mlsanityData to 7 Oct 2026

HKAN: Hierarchical Kolmogorov-Arnold Network without Backpropagation

arXiv 2501.18199 ↗First posted 30 Jan 2025cs.LG cs.AIcited by 0

Not on the map. Why?

Abstract (arXiv)

This paper introduces the Hierarchical Kolmogorov-Arnold Network (HKAN), a novel network architecture that offers a competitive alternative to the recently proposed Kolmogorov-Arnold Network (KAN). Unlike KAN, which relies on backpropagation, HKAN adopts a randomized learning approach, where the parameters of its basis functions are fixed, and linear aggregations are optimized using least-squares regression. HKAN utilizes a hierarchical multi-stacking framework, with each layer refining the predictions from the previous one by solving a series of linear regression problems. This non-iterative training method simplifies computation and eliminates sensitivity to local minima in the loss function. Empirical results show that HKAN delivers comparable, if not superior, accuracy and stability relative to KAN across various regression tasks, while also providing insights into variable importance. The proposed approach seamlessly integrates theoretical insights with practical applications, presenting a robust and efficient alternative for neural network modeling.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 41 of its 67 references that are in the map. First posted on arXiv 30 Jan 2025.

Builds on

41 of 67 references.

References · 41

  1. 2019Optuna: A Next-generation Hyperparameter Optimization Frameworkcited by 2,455
  2. 2024KAN: Kolmogorov-Arnold Networkscited by 634
  3. 2024U-KAN Makes Strong Backbone for Medical Image Segmentation and Generationcited by 176
  4. 2024Wav-KAN: Wavelet Kolmogorov-Arnold Networkscited by 118
  5. 2024KAN 2.0: Kolmogorov-Arnold Networks Meet Sciencecited by 116
  6. 2024Chebyshev Polynomial-Based Kolmogorov-Arnold Networks: An Efficient Architecture for Nonlinear Function Approximationcited by 115
  7. 2024A comprehensive and FAIR comparison between MLP and KAN representations for differential equations and operator networkscited by 103
  8. 2024Kolmogorov-Arnold Networks (KANs) for Time Series Analysiscited by 97
  9. 2024DeepOKAN: Deep Operator Network Based on Kolmogorov Arnold Networks for Mechanics Problemscited by 82
  10. 2024KAN or MLP: A Fairer Comparisoncited by 71
  11. 2024TKAN: Temporal Kolmogorov-Arnold Networkscited by 70
  12. 2024Kolmogorov-Arnold Networks for Time Series: Bridging Predictive Power and Interpretabilitycited by 69
29 more
  1. 2024fKAN: Fractional Kolmogorov-Arnold Networks with trainable Jacobi basis functionscited by 60
  2. 2024Kolmogorov-Arnold Transformercited by 56
  3. 2024A Temporal Kolmogorov-Arnold Transformer for Time Series Forecastingcited by 50
  4. 2024Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networkscited by 37
  5. 2024KANQAS: Kolmogorov-Arnold Network for Quantum Architecture Searchcited by 36
  6. 2024On the expressiveness and spectral bias of KANscited by 36
  7. 2022Random vector functional link network: recent developments, applications, and future directionscited by 33
  8. 2024ReLU-KAN: New Kolmogorov-Arnold Networks that Only Need Matrix Addition, Dot Multiplication, and ReLUcited by 32
  9. 2024GraphKAN: Enhancing Feature Extraction with Graph Kolmogorov Arnold Networkscited by 31
  10. 2024rKAN: Rational Kolmogorov-Arnold Networkscited by 31
  11. 2024A Benchmarking Study of Kolmogorov-Arnold Networks on Tabular Datacited by 25
  12. 2024Predictive Modeling of Flexible EHD Pumps using Kolmogorov-Arnold Networkscited by 23
  13. 2024Smooth Kolmogorov Arnold networks enabling structural knowledge representationcited by 22
  14. 2024Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementationcited by 22
  15. 2024CoxKAN: Kolmogorov-Arnold Networks for Interpretable, High-Performance Survival Analysiscited by 22
  16. 2024KAN-AD: Time Series Anomaly Detection with Kolmogorov-Arnold Networkscited by 20
  17. 2020Random Vector Functional Link Networks for Function Approximation on Manifoldscited by 19
  18. 2024FC-KAN: Function Combinations in Kolmogorov-Arnold Networkscited by 18
  19. 2024Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noisecited by 17
  20. 2024DropKAN: Regularizing KANs by masking post-activationscited by 14
  21. 2024F-KANs: Federated Kolmogorov-Arnold Networkscited by 14
  22. 2024SigKAN: Signature-Weighted Kolmogorov-Arnold Networks for Time Seriescited by 13
  23. 2017A Method of Generating Random Weights and Biases in Feedforward Neural Networks with Random Hidden Nodescited by 9
  24. 2024CF-KAN: Kolmogorov-Arnold Network-based Collaborative Filtering to Mitigate Catastrophic Forgetting in Recommender Systemscited by 8
  25. 2024A First Look at Kolmogorov-Arnold Networks in Surrogate-assisted Evolutionary Algorithmscited by 7
  26. 2019Generating Random Parameters in Feedforward Neural Networks with Random Hidden Nodes: Drawbacks of the Standard Method and How to Improve Itcited by 6
  27. 2024Gaussian Process Kolmogorov-Arnold Networkscited by 6
  28. 2024Residual Kolmogorov-Arnold Network for Enhanced Deep Learningcited by 5
  29. 2024GNN-SKAN: Harnessing the Power of SwallowKAN to Advance Molecular Representation Learning with GNNscited by 3

Built on by

Not cited yet.