GENSR: Symbolic Regression Based in Equation Generative Space
arXiv:2602.20557v1 Announce Type: new Abstract: Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior, leaving fitting error feedback too noisy to guide exploration. To address this challenge, we propose GenSR, a generative latent space-based SR framework following the `map construction -> coarse localization -> fine search'' paradigm. Specifically, GenSR first pretrains a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations into a generative latent space with symbolic continuity and local numerical smoothness. This space can be regarded as a well-structured `map'' of the equation space, providing directional signals for search. At inference, the CVAE coarsely localizes the input data to promising regions in the latent space. Then, a modified CMA-ES refines the cand
arXiv:2602.20557v1 Announce Type: new Abstract: Symbolic Regression (SR) tries to reveal the hidden equations behind observed data. However, most methods search within a discrete equation space, where the structural modifications of equations rarely align with their numerical behavior, leaving fitting error feedback too noisy to guide exploration. To address this challenge, we propose GenSR, a generative latent space-based SR framework following the `map construction -> coarse localization -> fine search'' paradigm. Specifically, GenSR first pretrains a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations into a generative latent space with symbolic continuity and local numerical smoothness. This space can be regarded as a well-structured `map'' of the equation space, providing directional signals for search. At inference, the CVAE coarsely localizes the input data to promising regions in the latent space. Then, a modified CMA-ES refines the candidate region, leveraging smooth latent gradients. From a Bayesian perspective, GenSR reframes the SR task as maximizing the conditional distribution $p(\mathrm{Equ.} \mid \mathrm{Num.})$, with CVAE training achieving this objective through the Evidence Lower Bound (ELBO). This new perspective provides a theoretical guarantee for the effectiveness of GenSR. Extensive experiments show that GenSR jointly optimizes predictive accuracy, expression simplicity, and computational efficiency, while remaining robust under noise.
Executive Summary
The article introduces GenSR, a novel framework for Symbolic Regression (SR) that leverages a generative latent space to improve the search for hidden equations behind observed data. GenSR utilizes a dual-branch Conditional Variational Autoencoder (CVAE) to reparameterize symbolic equations, providing a well-structured map of the equation space. This approach enables coarse localization and fine search, leading to improved predictive accuracy, expression simplicity, and computational efficiency. Extensive experiments demonstrate the effectiveness of GenSR, which reframes the SR task as maximizing the conditional distribution p(Equ. | Num.), offering a theoretical guarantee for its performance.
Key Points
- ▸ GenSR proposes a generative latent space-based SR framework
- ▸ Dual-branch CVAE is used for reparameterizing symbolic equations
- ▸ The approach achieves improved predictive accuracy, simplicity, and efficiency
Merits
Improved Efficiency
GenSR's approach enables faster and more efficient search for hidden equations, reducing computational costs.
Theoretical Guarantee
The framework provides a theoretical guarantee for its performance by reframing the SR task as maximizing the conditional distribution p(Equ. | Num.).
Demerits
Limited Robustness
While GenSR remains robust under noise, its performance may be affected by the quality and quantity of the input data.
Expert Commentary
The introduction of GenSR marks a significant advancement in the field of Symbolic Regression. By leveraging a generative latent space, GenSR overcomes the limitations of traditional discrete equation space search methods, providing a more efficient and effective approach to equation discovery. The theoretical guarantee offered by GenSR's framework is particularly noteworthy, as it provides a foundation for understanding the performance and limitations of the approach. As the field continues to evolve, it will be important to explore the applications and potential extensions of GenSR, including its use in conjunction with other machine learning techniques.
Recommendations
- ✓ Further research should be conducted to explore the applications and potential extensions of GenSR, including its use in conjunction with other machine learning techniques.
- ✓ The development of GenSR highlights the need for continued investment in research and development of advanced machine learning techniques for equation discovery and symbolic regression.
