mlsanityData to 7 Oct 2026

Smooth Kolmogorov Arnold networks enabling structural knowledge representation

arXiv 2405.11318 ↗First posted 18 May 2024cs.LG cond-mat.dis-nn cs.AIcited by 22

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Abstract (arXiv)

Kolmogorov-Arnold Networks (KANs) offer an efficient and interpretable alternative to traditional multi-layer perceptron (MLP) architectures due to their finite network topology. However, according to the results of Kolmogorov and Vitushkin, the representation of generic smooth functions by KAN implementations using analytic functions constrained to a finite number of cutoff points cannot be exact. Hence, the convergence of KAN throughout the training process may be limited. This paper explores the relevance of smoothness in KANs, proposing that smooth, structurally informed KANs can achieve equivalence to MLPs in specific function classes. By leveraging inherent structural knowledge, KANs may reduce the data required for training and mitigate the risk of generating hallucinated predictions, thereby enhancing model reliability and performance in computational biomedicine.

Key facts. Cited by 22 papers in the map (data through 7 Oct 2026). Builds on 1 of its 14 references that are in the map. First posted on arXiv 18 May 2024.

Builds on

1 of 14 references.

References · 1

  1. 2024KAN: Kolmogorov-Arnold Networkscited by 634

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 13; 2025: 7; 2026: 2.

22 papers.

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  1. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  2. 2024A Survey on Kolmogorov-Arnold Networkcited by 67
  3. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  4. 2024Exploring the Potential of Polynomial Basis Functions in Kolmogorov-Arnold Networks: A Comparative Study of Different Groups of Polynomialscited by 33
  5. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 31
  6. 2024iKAN: Global Incremental Learning with KAN for Human Activity Recognition Across Heterogeneous Datasetscited by 14
  7. 2024SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networkscited by 12
  8. 2025Surrogate Learning in Meta-Black-Box Optimization: A Preliminary Studycited by 7
  9. 2024Architectural Scaling Surpass Basis Complexity? Efficient KANs with Single-Parameter Designcited by 6
  10. 2024FourierKAN outperforms MLP on Text Classification Head Fine-tuningcited by 5
  11. 2026Inelastic Constitutive Kolmogorov-Arnold Networks: A generalized framework for automated discovery of interpretable inelastic material modelscited by 5
  12. 2024KAN we improve on HEP classification tasks? Kolmogorov-Arnold Networks applied to an LHC physics examplecited by 4
10 more
  1. 2024KAN v.s. MLP for Offline Reinforcement Learningcited by 3
  2. 2025Physics-informed KAN PointNet: Deep learning for simultaneous solutions to inverse problems in incompressible flow on numerous irregular geometriescited by 3
  3. 2024Kolmogorov Arnold Networks in Fraud Detection: Bridging the Gap Between Theory and Practicecited by 2
  4. 2025iTFKAN: Interpretable Time Series Forecasting with Kolmogorov-Arnold Networkcited by 2
  5. 2024KAT to KANs: A Review of Kolmogorov-Arnold Networks and the Neural Leap Forwardcited by 1
  6. 2025Flexible Swarm Learning May Outpace Foundation Models in Essential Taskscited by 1
  7. 2025PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structurecited by 1
  8. 2025HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagationcited by 0
  9. 2025Learning Fair Representations with Kolmogorov-Arnold Networkscited by 0
  10. 2026KANs need curvature: penalties for compositional smoothnesscited by 0