mlsanityData to 7 Oct 2026

Symbolic Regression via Neural-Guided Genetic Programming Population Seeding

arXiv 2111.00053 ↗First posted 29 Oct 2021cs.NE cs.AI cs.LGcited by 97

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Abstract (arXiv)

Symbolic regression is the process of identifying mathematical expressions that fit observed output from a black-box process. It is a discrete optimization problem generally believed to be NP-hard. Prior approaches to solving the problem include neural-guided search (e.g. using reinforcement learning) and genetic programming. In this work, we introduce a hybrid neural-guided/genetic programming approach to symbolic regression and other combinatorial optimization problems. We propose a neural-guided component used to seed the starting population of a random restart genetic programming component, gradually learning better starting populations. On a number of common benchmark tasks to recover underlying expressions from a dataset, our method recovers 65% more expressions than a recently published top-performing model using the same experimental setup. We demonstrate that running many genetic programming generations without interdependence on the neural-guided component performs better for symbolic regression than alternative formulations where the two are more strongly coupled. Finally, we introduce a new set of 22 symbolic regression benchmark problems with increased difficulty over existing benchmarks. Source code is provided at www.github.com/brendenpetersen/deep-symbolic-optimization.

Key facts. Cited by 97 papers in the map (data through 7 Oct 2026). Builds on 19 of its 58 references that are in the map. First posted on arXiv 29 Oct 2021.

Builds on

19 of 58 references.

References · 19

  1. 2015Continuous control with deep reinforcement learningcited by 3,279
  2. 2016Neural Combinatorial Optimization with Reinforcement Learningcited by 600
  3. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  4. 2019Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradientscited by 294
  5. 2017Grammar Variational Autoencodercited by 283
  6. 2018Learning Equations for Extrapolation and Controlcited by 151
  7. 2017Deep Neuroevolution: Genetic Algorithms Are a Competitive Alternative for Training Deep Neural Networks for Reinforcement Learningcited by 148
  8. 2020AutoML-Zero: Evolving Machine Learning Algorithms From Scratchcited by 137
  9. 2017Evolving Deep Neural Networkscited by 93
  10. 2018Evolution-Guided Policy Gradient in Reinforcement Learningcited by 78
  11. 2019Bayesian Symbolic Regressioncited by 77
  12. 2018CEM-RL: Combining evolutionary and gradient-based methods for policy searchcited by 53
7 more
  1. 2020Guiding Deep Molecular Optimization with Genetic Explorationcited by 51
  2. 2020Off-Policy Reinforcement Learning for Efficient and Effective GAN Architecture Searchcited by 25
  3. 2018Neural Program Synthesis with Priority Queue Trainingcited by 24
  4. 2019Deep Reinforcement Learning using Genetic Algorithm for Parameter Optimizationcited by 23
  5. 2014Neuroevolution in Games: State of the Art and Open Challengescited by 15
  6. 2021Improving exploration in policy gradient search: Application to symbolic optimizationcited by 14
  7. 2018Genetic-Gated Networks for Deep Reinforcementcited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 10; 2023: 14; 2024: 28; 2025: 29; 2026: 16.

97 papers.

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  1. 2022End-to-end symbolic regression with transformerscited by 195
  2. 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
  3. 2024LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discoverycited by 82
  4. 2022Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree searchcited by 61
  5. 2022SymFormer: End-to-end symbolic regression using transformer-based architecturecited by 56
  6. 2023Deep Generative Symbolic Regression with Monte-Carlo-Tree-Searchcited by 40
  7. 2024Discovering Preference Optimization Algorithms with and for Large Language Modelscited by 38
  8. 2023Generating Synergistic Formulaic Alpha Collections via Reinforcement Learningcited by 37
  9. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  10. 2024AlphaForge: A Framework to Mine and Dynamically Combine Formulaic Alpha Factorscited by 25
  11. 2024Bridging Evolutionary Algorithms and Reinforcement Learning: A Comprehensive Survey on Hybrid Algorithmscited by 23
  12. 2024Automate Strategy Finding with LLM in Quant Investmentcited by 21
38 more
  1. 2025DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experiencecited by 20
  2. 2023Controllable Neural Symbolic Regressioncited by 19
  3. 2022Taylor Genetic Programming for Symbolic Regressioncited by 18
  4. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
  5. 2024Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description lengthcited by 16
  6. 2023Efficient Generator of Mathematical Expressions for Symbolic Regressioncited by 13
  7. 2024MMSR: Symbolic Regression is a Multi-Modal Information Fusion Taskcited by 13
  8. 2024Automatically Learning Hybrid Digital Twins of Dynamical Systemscited by 13
  9. 2025Generative Discovery of Partial Differential Equations by Learning from Math Handbookscited by 12
  10. 2022GSR: A Generalized Symbolic Regression Approachcited by 11
  11. 2025Interpretable Machine Learning in Physics: A Reviewcited by 11
  12. 2023Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressionscited by 10
  13. 2024Discovering Mathematical Formulas from Data via GPT-guided Monte Carlo Tree Searchcited by 10
  14. 2024Neuro-Symbolic AI: Explainability, Challenges, and Future Trendscited by 10
  15. 2025A Systematic Survey on Large Language Models for Evolutionary Optimization: From Modeling to Solvingcited by 9
  16. 2022CoNSoLe: Convex Neural Symbolic Learningcited by 7
  17. 2023RSRM: Reinforcement Symbolic Regression Machinecited by 7
  18. 2023Explainable Fraud Detection with Deep Symbolic Classificationcited by 7
  19. 2025Can Large Language Models Adequately Perform Symbolic Reasoning Over Time Series?cited by 6
  20. 2025Improving Monte Carlo Tree Search for Symbolic Regressioncited by 6
  21. 2025Autonomous Data Agents: A New Opportunity for Smart Datacited by 6
  22. 2023MESSY Estimation: Maximum-Entropy based Stochastic and Symbolic densitY Estimationcited by 5
  23. 2024A Comparison of Recent Algorithms for Symbolic Regression to Genetic Programmingcited by 5
  24. 2025Grammar-based Ordinary Differential Equation Discoverycited by 5
  25. 2025Scaling Up Unbiased Search-based Symbolic Regressioncited by 5
  26. 2023Symbolic expression generation via Variational Auto-Encodercited by 4
  27. 2024PruneSymNet: A Symbolic Neural Network and Pruning Algorithm for Symbolic Regressioncited by 4
  28. 2024ChatSR: Multimodal Large Language Models for Scientific Formula Discoverycited by 4
  29. 2025Bridging the Domain Gap in Equation Distillation with Reinforcement Feedbackcited by 4
  30. 2026LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimizationcited by 4
  31. 2022Neural-Network-Directed Genetic Programmer for Discovery of Governing Equationscited by 3
  32. 2022What can we Learn by Predicting Accuracy?cited by 3
  33. 2022DISCOVER: Deep identification of symbolically concise open-form PDEs via enhanced reinforcement-learningcited by 3
  34. 2024Learning Heuristics for Transit Network Design and Improvement with Deep Reinforcement Learningcited by 3
  35. 2025Iterated Agent for Symbolic Regressioncited by 3
  36. 2023Symbolic Metamodels for Interpreting Black-boxes Using Primitive Functionscited by 2
  37. 2023Online Symbolic Regression with Informative Querycited by 2
  38. 2023Scalable Neural Symbolic Regression using Control Variablescited by 2

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