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Symbolic Regression with a Learned Concept Library

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arxiv 2409.09359 v3 pith:5SKZSC77 submitted 2024-09-14 cs.LG cs.AIcs.NEcs.SC

Arya Grayeli , Atharva Sehgal , Omar Costilla-Reyes , Miles Cranmer , Swarat Chaudhuri This is my paper
classification cs.LGcs.AIcs.NEcs.SC
keywords hypotheseslasrconceptsdiscoveralgorithmsconceptdiscoveredevolutionary
verification ladder T0 review T1 audit T2 compute T3 formal
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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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Cited by 10 Pith papers

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