# GSR: A Generalized Symbolic Regression Approach

arXiv: https://arxiv.org/abs/2205.15569 · HTML: https://mlsanity.com/paper/2205.15569/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 63 references that are in the map.
- First posted on arXiv 31 May 2022.

## Builds on (most cited first, 25 of 25)

- [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)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [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)
- [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)
- [SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics](https://mlsanity.com/paper/2004.02322/) (2020)
- [Extrapolation and learning equations](https://mlsanity.com/paper/1610.02995/) (2016)
- [SymbolicGPT: A Generative Transformer Model for Symbolic Regression](https://mlsanity.com/paper/2106.14131/) (2021)
- [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)
- [Guiding Deep Molecular Optimization with Genetic Exploration](https://mlsanity.com/paper/2007.04897/) (2020)
- [Where are we now? A large benchmark study of recent symbolic regression methods](https://mlsanity.com/paper/1804.09331/) (2018)
- [A Greedy Search Tree Heuristic for Symbolic Regression](https://mlsanity.com/paper/1801.01807/) (2018)
- [Improving exploration in policy gradient search: Application to symbolic optimization](https://mlsanity.com/paper/2107.09158/) (2021)
- [Elite Bases Regression: A Real-time Algorithm for Symbolic Regression](https://mlsanity.com/paper/1704.07313/) (2017)
- [A General Model Validation and Testing Tool](https://mlsanity.com/paper/1908.11251/) (2019)
- [A multilevel block building algorithm for fast modeling generalized separable systems](https://mlsanity.com/paper/1706.02281/) (2017)
- [Neural-Network-Directed Genetic Programmer for Discovery of Governing Equations](https://mlsanity.com/paper/2203.08808/) (2022)
- [Block building programming for symbolic regression](https://mlsanity.com/paper/1705.07877/) (2017)
- [A divide and conquer method for symbolic regression](https://mlsanity.com/paper/1705.08061/) (2017)
- [Fast Modeling Methods for Complex System with Separable Features](https://mlsanity.com/paper/1708.04583/) (2017)

## Built on by (most cited first, 11 of 11)

- [ODEFormer: Symbolic Regression of Dynamical Systems with Transformers](https://mlsanity.com/paper/2310.05573/) (2023)
- [Predicting Ordinary Differential Equations with Transformers](https://mlsanity.com/paper/2307.12617/) (2023)
- [Knowledge Integration for Physics-informed Symbolic Regression Using Pre-trained Large Language Models](https://mlsanity.com/paper/2509.03036/) (2025)
- [MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimation](https://mlsanity.com/paper/2306.04120/) (2023)
- [Racing Control Variable Genetic Programming for Symbolic Regression](https://mlsanity.com/paper/2309.07934/) (2023)
- [Data-Driven Discovery of PDEs via the Adjoint Method](https://mlsanity.com/paper/2401.17177/) (2024)
- [Generalizing the SINDy approach with nested neural networks](https://mlsanity.com/paper/2404.15742/) (2024)
- [ISR: Invertible Symbolic Regression](https://mlsanity.com/paper/2405.06848/) (2024)
- [An Efficient and Generalizable Symbolic Regression Method for Time Series Analysis](https://mlsanity.com/paper/2409.03986/) (2024)
- [Data-driven Discovery of Digital Twins in Biomedical Research](https://mlsanity.com/paper/2508.21484/) (2025)
- [Data Enrichment for Symbolic Regression Using Diffusion Models](https://mlsanity.com/paper/2606.00988/) (2026)

## Abstract (arXiv)

Identifying the mathematical relationships that best describe a dataset remains a very challenging problem in machine learning, and is known as Symbolic Regression (SR). In contrast to neural networks which are often treated as black boxes, SR attempts to gain insight into the underlying relationships between the independent variables and the target variable of a given dataset by assembling analytical functions. In this paper, we present GSR, a Generalized Symbolic Regression approach, by modifying the conventional SR optimization problem formulation, while keeping the main SR objective intact. In GSR, we infer mathematical relationships between the independent variables and some transformation of the target variable. We constrain our search space to a weighted sum of basis functions, and propose a genetic programming approach with a matrix-based encoding scheme. We show that our GSR method is competitive with strong SR benchmark methods, achieving promising experimental performance on the well-known SR benchmark problem sets. Finally, we highlight the strengths of GSR by introducing SymSet, a new SR benchmark set which is more challenging relative to the existing benchmarks.