Symbolic Regression with a Learned Concept Library

• URL: http://arxiv.org/abs/2409.09359v2
• Date: Thu, 31 Oct 2024 19:02:17 GMT
• Title: Symbolic Regression with a Learned Concept Library
• Authors: Arya Grayeli, Atharva Sehgal, Omar Costilla-Reyes, Miles Cranmer, Swarat Chaudhuri,
• Abstract summary: We present a novel method for searching for compact programmatic hypotheses that best explain a dataset. Our algorithm, called LaSR, uses zero-shot queries to a large language model to discover and evolve concepts. LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms.
• Score: 9.395222766576342
• License: http://creativecommons.org/licenses/by/4.0/
• 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. Moreover, we show that LaSR can be used to discover a novel and powerful scaling law for LLMs.

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