mlsanityData to 13 Oct 2026

Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients

arXiv 1912.04871 ↗First posted 10 Dec 2019cs.LG stat.MLcited by 298

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Abstract (arXiv)

Discovering the underlying mathematical expressions describing a dataset is a core challenge for artificial intelligence. This is the problem of textitsymbolic regression. Despite recent advances in training neural networks to solve complex tasks, deep learning approaches to symbolic regression are underexplored. We propose a framework that leverages deep learning for symbolic regression via a simple idea: use a large model to search the space of small models. Specifically, we use a recurrent neural network to emit a distribution over tractable mathematical expressions and employ a novel risk-seeking policy gradient to train the network to generate better-fitting expressions. Our algorithm outperforms several baseline methods (including Eureqa, the gold standard for symbolic regression) in its ability to exactly recover symbolic expressions on a series of benchmark problems, both with and without added noise. More broadly, our contributions include a framework that can be applied to optimize hierarchical, variable-length objects under a black-box performance metric, with the ability to incorporate constraints in situ, and a risk-seeking policy gradient formulation that optimizes for best-case performance instead of expected performance.

Key facts. Cited by 298 papers in the map (data through 13 Oct 2026). First posted on arXiv 10 Dec 2019.

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Citing papers per year: 2021: 11; 2022: 31; 2023: 46; 2024: 66; 2025: 70; 2026: 74.

298 papers.

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  1. 2022End-to-end symbolic regression with transformerscited by 196
  2. 2022HyperTree Proof Search for Neural Theorem Provingcited by 195
  3. 2021Neural Symbolic Regression that Scalescited by 186
  4. 2024LLM-SR: Scientific Equation Discovery via Programming with Large Language Modelscited by 123
  5. 2021SymbolicGPT: A Generative Transformer Model for Symbolic Regressioncited by 102
  6. 2021Symbolic Regression via Neural-Guided Genetic Programming Population Seedingcited by 98
  7. 2021Chaos as an interpretable benchmark for forecasting and data-driven modellingcited by 88
  8. 2024LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discoverycited by 84
  9. 2024Symbolic Regression with a Learned Concept Librarycited by 78
  10. 2023Transformer-based Planning for Symbolic Regressioncited by 73
  11. 2022Symbolic Regression is NP-hardcited by 69
  12. 2025LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Modelscited by 65
38 more
  1. 2022Symbolic Physics Learner: Discovering governing equations via Monte Carlo tree searchcited by 63
  2. 2023ODEFormer: Symbolic Regression of Dynamical Systems with Transformerscited by 60
  3. 2022SymFormer: End-to-end symbolic regression using transformer-based architecturecited by 57
  4. 2022Deep Symbolic Regression for Recurrent Sequencescited by 53
  5. 2023Interpretable Machine Learning for Science with PySR and SymbolicRegression.jlcited by 46
  6. 2022Rethinking Symbolic Regression Datasets and Benchmarks for Scientific Discoverycited by 45
  7. 2023SNIP: Bridging Mathematical Symbolic and Numeric Realms with Unified Pre-trainingcited by 42
  8. 2025R&D-Agent-Quant: A Multi-Agent Framework for Data-Centric Factors and Model Joint Optimizationcited by 41
  9. 2023Deep Generative Symbolic Regression with Monte-Carlo-Tree-Searchcited by 40
  10. 2024Discovering Preference Optimization Algorithms with and for Large Language Modelscited by 40
  11. 2023Generating Synergistic Formulaic Alpha Collections via Reinforcement Learningcited by 38
  12. 2023Discovering Causal Relations and Equations from Datacited by 35
  13. 2024A review on data-driven constitutive laws for solidscited by 35
  14. 2025NewtonBench: Benchmarking Generalizable Scientific Law Discovery in LLM Agentscited by 35
  15. 2023Understanding Addition in Transformerscited by 34
  16. 2022A computational framework for physics-informed symbolic regression with straightforward integration of domain knowledgecited by 31
  17. 2025SR-Scientist: Scientific Equation Discovery With Agentic AIcited by 30
  18. 2022Exhaustive Symbolic Regressioncited by 29
  19. 2024In-Context Symbolic Regression: Leveraging Large Language Models for Function Discoverycited by 29
  20. 2021Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledgecited by 27
  21. 2023Deep Generative Symbolic Regressioncited by 27
  22. 2023Predicting Ordinary Differential Equations with Transformerscited by 26
  23. 2024AlphaForge: A Framework to Mine and Dynamically Combine Formulaic Alpha Factorscited by 26
  24. 2021How to transfer algorithmic reasoning knowledge to learn new algorithms?cited by 22
  25. 2024Symbol: Generating Flexible Black-Box Optimizers through Symbolic Equation Learningcited by 22
  26. 2022Finite Expression Method for Solving High-Dimensional Partial Differential Equationscited by 21
  27. 2025DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experiencecited by 21
  28. 2023Benchmarking sparse system identification with low-dimensional chaoscited by 19
  29. 2022Taylor Genetic Programming for Symbolic Regressioncited by 18
  30. 2023Automated Scientific Discovery: From Equation Discovery to Autonomous Discovery Systemscited by 18
  31. 2024Symbolic regression via MDLformer-guided search: from minimizing prediction error to minimizing description lengthcited by 16
  32. 2022Simplifying Polylogarithms with Machine Learningcited by 15
  33. 2021Improving exploration in policy gradient search: Application to symbolic optimizationcited by 14
  34. 2023A Neural-Guided Dynamic Symbolic Network for Exploring Mathematical Expressions from Datacited by 14
  35. 2024LLM4ED: Large Language Models for Automatic Equation Discoverycited by 14
  36. 2024Automatically Learning Hybrid Digital Twins of Dynamical Systemscited by 14
  37. 2025PhysGym: Benchmarking LLMs in Interactive Physics Discovery with Controlled Priorscited by 14
  38. 2023Efficient Generator of Mathematical Expressions for Symbolic Regressioncited by 13

50 most cited of 298 All 298 (JSON)