# GENSR: Symbolic Regression Based in Equation Generative Space

arXiv: https://arxiv.org/abs/2602.20557 · HTML: https://mlsanity.com/paper/2602.20557/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 32 of its 51 references that are in the map.
- First posted on arXiv 24 Feb 2026.

## Builds on (most cited first, 30 of 32)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [The CMA Evolution Strategy: A Tutorial](https://mlsanity.com/paper/1604.00772/) (2016)
- [Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients](https://mlsanity.com/paper/1912.04871/) (2019)
- [Deep Learning for Symbolic Mathematics](https://mlsanity.com/paper/1912.01412/) (2019)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [End-to-end symbolic regression with transformers](https://mlsanity.com/paper/2204.10532/) (2022)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularity](https://mlsanity.com/paper/2006.10782/) (2020)
- [PMLB: A Large Benchmark Suite for Machine Learning Evaluation and Comparison](https://mlsanity.com/paper/1703.00512/) (2017)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Symbolic Regression with a Learned Concept Library](https://mlsanity.com/paper/2409.09359/) (2024)
- [Transformer-based Planning for Symbolic Regression](https://mlsanity.com/paper/2303.06833/) (2023)
- [Bayesian Symbolic Regression](https://mlsanity.com/paper/1910.08892/) (2019)
- [Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree search](https://mlsanity.com/paper/2205.13134/) (2022)
- [SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-training](https://mlsanity.com/paper/2310.02227/) (2023)
- [Any equation is a forest: Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE)](https://mlsanity.com/paper/2106.11927/) (2021)
- [Context-Alignment: Activating and Enhancing LLM Capabilities in Time Series](https://mlsanity.com/paper/2501.03747/) (2025)
- [Learning concise representations for regression by evolving networks of trees](https://mlsanity.com/paper/1807.00981/) (2018)
- [Epsilon-Lexicase Selection for Regression](https://mlsanity.com/paper/1905.13266/) (2019)
- [Deep Generative Symbolic Regression](https://mlsanity.com/paper/2401.00282/) (2023)
- [Noisy but Valid: Robust Statistical Evaluation of LLMs with Imperfect Judges](https://mlsanity.com/paper/2601.20913/) (2026)
- [Seeing Sound, Hearing Sight: Uncovering Modality Bias and Conflict of AI models in Sound Localization](https://mlsanity.com/paper/2505.11217/) (2025)
- [Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description length](https://mlsanity.com/paper/2411.03753/) (2024)
- [Discrete Point-wise Attack Is Not Enough: Generalized Manifold Adversarial Attack for Face Recognition](https://mlsanity.com/paper/2301.06083/) (2022)
- [Efficient Generator of Mathematical Expressions for Symbolic Regression](https://mlsanity.com/paper/2302.09893/) (2023)
- [PROSAC: Provably Safe Certification for Machine Learning Models under Adversarial Attacks](https://mlsanity.com/paper/2402.02629/) (2024)
- [Focus on Hiders: Exploring Hidden Threats for Enhancing Adversarial Training](https://mlsanity.com/paper/2312.07067/) (2023)
- [Retention Time Prediction for Chromatographic Enantioseparation by Quantile Geometry-enhanced Graph Neural Network](https://mlsanity.com/paper/2211.03602/) (2022)
- [RSRM: Reinforcement Symbolic Regression Machine](https://mlsanity.com/paper/2305.14656/) (2023)
- [Detecting Misbehaviors of Large Vision-Language Models by Evidential Uncertainty Quantification](https://mlsanity.com/paper/2602.05535/) (2026)

## Built on by (most cited first, 9 of 9)

- [Data-driven discovery of governing differential equations across physical systems](https://mlsanity.com/paper/2606.09638/) (2026)
- [Neuro-Symbolic ODE Discovery with Latent Grammar Flow](https://mlsanity.com/paper/2604.16232/) (2026)
- [Multi-Modal Learning meets Genetic Programming: Analyzing Alignment in Latent Space Optimization](https://mlsanity.com/paper/2604.08324/) (2026)
- [Symbolic Regression via Latent Iterative Refinement](https://mlsanity.com/paper/2605.27245/) (2026)
- [Hypothesize, Evaluate, Refine: A Scientific Agent for PDE Discovery with Unknown Spatial Coefficient Fields](https://mlsanity.com/paper/2608.27475/) (2026)
- [Enhancing Transformer Representations of Symbolic ODE Expressions](https://mlsanity.com/paper/2609.24746/) (2026)
- [DASS: A Solver-Adaptable Dynamic Auxiliary Search Strategy for Symbolic Regression](https://mlsanity.com/paper/2610.16812/) (2026)
- [Learning to Design SR Solvers: Harness Optimization for Symbolic Regression](https://mlsanity.com/paper/2610.16966/) (2026)
- [Beyond Equation Search: Conjecture-Guided Discovery with SCOPE and ClosureBench](https://mlsanity.com/paper/2610.18938/) (2026)

## Abstract (arXiv)

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(Equ. mid 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.