Symbolic expression generation via variational auto-encoder.

Area of Science:

• Physics
• Biology
• Natural Sciences
• Machine Learning

Background:

• Symbolic regression offers interpretable insights into natural laws, unlike deep neural networks.
• Current symbolic regression methods lack a dominant solution, creating a need for improved algorithms.

Purpose of the Study:

• To develop a novel deep learning framework for symbolic expression generation.
• To address the limitations of existing methods in symbolic regression tasks.

Main Methods:

• A variational autoencoder (VAE) is employed for generating mathematical expressions.
• A training strategy ensures generated formulas accurately fit given datasets.
• Apriori knowledge is encoded into fast-check predicates to accelerate optimization.

Main Results:

• The proposed method, SEGVAE, outperforms existing symbolic regression benchmarks, particularly in noisy conditions.
• Achieved a 65% recovery rate on the Nguyen dataset with 10% noise, a 20% improvement over prior state-of-the-art.
• Demonstrated that performance varies with dataset characteristics, with potential for higher recovery rates.

Conclusions:

• The novel VAE-based framework effectively generates symbolic expressions for scientific discovery.
• The method offers a significant advancement in symbolic regression, especially for complex and noisy datasets.
• Future work can explore further optimizations and applications across various scientific domains.