mlsanityData to 7 Oct 2026

KAN 2.0: Kolmogorov-Arnold Networks Meet Science

arXiv 2408.10205 ↗First posted 19 Aug 2024cs.LG cs.AI physics.comp-phcited by 116

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Abstract (arXiv)

A major challenge of AI + Science lies in their inherent incompatibility: today's AI is primarily based on connectionism, while science depends on symbolism. To bridge the two worlds, we propose a framework to seamlessly synergize Kolmogorov-Arnold Networks (KANs) and science. The framework highlights KANs' usage for three aspects of scientific discovery: identifying relevant features, revealing modular structures, and discovering symbolic formulas. The synergy is bidirectional: science to KAN (incorporating scientific knowledge into KANs), and KAN to science (extracting scientific insights from KANs). We highlight major new functionalities in the pykan package: (1) MultKAN: KANs with multiplication nodes. (2) kanpiler: a KAN compiler that compiles symbolic formulas into KANs. (3) tree converter: convert KANs (or any neural networks) to tree graphs. Based on these tools, we demonstrate KANs' capability to discover various types of physical laws, including conserved quantities, Lagrangians, symmetries, and constitutive laws.

Key facts. Cited by 116 papers in the map (data through 7 Oct 2026). Builds on 72 of its 101 references that are in the map. First posted on arXiv 19 Aug 2024.

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72 of 101 references.

References · 72

  1. 2022Locating and Editing Factual Associations in GPTcited by 2,609
  2. 2023Sparse Autoencoders Find Highly Interpretable Features in Language Modelscited by 1,359
  3. 2022Interpretability in the Wild: a Circuit for Indirect Object Identification in GPT-2 smallcited by 1,130
  4. 2022Toy Models of Superpositioncited by 928
  5. 2020Learning to Simulate Complex Physics with Graph Networkscited by 867
  6. 2023Progress measures for grokking via mechanistic interpretabilitycited by 822
  7. 2019Hamiltonian Neural Networkscited by 702
  8. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  9. 2022Emergent World Representations: Exploring a Sequence Model Trained on a Synthetic Taskcited by 417
  10. 2023LeanDojo: Theorem Proving with Retrieval-Augmented Language Modelscited by 414
  11. 2020Lagrangian Neural Networkscited by 388
  12. 2020Discovering Symbolic Models from Deep Learning with Inductive Biasescited by 335
38 more
  1. 2024Not All Language Model Features Are One-Dimensionally Linearcited by 201
  2. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 176
  3. 2023The Clock and the Pizza: Two Stories in Mechanistic Explanation of Neural Networkscited by 153
  4. 2020AI Feynman 2.0: Pareto-optimal symbolic regression exploiting graph modularitycited by 140
  5. 2024Kolmogorov-Arnold Networks are Radial Basis Function Networkscited by 125
  6. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  7. 2016Extrapolation and learning equationscited by 106
  8. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  9. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
  10. 2024LLM and Simulation as Bilevel Optimizers: A New Paradigm to Advance Physical Scientific Discoverycited by 82
  11. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 82
  12. 2020AI Poincar'e: Machine Learning Conservation Laws from Trajectoriescited by 77
  13. 2024Convolutional Kolmogorov-Arnold Networkscited by 76
  14. 2022Rediscovering orbital mechanics with machine learningcited by 71
  15. 2024KAN or MLP: A Fairer Comparisoncited by 71
  16. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 70
  17. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 69
  18. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  19. 2023Learning Neural Constitutive Laws From Motion Observations for Generalizable PDE Dynamicscited by 56
  20. 2024GKAN: Graph Kolmogorov-Arnold Networkscited by 52
  21. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 50
  22. 2024KAGNNs: Kolmogorov-Arnold Networks meet Graph Learningcited by 48
  23. 2017Unsupervised learning of phase transitions: from principal component analysis to variational autoencoderscited by 47
  24. 2024Kolmogorov-Arnold Network for Satellite Image Classification in Remote Sensingcited by 46
  25. 2024BSRBF-KAN: A combination of B-splines and Radial Basis Functions in Kolmogorov-Arnold Networkscited by 43
  26. 2024Enhancing Graph Collaborative Filtering with FourierKAN Feature Transformationcited by 41
  27. 2023Generative Adversarial Symmetry Discoverycited by 40
  28. 2024Demonstrating the Efficacy of Kolmogorov-Arnold Networks in Vision Taskscited by 39
  29. 2023Seeing is Believing: Brain-Inspired Modular Training for Mechanistic Interpretabilitycited by 38
  30. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
  31. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 36
  32. 2024Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problemscited by 35
  33. 2020Discovering Symmetry Invariants and Conserved Quantities by Interpreting Siamese Neural Networkscited by 33
  34. 2020Detecting Symmetries with Neural Networkscited by 33
  35. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
  36. 2024Unveiling the Power of Wavelets: A Wavelet-based Kolmogorov-Arnold Network for Hyperspectral Image Classificationcited by 33
  37. 2024Suitability of KANs for Computer Vision: A preliminary investigationcited by 33
  38. 2021Machine-learning hidden symmetriescited by 31

50 most cited of 72 All 72 (JSON)

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 28; 2025: 55; 2026: 33.

116 papers.

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  1. 2024From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learningcited by 73
  2. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  3. 2024Kolmogorov-Arnold Transformercited by 56
  4. 2024On the expressiveness and spectral bias of KANscited by 36
  5. 2024KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networkscited by 20
  6. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 18
  7. 2025KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluationcited by 13
  8. 2024SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networkscited by 12
  9. 2025LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behaviorcited by 12
  10. 2025Sub-Sequential Physics-Informed Learning with State Space Modelcited by 10
  11. 2025A Neural Symbolic Model for Space Physicscited by 10
  12. 2024Multifidelity Kolmogorov-Arnold Networkscited by 9
38 more
  1. 2024Kolmogorov-Arnold Network Autoencoderscited by 8
  2. 2024Exploring Kolmogorov-Arnold Networks for Interpretable Time Series Classificationcited by 8
  3. 2025MedKAN: An Advanced Kolmogorov-Arnold Network for Medical Image Classificationcited by 8
  4. 2025QKAN-LSTM: Quantum-inspired Kolmogorov-Arnold Long Short-term Memorycited by 8
  5. 2025High precision PINNs in unbounded domains: application to singularity formulation in PDEscited by 6
  6. 2025KANO: Kolmogorov-Arnold Neural Operatorcited by 6
  7. 2024Exploring Kolmogorov-Arnold networks for realistic image sharpness assessmentcited by 5
  8. 2024Residual Kolmogorov-Arnold Network for Enhanced Deep Learningcited by 5
  9. 2025Kolmogorov Arnold Neural Interpolator for Downscaling and Correcting Meteorological Fields from In-Situ Observationscited by 5
  10. 2025CVKAN: Complex-Valued Kolmogorov-Arnold Networkscited by 5
  11. 2025KHRONOS: a Kernel-Based Neural Architecture for Rapid, Resource-Efficient Scientific Computationcited by 5
  12. 2024Incorporating Arbitrary Matrix Group Equivariance into KANscited by 4
  13. 2025Exploring Adversarial Transferability between Kolmogorov-arnold Networkscited by 4
  14. 2025ChemKANs for Combustion Chemistry Modeling and Accelerationcited by 4
  15. 2025Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinementcited by 4
  16. 2025Multi-Exit Kolmogorov-Arnold Networks: enhancing accuracy and parsimonycited by 4
  17. 2024KAN-HyperpointNet for Point Cloud Sequence-Based 3D Human Action Recognitioncited by 3
  18. 2024KAN v.s. MLP for Offline Reinforcement Learningcited by 3
  19. 2024HiPPO-KAN: Efficient KAN Model for Time Series Analysiscited by 3
  20. 2024Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamicscited by 3
  21. 2025AF-KAN: Activation Function-Based Kolmogorov-Arnold Networks for Efficient Representation Learningcited by 3
  22. 2025Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learningcited by 3
  23. 2025A Unified Benchmark of Federated Learning with Kolmogorov-Arnold Networks for Medical Imagingcited by 3
  24. 2025Interpretable Clinical Classification with Kolmogorov-Arnold Networkscited by 3
  25. 2026Symbolic--KAN: Kolmogorov-Arnold Networks with Discrete Symbolic Structure for Interpretable Learningcited by 3
  26. 2026Making Gaussian Kolmogorov-Arnold Networks Reliable and Accuratecited by 3
  27. 2024Explainable fault and severity classification for rolling element bearings using Kolmogorov-Arnold networkscited by 2
  28. 2024KAE: Kolmogorov-Arnold Auto-Encoder for Representation Learningcited by 2
  29. 2025Kolmogorov-Arnold Attention: Is Learnable Attention Better For Vision Transformers?cited by 2
  30. 2025iTFKAN: Interpretable Time Series Forecasting with Kolmogorov-Arnold Networkcited by 2
  31. 2025On the Rate of Convergence of Kolmogorov-Arnold Network Regression Estimatorscited by 2
  32. 2025CausalKANs: interpretable treatment effect estimation with Kolmogorov-Arnold networkscited by 2
  33. 2025Shift-Invariant Attribute Scoring for Kolmogorov-Arnold Networks via Shapley Valuecited by 2
  34. 2025Automating modeling in mechanics: LLMs as designers of physics-constrained neural networks for constitutive modeling of materialscited by 2
  35. 2025Softly Symbolifying Kolmogorov-Arnold Networkscited by 2
  36. 2026Vision KAN: Towards an Attention-Free Backbone for Vision with Kolmogorov-Arnold Networkscited by 2
  37. 2026SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networkscited by 2
  38. 2024Uncertainty Quantification with Bayesian Higher Order ReLU KANscited by 1

50 most cited of 116 All 116 (JSON)