🤖 AI Summary
This work addresses symbol regression without predefined functional bases. The proposed method introduces an image-driven, multimodal end-to-end framework: first, a vision-language model (VLM) generates initial mathematical expressions directly from function plots; second, Kolmogorov–Arnold networks (KANs) decompose multivariate regression into learnable univariate edge functions, embodying the “univariate suffices” principle; third, prompt-engineered language models guide genetic optimization and symbolic simplification to discover conditional, interpretable closed-form expressions. The approach requires no handcrafted function set, supports arbitrary prompt-based control and constraint modeling, and enables direct mapping from visual input to symbolic output. Evaluated on standard benchmarks, it significantly improves expression accuracy, generalization, and interpretability—establishing, for the first time, a multimodal symbol regression paradigm bridging images and symbolic expressions.
📝 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 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.