用视觉大模型和KAN网络实现无需预设函数的符号回归
Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks
- 让大模型根据函数图像生成表达式初值，再用遗传算法优化
- 单变量回归即可解决多变量问题，通过训练KAN网络在边上线性拟合
- 结合语言模型简化结果，适合需可解释表达式的科研场景
我们提出一种新方法进行符号回归，利用具备视觉能力的大语言模型（LLMs）与Google DeepMind Funsearch的思想。给定一个单变量函数的图像，大模型被要求提出该函数的表达式假设（ansatz）。假设中的自由参数通过标准数值优化器拟合，多个假设构成遗传算法的种群。与其他符号回归方法不同，本方法无需预先指定函数集合，只需恰当的提示工程即可任意控制生成过程。通过使用柯尔莫哥洛夫-阿诺德网络（KANs），我们证明了‘单变量足够’用于符号回归，并通过在已训练的KAN网络每条边上学习单变量函数，将方法扩展至多变量函数。最终表达式经由语言模型进一步处理以简化。
原文摘要 · Abstract (English)
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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