B models underperform on MM and CMN (about 0.51-0.66 AUC) while 14B+ models reach about 0.88-1.00.

Surprising findings

• Smaller 8B LLMs fail badly on MM and CMN, while Spring and Kuramoto remain near ceiling across all LLMs tested.

Limitations

• Complex dynamics place heavier demands on the outer-loop LLM, and sparse symbolic expressivity is bounded.
• Under finite noisy data, symbolic equation discovery may be non-identifiable with near-equivalent terms.
• Results on some graph/system pairs (e.g., CMN BA) are less dominant than others.

Experimental setup

Datasets: synthetic dynamics on ER, BA, WS graphs (N=50) COVID-19 data from four U.S. states (mobility graphs)

Benchmarks: MM Diff Spr Kura FJ CMN synthetic systems on ER/BA/WS graphs COVID-19 four-state epidemic data

Metrics: AUC term accuracy NLL training time GPU memory

Baselines: GC MI TE NRI GDP RIVA

Builds on: Neural Relational Inference SINDy LaSR RIVA

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