# Exhaustive Canonical Skeletons Generation: A Formal Dataset for Decomposable Symbolic Regression

arXiv: https://arxiv.org/abs/2610.20108 · HTML: https://mlsanity.com/paper/2610.20108/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 19 references that are in the map.
- First posted on arXiv 14 Oct 2026.

## Builds on (most cited first, 12 of 12)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [Taylor Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2205.09751/) (2022)
- [Grammar-based Ordinary Differential Equation Discovery](https://mlsanity.com/paper/2504.02630/) (2025)
- [Univariate Skeleton Prediction in Multivariate Systems Using Transformers](https://mlsanity.com/paper/2406.17834/) (2024)

## Abstract (arXiv)

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.