ViSymRe: Vision-guided Multimodal Symbolic Regression

Abstract

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.