AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity

TL;DR

AI Feynman 2.0 introduces a robust symbolic regression method that leverages graph modularity and symmetry detection, significantly improving accuracy and noise robustness over previous approaches, and extends to probabilistic data using normalizing flows.

Contribution

The paper presents a novel symbolic regression technique that exploits graph modularity and symmetry, enhancing robustness and applicability to probabilistic data.

Findings

Achieves orders of magnitude better noise robustness.

Discovers formulas that previous methods could not find.

Effectively generalizes to probability distributions using normalizing flows.

Abstract

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically being orders of magnitude more robust toward noise and bad data, and also by discovering many formulas that stumped previous methods. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize our symbolic regression method to probability distributions from which we only have samples, and employ statistical hypothesis testing to accelerate robust brute-force search.