# Taylor Genetic Programming for Symbolic Regression

arXiv: https://arxiv.org/abs/2205.09751 · HTML: https://mlsanity.com/paper/2205.09751/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 53 references that are in the map.
- First posted on arXiv 28 Apr 2022.

## Builds on (most cited first, 17 of 17)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [Symbolic Regression via Neural-Guided Genetic Programming Population Seeding](https://mlsanity.com/paper/2111.00053/) (2021)
- [Integration of Neural Network-Based Symbolic Regression in Deep Learning for Scientific Discovery](https://mlsanity.com/paper/1912.04825/) (2019)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)

## Built on by (most cited first, 19 of 19)

- [DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experience](https://mlsanity.com/paper/2506.04282/) (2025)
- [MMSR: Symbolic Regression is a Multi-Modal Information Fusion Task](https://mlsanity.com/paper/2402.18603/) (2024)
- [Symbolic Regression via Control Variable Genetic Programming](https://mlsanity.com/paper/2306.08057/) (2023)
- [Symbolic Regression for PDEs using Pruned Differentiable Programs](https://mlsanity.com/paper/2303.07009/) (2023)
- [LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search](https://mlsanity.com/paper/2606.25039/) (2026)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [StruSR: Structure-Aware Symbolic Regression with Physics-Informed Taylor Guidance](https://mlsanity.com/paper/2510.06635/) (2025)
- [Racing Control Variable Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2309.07934/) (2023)
- [Physics Informed Symbolic Networks](https://mlsanity.com/paper/2207.06240/) (2022)
- [Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching](https://mlsanity.com/paper/2409.01416/) (2024)
- [Univariate Skeleton Prediction in Multivariate Systems Using Transformers](https://mlsanity.com/paper/2406.17834/) (2024)
- [Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression](https://mlsanity.com/paper/2506.08267/) (2025)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Vertical Symbolic Regression](https://mlsanity.com/paper/2312.11955/) (2023)
- [A Personalised Learning Tool for Physics Undergraduate Students Built On a Large Language Model for Symbolic Regression](https://mlsanity.com/paper/2407.00065/) (2024)
- [Deep Neural Network for Constraint Acquisition through Tailored Loss Function](https://mlsanity.com/paper/2403.02042/) (2024)
- [SMILE: Bridging Continuous Optimization and Discrete Symbolic Recovery](https://mlsanity.com/paper/2609.04639/) (2026)
- [MOSAIC-SR: Transformer-Guided Symbolic Regression for Scientific Equation Recovery](https://mlsanity.com/paper/2609.20997/) (2026)
- [Exhaustive Canonical Skeletons Generation: A Formal Dataset for Decomposable Symbolic Regression](https://mlsanity.com/paper/2610.20108/) (2026)

## Abstract (arXiv)

Genetic programming (GP) is a commonly used approach to solve symbolic regression (SR) problems. Compared with the machine learning or deep learning methods that depend on the pre-defined model and the training dataset for solving SR problems, GP is more focused on finding the solution in a search space. Although GP has good performance on large-scale benchmarks, it randomly transforms individuals to search results without taking advantage of the characteristics of the dataset. So, the search process of GP is usually slow, and the final results could be unstable.To guide GP by these characteristics, we propose a new method for SR, called Taylor genetic programming (TaylorGP) (Code and appendix at https://kgae-cup.github.io/TaylorGP/). TaylorGP leverages a Taylor polynomial to approximate the symbolic equation that fits the dataset. It also utilizes the Taylor polynomial to extract the features of the symbolic equation: low order polynomial discrimination, variable separability, boundary, monotonic, and parity. GP is enhanced by these Taylor polynomial techniques. Experiments are conducted on three kinds of benchmarks: classical SR, machine learning, and physics. The experimental results show that TaylorGP not only has higher accuracy than the nine baseline methods, but also is faster in finding stable results.