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This paper introduces a deterministic dataset of canonical skeletons designed to eliminate structural redundancy in neural symbolic regression, addressing critical limitations in current stochastic sampling methods. By establishing a benchmark of 150 problems, the authors demonstrate that existing state-of-the-art models struggle significantly with this more compact and uniformly distributed data, highlighting the need for improved functional coverage in training sets. The work advances the foundational infrastructure for machine learning by providing a rigorous framework for decomposable symbolic regression without assuming linear separability.
Exhaustive Canonical Skeletons Generation: A Formal Dataset for Decomposable Symbolic Regression
arXiv:2610.20108v1 Announce Type: new 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.
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.
Machine Learning (cs.LG)
arXiv:2610.20108 [cs.LG]
(or arXiv:2610.20108v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.20108 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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