Symbolic regression automatically searches for mathematical equations to reveal underlying mechanisms within datasets, offering enhanced interpretability compared to black box models. Traditionally, symbolic regression has been considered to be purely numeric-driven, with insufficient attention given to the potential contributions of visual information in augmenting this process. When dealing with high-dimensional and complex datasets, existing symbolic regression models are often inefficient and tend to generate overly complex equations, making subsequent mechanism analysis complicated. In this paper, we propose the vision-guided multimodal symbolic regression model, called ViSymRe, that systematically explores how visual information can improve various metrics of symbolic regression. Compared to traditional models, our proposed model has the following innovations: (1) It integrates three modalities: vision, symbol and numeric to enhance symbolic regression, enabling the model to benefit from the strengths of each modality; (2) It establishes a meta-learning framework that can learn from historical experiences to efficiently solve new symbolic regression problems; (3) It emphasizes the simplicity and structural rationality of the equations rather than merely numerical fitting. Extensive experiments show that our proposed model exhibits strong generalization capability and noise resistance. The equations it generates outperform state-of-the-art numeric-only baselines in terms of fitting effect, simplicity and structural accuracy, thus being able to facilitate accurate mechanism analysis and the development of theoretical models.

翻译：符号回归通过自动搜索数学方程来揭示数据集中的潜在机制，相比黑盒模型具有更强的可解释性。传统上，符号回归被认为完全由数值驱动，视觉信息在增强该过程中的潜在贡献未得到充分关注。在处理高维复杂数据集时，现有符号回归模型通常效率低下，且倾向于生成过于复杂的方程，使得后续机制分析变得困难。本文提出一种视觉引导的多模态符号回归模型，称为ViSymRe，系统探索视觉信息如何提升符号回归的各项指标。与传统模型相比，我们提出的模型具有以下创新点：（1）整合视觉、符号与数值三种模态以增强符号回归，使模型能受益于各模态的优势；（2）建立元学习框架，能够从历史经验中学习以高效解决新的符号回归问题；（3）强调方程的简洁性与结构合理性，而非仅追求数值拟合。大量实验表明，我们提出的模型展现出强大的泛化能力与抗噪性。其生成的方程在拟合效果、简洁性和结构准确性方面均优于仅使用数值的先进基线方法，从而能够促进精确的机制分析与理论模型构建。