Extracting simple mathematical expression from an observational dataset to describe complex natural phenomena is one of the core objectives of artificial intelligence (AI). This field is known as symbolic regression (SR). Traditional SR models are based on genetic programming (GP) or reinforcement learning (RL), facing well-known challenges, such as low efficiency and overfitting. Recent studies have integrated SR with large language models (LLMs), enabling fast zero-shot inference by learning mappings from millions of dataset-expression pairs. However, since the input and output are inherently different modalities, such models often struggle to converge effectively. In this paper, we introduce ViSymRe, a vision-guided multimodal SR model that incorporates the third resource, expression graph, to bridge the modality gap. Different from traditional multimodal models, ViSymRe is trained to extract vision, termed virtual vision, from datasets, without relying on the global availability of expression graphs, which addresses the essential challenge of visual SR, i.e., expression graphs are not available during inference. Evaluation results on multiple mainstream benchmarks show that ViSymRe achieves more competitive performance than the state-of-the-art dataset-only baselines. The expressions predicted by ViSymRe not only fit the dataset well but are also simple and structurally accurate, goals that SR models strive to achieve.

翻译：从观测数据集中提取简单的数学表达式以描述复杂的自然现象，是人工智能（AI）的核心目标之一。这一领域被称为符号回归（SR）。传统的SR模型基于遗传规划（GP）或强化学习（RL），面临着众所周知的挑战，例如效率低下和过拟合。近期研究将SR与大型语言模型（LLMs）相结合，通过学习数百万个数据集-表达式对的映射，实现了快速的零样本推理。然而，由于输入和输出本质上是不同的模态，此类模型往往难以有效收敛。本文提出ViSymRe，一种视觉引导的多模态SR模型，它引入了第三种资源——表达式图，以弥合模态鸿沟。与传统多模态模型不同，ViSymRe被训练从数据集中提取视觉信息（称为虚拟视觉），而无需依赖表达式图的全局可用性，这解决了视觉SR的一个核心挑战，即在推理过程中表达式图并不可用。在多个主流基准上的评估结果表明，ViSymRe取得了比当前最先进的仅使用数据集的基线模型更具竞争力的性能。ViSymRe预测的表达式不仅与数据集拟合良好，而且结构简单准确，这正是SR模型力求实现的目标。