Symbolic regression accuracy boosted by dynamic auxiliary search strategy
DASS: A Solver-Adaptable Dynamic Auxiliary Search Strategy for Symbolic Regression
Machine Learning
Summary
Symbolic regression tries to find simple math formulas that explain data but struggles because there are too many possibilities to check. The authors introduce DASS, a helper method that improves search by focusing on promising parts of the formula space and updating guidance based on solver feedback. This creates a loop that helps find better formulas more efficiently. DASS works with various existing solvers and improves their accuracy with only a modest increase in computing time.
What this means in practice
- •For data scientists: Improve mathematical model discovery from experimental or observational data by integrating a dynamic guided search method into existing symbolic regression tools.
- •For automated machine learning teams: Enhance automated symbolic model search processes to produce more accurate predictive equations with manageable computational cost.
Authors
Yuxiao Hu, Qian Li, Ding Wang, Yekun Zheng, Jinyue Yan, Yuntian Chen
Abstract
Symbolic regression (SR) aims to discover interpretable mathematical expressions from data and plays a key role in scientific discovery. However, existing methods face a common bottleneck: the enormous search space and severe combinatorial explosion make it difficult to achieve a favorable trade-off between accuracy and algorithmic efficiency. We argue that, in addition to designing increasingly complex solver-specific SR strategies, an equally promising direction is to equip them with a shareable auxiliary strategy that can provide reliable search guidance. To this end, we propose DASS, a solver-adaptable Dynamic Auxiliary Search Strategy that improves SR by constructing and refining a high-potential auxiliary search subspace. DASS represents the auxiliary search space as a functional subspace spanned by a set of high-potential basis function terms. It estimates term utility through multi-environment evaluation, filters unstable guidance, and updates term potential scores with a Gibbs posterior, thereby calibrating the subspace to provide more reliable guidance for downstream solvers. The high-quality solutions produced by the solver are used to update the set of basis terms. This forms a virtuous closed-loop optimization process: the subspace guides the downstream solver, and the solver feedback reshapes the subspace for subsequent exploration. DASS can be easily integrated with various types of SR solvers. Extensive experiments on LLM-SRBench show that DASS significantly improves the accuracy of original solvers with a manageable increase in runtime.