Shu Wei

Jingyi Liu, Yanjie Li, Lina Yu et al.

Noise ubiquitously exists in signals due to numerous factors including physical, electronic, and environmental effects. Traditional methods of symbolic regression, such as genetic programming or deep learning models, aim to find the most fitting expressions for these signals. However, these methods often overlook the noise present in real-world data, leading to reduced fitting accuracy. To tackle this issue, we propose \textit{\textbf{D}eep Symbolic Regression against \textbf{N}oise via \textbf{C}ontrastive \textbf{L}earning (DN-CL)}. DN-CL employs two parameter-sharing encoders to embed data points from various data transformations into feature shields against noise. This model treats noisy data and clean data as different views of the ground-truth mathematical expressions. Distances between these features are minimized, utilizing contrastive learning to distinguish between 'positive' noise-corrected pairs and 'negative' contrasting pairs. Our experiments indicate that DN-CL demonstrates superior performance in handling both noisy and clean data, presenting a promising method of symbolic regression.

Yanjie Li, Lina Yu, Weijun Li et al.

Formulas are the language of communication between humans and nature. The discovery of formulas to describe natural laws from observational data is the purpose of scientific research. It is also an important research topic in artificial intelligence, which is called a symbolic regression problem. Most of the existing symbolic regression methods generate expressions directly from observed data. Although in some methods, we can inject some prior knowledge into the model by adding constraints or introducing some special character hints. However, these methods can only introduce a limited amount of prior knowledge specified in advance. Not to mention understanding natural language instructions. In this article, based on the powerful knowledge reserve and language understanding ability of multi-modal large language models, we present ChatSR, which acts like a knowledgeable human scientist, and we can tell it any prior knowledge through natural language to guide it in formula generation. By testing on 13 datasets, ChatSR not only shows state-of-the-art performance on traditional symbolic regression tasks. More notably, ChatSR can well understand the prior knowledge contained in natural language prompts and improve the quality of generated expressions. In addition, it is exciting that ChatSR has a good zero-shot capability to understand prior knowledge that is not present in the training data.