Exhaustive dataset improves symbolic regression with less repetition
Exhaustive Canonical Skeletons Generation: A Formal Dataset for Decomposable Symbolic Regression
Machine Learning
Summary
Finding mathematical formulas from data is hard, and training AI models to do this needs lots of varied examples. The authors created a new, carefully built set of basic formula structures that cover all possibilities without repeating similar ones. This helps AI learn better and avoids problems seen in previous datasets. Their method also makes it easier to tackle complicated formulas involving multiple variables by breaking them down. They tested existing AI tools on these new problems and found that they still struggle, suggesting the dataset is a challenging benchmark.
What this means in practice
- •For machine learning engineers: Train symbolic regression models with a comprehensive and non-redundant dataset to improve model robustness and reduce training inefficiency.
- •For data scientists in physics: Use a structured set of formula skeletons to more effectively discover complex relationships in physics data without linear simplifications.
Authors
Giorgio Morales, Anikó Ekárt
Abstract
Neural symbolic regression (SR) models require diverse datasets of mathematical expressions for robust training. However, existing datasets rely predominantly on stochastic sampling methods, which suffer from high structural redundancy and incomplete functional coverage. To address this, we introduce an exhaustive dataset of univariate canonical skeletons generated via a deterministic constrained context-free grammar. A canonical skeleton acts as a generic structural representation that subsumes more specific functional forms, eliminating redundant expressions and avoiding repeated computational efforts. Although our dataset consists of univariate skeletons, it is designed to support the decomposable SR paradigm to solve multivariate SR problems without assuming linear separability. Furthermore, we pair this dataset with a sampling strategy that generates clean numerical data without triggering numerical instabilities or relying on artificial protected operators. Canonicalizing two existing neural SR datasets reveals that our dataset is substantially more compact, eliminates structural repetitions, and achieves a uniform operator distribution free of simplicity bias. Finally, we establish a benchmark of 150 SR problems across three tiers, on which state-of-the-art SR methods are shown to struggle significantly.