Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks
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arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908370113396736 |
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| author | Harvey, Thomas R. Ruehle, Fabian Fraser-Taliente, Kit Halverson, James |
| author_facet | Harvey, Thomas R. Ruehle, Fabian Fraser-Taliente, Kit Halverson, James |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_07956 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks Harvey, Thomas R. Ruehle, Fabian Fraser-Taliente, Kit Halverson, James Machine Learning Neural and Evolutionary Computing Symbolic Computation 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. |
| title | Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks |
| topic | Machine Learning Neural and Evolutionary Computing Symbolic Computation |
| url | https://arxiv.org/abs/2505.07956 |