# Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks

arXiv: https://arxiv.org/abs/2505.07956 · HTML: https://mlsanity.com/paper/2505.07956/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in MLLM training and visual instruction tuning, one of 16 directions in Multimodal LLMs / vision-language models.
- Builds on 11 of its 19 references that are in the map.
- First posted on arXiv 12 May 2025.

## Placed in

- Multimodal LLMs / vision-language models / [MLLM training and visual instruction tuning](https://mlsanity.com/mllm/mllm-training-and-visual-instruction-tuning/)

## Builds on (most cited first, 11 of 11)

- [KAN: Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2404.19756/) (2024)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [In-Context Symbolic Regression: Leveraging Large Language Models for Function Discovery](https://mlsanity.com/paper/2404.19094/) (2024)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [TRUCE: Private Benchmarking to Prevent Contamination and Improve Comparative Evaluation of LLMs](https://mlsanity.com/paper/2403.00393/) (2024)
- [Generative Modeling for Mathematical Discovery](https://mlsanity.com/paper/2503.11061/) (2025)
- [Refining Integration-by-Parts Reduction of Feynman Integrals with Machine Learning](https://mlsanity.com/paper/2502.05121/) (2025)

## Built on by (most cited first, 3 of 3)

- [SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks](https://mlsanity.com/paper/2603.18548/) (2026)
- [DeepInflation: an AI agent for research and model discovery of inflation](https://mlsanity.com/paper/2601.14288/) (2026)
- [From Residuals to Reasons: LLM-Guided Mechanism Inference from Tabular Data](https://mlsanity.com/paper/2605.22897/) (2026)

## Abstract (arXiv)

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 ans"atze 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.