# Differentiable Genetic Programming

arXiv: https://arxiv.org/abs/1611.04766 · HTML: https://mlsanity.com/paper/1611.04766/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Nov 2016.

## Built on by (most cited first, 7 of 7)

- [AI Descartes: Combining Data and Theory for Derivable Scientific Discovery](https://mlsanity.com/paper/2109.01634/) (2021)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [Behavior-based Neuroevolutionary Training in Reinforcement Learning](https://mlsanity.com/paper/2105.07960/) (2021)
- [On genetic programming representations and fitness functions for interpretable dimensionality reduction](https://mlsanity.com/paper/2203.00528/) (2022)
- [Symbolic Regression for Space Applications: Differentiable Cartesian Genetic Programming Powered by Multi-objective Memetic Algorithms](https://mlsanity.com/paper/2206.06213/) (2022)
- [Closing the Gap Between SGP4 and High-Precision Propagation via Differentiable Programming](https://mlsanity.com/paper/2402.04830/) (2024)
- [A Personalised Learning Tool for Physics Undergraduate Students Built On a Large Language Model for Symbolic Regression](https://mlsanity.com/paper/2407.00065/) (2024)

## Abstract (arXiv)

We introduce the use of high order automatic differentiation, implemented via the algebra of truncated Taylor polynomials, in genetic programming. Using the Cartesian Genetic Programming encoding we obtain a high-order Taylor representation of the program output that is then used to back-propagate errors during learning. The resulting machine learning framework is called differentiable Cartesian Genetic Programming (dCGP). In the context of symbolic regression, dCGP offers a new approach to the long unsolved problem of constant representation in GP expressions. On several problems of increasing complexity we find that dCGP is able to find the exact form of the symbolic expression as well as the constants values. We also demonstrate the use of dCGP to solve a large class of differential equations and to find prime integrals of dynamical systems, presenting, in both cases, results that confirm the efficacy of our approach.