mlsanityData to 7 Oct 2026

Symbolic Regression with a Learned Concept Library

arXiv 2409.09359 ↗First posted 14 Sep 2024cs.LG cs.AI cs.NEcited by 76

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Abstract (arXiv)

We present a novel method for symbolic regression (SR), the task of searching for compact programmatic hypotheses that best explain a dataset. The problem is commonly solved using genetic algorithms; we show that we can enhance such methods by inducing a library of abstract textual concepts. Our algorithm, called LaSR, uses zero-shot queries to a large language model (LLM) to discover and evolve concepts occurring in known high-performing hypotheses. We discover new hypotheses using a mix of standard evolutionary steps and LLM-guided steps (obtained through zero-shot LLM queries) conditioned on discovered concepts. Once discovered, hypotheses are used in a new round of concept abstraction and evolution. We validate LaSR on the Feynman equations, a popular SR benchmark, as well as a set of synthetic tasks. On these benchmarks, LaSR substantially outperforms a variety of state-of-the-art SR approaches based on deep learning and evolutionary algorithms. Moreover, we show that LaSR can be used to discover a novel and powerful scaling law for LLMs.

Key facts. Cited by 76 papers in the map (data through 7 Oct 2026). Builds on 31 of its 56 references that are in the map. First posted on arXiv 14 Sep 2024.

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31 of 56 references.

References · 31

  1. 2020Language Models are Few-Shot Learnerscited by 32,199
  2. 2021Evaluating Large Language Models Trained on Codecited by 8,053
  3. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,767
  4. 2022Training Compute-Optimal Large Language Modelscited by 2,927
  5. 2022Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language modelscited by 1,970
  6. 2024Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameterscited by 1,928
  7. 2022Competition-Level Code Generation with AlphaCodecited by 1,427
  8. 2018Regularized Evolution for Image Classifier Architecture Searchcited by 902
  9. 2023ViperGPT: Visual Inference via Python Execution for Reasoningcited by 591
  10. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 536
  11. 2022Visual Programming: Compositional visual reasoning without trainingcited by 507
  12. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
19 more
  1. 2019Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradientscited by 294
  2. 2021Contemporary Symbolic Regression Methods and their Relative Performancecited by 209
  3. 2020DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learningcited by 159
  4. 2022Revisiting Neural Scaling Laws in Language and Visioncited by 129
  5. 2017RobustFill: Neural Program Learning under Noisy I/Ocited by 124
  6. 2023Language Model Crossover: Variation through Few-Shot Promptingcited by 119
  7. 2024LLM-SR: Scientific Equation Discovery via Programming with Large Language Modelscited by 117
  8. 2022Interpretable Scientific Discovery with Symbolic Regression: A Reviewcited by 105
  9. 2022Broken Neural Scaling Lawscited by 102
  10. 2022Rediscovering orbital mechanics with machine learningcited by 71
  11. 2022Parsel: Algorithmic Reasoning with Language Models by Composing Decompositionscited by 62
  12. 2022Top-Down Synthesis for Library Learningcited by 57
  13. 2023LILO: Learning Interpretable Libraries by Compressing and Documenting Codecited by 46
  14. 2021Leveraging Language to Learn Program Abstractions and Search Heuristicscited by 44
  15. 2021SpreadsheetCoder: Formula Prediction from Semi-structured Contextcited by 41
  16. 2019Program Synthesis and Semantic Parsing with Learned Code Idiomscited by 34
  17. 2020Learning Differentiable Programs with Admissible Neural Heuristicscited by 30
  18. 2019Fast, accurate, and transferable many-body interatomic potentials by symbolic regressioncited by 23
  19. 2024Evolving Interpretable Visual Classifiers with Large Language Modelscited by 18

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 2; 2025: 31; 2026: 43.

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  1. 2025AlphaEvolve: A coding agent for scientific and algorithmic discoverycited by 763
  2. 2025LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Modelscited by 61
  3. 2025SR-Scientist: Scientific Equation Discovery With Agentic AIcited by 30
  4. 2025DrSR: LLM based Scientific Equation Discovery with Dual Reasoning from Data and Experiencecited by 20
  5. 2025Autonomous Code Evolution Meets NP-Completenesscited by 14
  6. 2026Think like a Scientist: Physics-guided LLM Agent for Equation Discoverycited by 13
  7. 2025AlphaOPT: Formulating Optimization Programs with Self-Improving LLM Experience Librarycited by 12
  8. 2025A Neural Symbolic Model for Space Physicscited by 10
  9. 2026Can We Predict Before Executing Machine Learning Agents?cited by 10
  10. 2024In Context Learning and Reasoning for Symbolic Regression with Large Language Modelscited by 7
  11. 2026LLM-AutoSciLab: Closed-Loop Scientific Discovery via Active Experimentation with LLMscited by 7
  12. 2025Discovering Symbolic Differential Equations with Symmetry Invariantscited by 6
38 more
  1. 2025Mimicking the Physicist's Eye:A VLM-centric Approach for Physics Formula Discoverycited by 6
  2. 2025Man-Made Heuristics Are Dead. Long Live Code Generators!cited by 6
  3. 2025Foundation Models for Scientific Discovery: From Paradigm Enhancement to Paradigm Transitioncited by 6
  4. 2025When is a System Discoverable from Data? Discovery Requires Chaoscited by 6
  5. 2026GENSR: Symbolic Regression Based in Equation Generative Spacecited by 6
  6. 2026Autonomous Research Agents: A Survey of AI Scientists and the Verification Gapcited by 6
  7. 2026LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Searchcited by 5
  8. 2024Generative Design of Functional Metal Complexes Utilizing the Internal Knowledge of Large Language Modelscited by 4
  9. 2025Large Language Models for Extrapolative Modeling of Manufacturing Processescited by 4
  10. 2025LLM-Meta-SR: In-Context Learning for Evolving Selection Operators in Symbolic Regressioncited by 4
  11. 2025Physics-Grounded Motion Forecasting via Equation Discovery for Trajectory-Guided Image-to-Video Generationcited by 4
  12. 2025Program Synthesis via Test-Time Transductioncited by 4
  13. 2026OpInf-LLM: Parametric PDE Solving with LLMs via Operator Inferencecited by 4
  14. 2026LLM-Based Scientific Equation Discovery via Physics-Informed Token-Regularized Policy Optimizationcited by 4
  15. 2026What Makes an LLM a Good Optimizer? A Trajectory Analysis of LLM-Guided Evolutionary Searchcited by 4
  16. 2026A-SR: Self-Evolving Agentic LLMs for Symbolic Regression via Hierarchical Coordinationcited by 4
  17. 2025DiSciPLE: Learning Interpretable Programs for Scientific Visual Discoverycited by 3
  18. 2025Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networkscited by 3
  19. 2025Automated Model Discovery via Multi-modal & Multi-step Pipelinecited by 3
  20. 2026Data-driven discovery of governing differential equations across physical systemscited by 3
  21. 2025Self-Evolving Visual Concept Library using Vision-Language Criticscited by 2
  22. 2025Data-driven Discovery of Digital Twins in Biomedical Researchcited by 2
  23. 2025Analyzing Generalization in Pre-Trained Symbolic Regressioncited by 2
  24. 2025SAIL: Sound Abstract Interpreters with LLMscited by 2
  25. 2025Learning Interestingness in Automated Mathematical Theory Formationcited by 2
  26. 2026Agentic Framework for Epidemiological Modelingcited by 2
  27. 2026STRIDE: A Self-Reflective Agent Framework for Reliable Automatic Equation Discoverycited by 2
  28. 2025Can Test-time Computation Mitigate Reproduction Bias in Neural Symbolic Regression?cited by 1
  29. 2025SURFACEBENCH: A Geometry-Aware Benchmark for Symbolic Surface Discoverycited by 1
  30. 2025Dynamic Bayesian Optimization Framework for Instruction Tuning in Partial Differential Equation Discoverycited by 1
  31. 2026NSR-Boost: A Neuro-Symbolic Residual Boosting Framework for Industrial Legacy Modelscited by 1
  32. 2026DeepInflation: an AI agent for research and model discovery of inflationcited by 1
  33. 2026Contrastive Concept-Tree Search for LLM-Assisted Algorithm Discoverycited by 1
  34. 2026Prior-Guided Symbolic Regression: Towards Scientific Consistency in Equation Discoverycited by 1
  35. 2026Programmatic Context Augmentation for LLM-based Symbolic Regressioncited by 1
  36. 2026Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Wavescited by 1
  37. 2026FePySR: A Neural Feature Extraction Framework for Efficient and Scalable Symbolic Regressioncited by 1
  38. 2026Towards Diverse Scientific Hypothesis Search with Large Language Modelscited by 1

50 most cited of 76 All 76 (JSON)