Contrastive diffusion model for exploring mathematical expressions from data.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Computational Mathematics

Background:

• Symbolic regression aims to find mathematical expressions fitting data, crucial for science and engineering.
• Current deep generative models use autoregressive methods, struggling with the global structure of expressions.
• Unidirectional dependencies in autoregressive models limit capturing complex, bidirectional relationships within mathematical formulas.

Purpose of the Study:

• To develop an advanced non-autoregressive approach for symbolic regression using diffusion models.
• To improve the modeling of global semantic logic in mathematical expression generation.
• To enhance the utilization of multimodal data and semantic understanding through contrastive learning.

Main Methods:

• An iterative non-autoregressive diffusion model was developed to generate entire mathematical expressions in a latent space.
• Contrastive learning was integrated to align data point features with symbolic expression features, reducing modal discrepancies.
• The model refines expression generation by considering global semantic relationships.

Main Results:

• The proposed diffusion model significantly outperforms existing mainstream baselines on benchmark datasets.
• The model efficiently discovers mathematical expression solutions, achieving superior fitting accuracy.
• The approach ensures a high degree of simplicity in the generated mathematical expressions.

Conclusions:

• The non-autoregressive diffusion model effectively captures the global perspective of mathematical expressions.
• This method offers an efficient and powerful solution for the challenging symbolic regression problem.
• Integrating contrastive learning enhances multimodal data utilization and semantic understanding for improved generation.