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A Survey on Kolmogorov-Arnold Network

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arxiv 2411.06078 v1 pith:LZDZIBCD submitted 2024-11-09 cs.LG

Shriyank Somvanshi , Syed Aaqib Javed , Md Monzurul Islam , Diwas Pandit , Subasish Das This is my paper · ORCID
classification cs.LG
keywords computationalfunctionsneuralapplicationsefficiencykolmogorov-arnoldnetworksactivation
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This systematic review explores the theoretical foundations, evolution, applications, and future potential of Kolmogorov-Arnold Networks (KAN), a neural network model inspired by the Kolmogorov-Arnold representation theorem. KANs distinguish themselves from traditional neural networks by using learnable, spline-parameterized functions instead of fixed activation functions, allowing for flexible and interpretable representations of high-dimensional functions. This review details KAN's architectural strengths, including adaptive edge-based activation functions that improve parameter efficiency and scalability in applications such as time series forecasting, computational biomedicine, and graph learning. Key advancements, including Temporal-KAN, FastKAN, and Partial Differential Equation (PDE) KAN, illustrate KAN's growing applicability in dynamic environments, enhancing interpretability, computational efficiency, and adaptability for complex function approximation tasks. Additionally, this paper discusses KAN's integration with other architectures, such as convolutional, recurrent, and transformer-based models, showcasing its versatility in complementing established neural networks for tasks requiring hybrid approaches. Despite its strengths, KAN faces computational challenges in high-dimensional and noisy data settings, motivating ongoing research into optimization strategies, regularization techniques, and hybrid models. This paper highlights KAN's role in modern neural architectures and outlines future directions to improve its computational efficiency, interpretability, and scalability in data-intensive applications.

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Cited by 11 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Kolmogorov--Arnold Networks for Small Language Models

    cs.LG 2026-07 conditional novelty 7.0 of 10

    In small language models, KAN feed-forward blocks are auditable and pruneable, but on standardized benchmarks and scale tests they show no consistent accuracy, quality, or latency advantage over MLP baselines.

  2. Kolmogorov-Arnold Network for Gene Regulatory Network Inference

    cs.CE 2025-06 conditional novelty 6.0 of 10

    scKAN uses Kolmogorov-Arnold networks in a one-vs-rest regression and treats model gradients as signed gene regulation strengths, outperforming baselines on several BEELINE benchmark tasks.

  3. PRKAN: Parameter-Reduced Kolmogorov-Arnold Networks

    cs.LG 2025-01 conditional novelty 6.0 of 10

    PRKAN lowers KAN parameter counts to near-MLP levels via attention, convolution/pooling, dimension summation, and feature-vector projections, reaching MLP-like accuracy on MNIST and Fashion-MNIST.

  4. KKANs: Kurkova-Kolmogorov-Arnold Networks and Their Learning Dynamics

    cs.LG 2024-12 conditional novelty 6.0 of 10

    KKANs, a two-block KART-based architecture with MLP inner functions and basis-function outer functions, universally approximate continuous functions and empirically outperform MLP and cKAN baselines in regression, PIN...

  5. Leveraging KANs for Expedient Training of Multichannel MLPs via Preconditioning and Geometric Refinement

    cs.LG 2025-05 conditional novelty 5.0 of 10

    Training in a B-spline KAN basis is equivalent to preconditioned gradient descent on a multichannel ReLU MLP, and geometric refinement plus trainable knots accelerate and improve training.

  6. Low Tensor-Rank Adaptation of Kolmogorov--Arnold Networks

    cs.LG 2025-02 conditional novelty 5.0 of 10

    A low tensor-rank adaptation (LoTRA) method and learning-rate guidance enable efficient fine-tuning of Kolmogorov-Arnold networks, validated on PDE solving and representation tasks.

  7. Efficiency Bottlenecks of Convolutional Kolmogorov-Arnold Networks: A Comprehensive Scrutiny with ImageNet, AlexNet, LeNet and Tabular Classification

    cs.CV 2025-01 reject novelty 5.0 of 10

    CKANs are measurably less efficient than standard CNNs, and on ImageNet the accuracy gap is large, but the paper's baseline and timing comparisons are not controlled.

  8. CIKAN: Constraint Informed Kolmogorov-Arnold Networks for Autonomous Spacecraft Rendezvous using Time Shift Governor

    eess.SY 2024-12 conditional novelty 5.0 of 10

    CIKAN, a KAN-based constraint-informed network, approximates the Time Shift Governor for spacecraft rendezvous and, in simulation, enforces constraints while reducing average computation time and fuel use relative to ...

  9. FORTRESS: Function-composition Optimized Real-Time Resilient Structural Segmentation via Kolmogorov-Arnold Enhanced Spatial Attention Networks

    cs.CV 2025-07 reject novelty 4.0 of 10

    FORTRESS combines depthwise separable convolutions and a gated Kolmogorov-Arnold module to report F1 of 0.771 and mIoU of 0.677 on the CSDD benchmark, but the core KAN contribution is not isolated by ablation.

  10. Capsule-ConvKAN: A Hybrid Neural Approach to Medical Image Classification

    eess.IV 2025-07 conditional novelty 4.0 of 10

    A hybrid Capsule-ConvKAN model reports 91.21% accuracy on histopathological image classification, outperforming CNN, CapsNet, and ConvKAN baselines on a single dataset.

  11. KANs for Computer Vision: An Experimental Study

    cs.CV 2024-11 conditional novelty 2.0 of 10

    On MNIST, CIFAR-10, and Fashion-MNIST, KANs match MLP accuracy while using significantly more parameters and showing higher sensitivity to grid and order settings.

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