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Neuro-Guided Graph Search for Symbolic Regression (Student Abstract)
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Proposes NUDGE, a GNN-guided bottom-up graph expansion search for symbolic regression, and EvoNUDGE, which seeds and guides an evolutionary algorithm with subexpressions from the NUDGE graph.
Problem
Symbolic regression requires a joint combinatorial search over formula structures and continuous parameters; the space of expressions grows exponentially with depth, making exhaustive search infeasible.
Approach
Iteratively expands a graph of SR subexpressions bottom-up, using a GAT-based graph neural network (with cross-example attention and a stateful variant) to select which application nodes to expand, trained with binary cross-entropy on trajectories derived from target programs; a library of discovered subexpressions then initialises and mutates an evolutionary search.
Key results
- GATState (BIN) reaches 15.32% success at k=3 expansions versus 12.57% for the GAT baseline at 60s on the generated test set (Table 1 lists GAT* 14.93 at 60s).
- On AI Feynman, EvoNUDGE configurations reach up to 30.93% success versus 21.65% for GP (IMM, h=1).
- Standalone NUDGE (GATState BIN) reaches only 4.12-7.22% on AI Feynman, below GP.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add graph state across expansion iterations (GATState vs GAT) (ablation) | NUDGE · Generated SR test problems, k = 2 | success rate: 9.04 -> 10.61 | Helped |
| Add graph state across expansion iterations (GATState vs GAT) (ablation) | NUDGE · Generated SR test problems, k = 3 | success rate: 11.79 -> 14.54 | Helped |
| Add graph state across expansion iterations (GATState vs GAT) (ablation) | NUDGE · Generated SR test problems, t = 60s | success rate: 12.57 -> 15.32 | Helped |
| Add NUDGE-guided library-based evolutionary search rather than GP from a random population | EvoNUDGE · AI Feynman suite, h = 1 | success rate: 21.65 -> 30.93 | Helped |
| Add NUDGE-guided library-based evolutionary search rather than GP from a random population | EvoNUDGE · AI Feynman suite, h = 2 | success rate: +3.09 | Helped |
| Add NUDGE-guided library-based evolutionary search rather than GP from a random population | EvoNUDGE · AI Feynman suite, h = 3 | success rate: 21.65 -> 28.87 | Helped |
| Add library-based mutation (ablation) | EvoNUDGE · AI Feynman suite | success rate | Helped |
| Add library-based initialization (ablation) | EvoNUDGE · AI Feynman suite | success rate | Mixed |
| Use library-based mutation only rather than initialization only (ablation) | EvoNUDGE · AI Feynman suite, h = 1 | success rate: 22.68 -> 27.84 | Helped |
| Use library-based mutation only rather than initialization only (ablation) | EvoNUDGE · AI Feynman suite, h = 2 | success rate: 23.71 -> 27.84 | Helped |
| Use library-based mutation only rather than initialization only (ablation) | EvoNUDGE · AI Feynman suite, h = 3 | success rate: 23.71 -> 28.87 | Helped |
Surprising findings
- Standalone NUDGE underperforms the purely evolutionary GP baseline on AI Feynman, and its gains only materialise when combined with evolution.
Limitations
- Exponential growth of the search front limits standalone NUDGE scalability
- Training requires target programs to derive expansion trajectories
- Evaluation on a self-generated problem set and a limited AI Feynman subset
Experimental setup
Datasets: self-generated SR problem database (1032 problems: 522 train, 510 test) AI Feynman suite
Benchmarks: generated SR test set (510 problems) AI Feynman suite
Metrics: success rate (test MSE < 1e-10)
Baselines: GAT* GP GATState (BIN)
Builds on: Graph Attention Network genetic programming Kamienny et al. 2022 value encoding Wyrwiński and Krawiec 2024 GP-GNN
Closest papers by meaning
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- SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery (NeurIPS 2026 · similarity 0.84)
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