Symbolic Regression with a Learned Concept Library

Arya Grayeli, Atharva Sehgal, Omar Costilla Reyes, Miles Cranmer, Swarat Chaudhuri

Keywords: symbolic regression, scientific discovery. programming, program synthesis, generative modelling, foundation models

TL;DR: We use concept guidance to accelerate symbolic regression for scientific discovery.

Abstract:

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR,
uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark,
as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms.

Submission Number: 72