Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

By Brenden K. Petersen, Mikel Landajuela. International Conference on Learning Representations, 2019

486 citations recorded by the source corpus.

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of $\textit{symbolic}$ $\textit{regression.}$ Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that combines deep learning with symbolic regression via a simple idea: use a large model to search the space of small models. More specifically, we use a recurrent neural network to emit a distribution over tractable mathematical expressions, and employ reinforcement learning to train the network to generate better-fitting expressions. Our algorithm significantly outperforms standard genetic programming-based symbolic regression in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a black-box performance metric, with the ability to incorporate a priori constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/3ee45877f7f14c8ee4872a7249f74eef7dc2255f

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Statistical and Nonlinear Physics

Citations in the corpus

Scientific discovery in the age of artificial intelligence (2023, methodology): “Reinforcement learning uses neural networks to generate a mathematical expression sequentially by adding mathematical symbols from a predefined vocabulary and using the learned policy to decide which notation symbol to be added next 140 .”
Contemporary Symbolic Regression Methods and their Relative Performance (2021, methodology): “DSR introduces a variant of the Monte Carlo policy gradient algorithm [62] dubbed a “risk-seeking policy gradient" in an effort to bias the generative model towards exact expressions.”
End-to-end symbolic regression with transformers (2022, unknown): “Neural networks have been combined with GP algorithms, e.g. to simplify the original dataset [1], or to propose a good starting distribution over mathematical expressions[20].”
HyperTree Proof Search for Neural Theorem Proving (2022, methodology): “These model perform quite well on formal tasks such as expression simplification [26], solving differential equations [27], symbolic regression [28, 29], or predicting complex properties of mathematical objects [30].”