L2G-SR Framework Revolutionizes LLM-based Symbolic Regression with Structural Verification
Summary:L2G-SR is a novel framework for LLM-based symbolic regression that introduces a learned structural verifier to guide the search process. By leveraging tree edit distance (TED) to construct structural supervision signals and using the verifier to complement numerical error, L2G-SR effectively balances numerical fit and structural accuracy during the search. Experimental results on the LLM-SRBench benchmark demonstrate that L2G-SR achieves state-of-the-art performance in numerical fit, equation-le
1. Introduction
Symbolic regression aims to find mathematical equations that explain observed data. Traditional methods rely heavily on numerical error to guide the search, but this often leads to favoring candidates with accurate numerical fits but incorrect structures. L2G-SR addresses this limitation by introducing a structural verification mechanism.
2. Technical Mechanism
The core innovation of L2G-SR lies in its structural verification mechanism, which involves the following steps:
- Structural Supervision Signal Construction: Utilizes tree edit distance (TED) to calculate the structural differences between candidate and target equations, considering commutative operators and alternative expression forms.
- Structural Verifier Training: Aligns numerical observations with formulas and learns to score the structural similarity of candidate equations.
- Search Process Optimization: During the search, the target equation is hidden, and the verifier works alongside numerical error to guide parent node selection.
- Analyst Feedback and Revision: Analysts use verifier feedback and diagnostic tools to propose revisions, which the generator converts into refined expressions.
3. Engineering Trade-offs and Performance
L2G-SR demonstrates superior performance on the LLM-SRBench benchmark, outperforming existing methods in numerical fit, equation-level accuracy, and TED metrics. Its main advantages include:
- Enhanced Structural Accuracy: The structural verification mechanism allows L2G-SR to better capture the intrinsic structure of equations, avoiding the overfitting issues common in traditional methods.
- Flexibility and Scalability: The framework is compatible with various LLM architectures and supports symbolic regression tasks across different domains.
However, L2G-SR also has limitations, such as its reliance on high-quality structured data and its performance on extremely complex equations, which still needs improvement.
4. Developer Deployment Recommendations
For developers, L2G-SR offers a new solution for symbolic regression, particularly in scenarios where high-precision structured results are required. Here are some deployment recommendations:
- Data Preparation: Ensure the provision of high-quality structured data to fully leverage the advantages of the structural verification mechanism.
- Model Selection: Choose the appropriate LLM architecture based on specific task requirements and perform necessary fine-tuning.
- Validation and Iteration: Utilize verifier feedback and diagnostic tools to continuously optimize model performance.
5. Conclusion
The L2G-SR framework significantly enhances the performance of LLM-driven symbolic regression by introducing a structural verification mechanism, opening new possibilities for the automatic discovery of complex equations.
— END —Source: ArXiv AI (cs.AI) (2026-10-16)
Tags: #Large Language Models #Symbolic Regression #Structural Verification #LLMs & Foundation Models #arXiv
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