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arXiv · 2505.07956

Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks

Thomas R. Harvey·Fabian Ruehle·Kit Fraser-Taliente·James Halverson
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Abstract

We present a novel approach to symbolic regression using vision-capable large language models (LLMs) and the ideas behind Google DeepMind's Funsearch. The LLM is given a plot of a univariate function and tasked with proposing an ansatz for that function. The free parameters of the ansatz are fitted using standard numerical optimisers, and a collection of such ansätze make up the population of a genetic algorithm. Unlike other symbolic regression techniques, our method does not require the specification of a set of functions to be used in regression, but with appropriate prompt engineering, we can arbitrarily condition the generative step. By using Kolmogorov Arnold Networks (KANs), we demonstrate that ``univariate is all you need'' for symbolic regression, and extend this method to multivariate functions by learning the univariate function on each edge of a trained KAN. The combined expression is then simplified by further processing with a language model.

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Thomas R. Harvey, Fabian Ruehle, Kit Fraser-Taliente, James Halverson. 2025-05-12. Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks. https://arxiv.org/abs/2505.07956

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