# Convolutional Kolmogorov-Arnold Networks

arXiv: https://arxiv.org/abs/2406.13155 · HTML: https://mlsanity.com/paper/2406.13155/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 9 references that are in the map.
- First posted on arXiv 19 Jun 2024.

## Builds on (most cited first, 3 of 3)

- [Predicting Parameters in Deep Learning](https://mlsanity.com/paper/1306.0543/) (2013)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Kolmogorov-Arnold Networks are Radial Basis Function Networks](https://mlsanity.com/paper/2405.06721/) (2024)

## Built on by (most cited first, 30 of 77)

- [KAN 2.0: Kolmogorov-Arnold Networks Meet Science](https://mlsanity.com/paper/2408.10205/) (2024)
- [A Survey on Kolmogorov-Arnold Network](https://mlsanity.com/paper/2411.06078/) (2024)
- [Kolmogorov-Arnold Transformer](https://mlsanity.com/paper/2409.10594/) (2024)
- [KAGNNs: Kolmogorov-Arnold Networks meet Graph Learning](https://mlsanity.com/paper/2406.18380/) (2024)
- [On the expressiveness and spectral bias of KANs](https://mlsanity.com/paper/2410.01803/) (2024)
- [Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems](https://mlsanity.com/paper/2406.19662/) (2024)
- [TimeKAN: KAN-based Frequency Decomposition Learning Architecture for Long-term Time Series Forecasting](https://mlsanity.com/paper/2502.06910/) (2025)
- [Exploring the Limitations of Kolmogorov-Arnold Networks in Classification: Insights to Software Training and Hardware Implementation](https://mlsanity.com/paper/2407.17790/) (2024)
- [Reduced Effectiveness of Kolmogorov-Arnold Networks on Functions with Noise](https://mlsanity.com/paper/2407.14882/) (2024)
- [PointNet with KAN versus PointNet with MLP for 3D Classification and Segmentation of Point Sets](https://mlsanity.com/paper/2410.10084/) (2024)
- [DropKAN: Regularizing KANs by masking post-activations](https://mlsanity.com/paper/2407.13044/) (2024)
- [F-KANs: Federated Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2407.20100/) (2024)
- [KANEL'E: Kolmogorov-Arnold Networks for Efficient LUT-based Evaluation](https://mlsanity.com/paper/2512.12850/) (2025)
- [LeanKAN: A Parameter-Lean Kolmogorov-Arnold Network Layer with Improved Memory Efficiency and Convergence Behavior](https://mlsanity.com/paper/2502.17844/) (2025)
- [Generalization Bounds and Model Complexity for Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.08026/) (2024)
- [Evolving Medical Imaging Agents via Experience-driven Self-skill Discovery](https://mlsanity.com/paper/2603.05860/) (2026)
- [Multifidelity Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2410.14764/) (2024)
- [MedKAN: An Advanced Kolmogorov-Arnold Network for Medical Image Classification](https://mlsanity.com/paper/2502.18416/) (2025)
- [Bayesian Kolmogorov Arnold Networks (Bayesian_KANs): A Probabilistic Approach to Enhance Accuracy and Interpretability](https://mlsanity.com/paper/2408.02706/) (2024)
- [Kolmogorov-Arnold Network Autoencoders](https://mlsanity.com/paper/2410.02077/) (2024)
- [KAN versus MLP on Irregular or Noisy Functions](https://mlsanity.com/paper/2408.07906/) (2024)
- [A preliminary study on continual learning in computer vision using Kolmogorov-Arnold Networks](https://mlsanity.com/paper/2409.13550/) (2024)
- [TransUKAN:Computing-Efficient Hybrid KAN-Transformer for Enhanced Medical Image Segmentation](https://mlsanity.com/paper/2409.14676/) (2024)
- [Free-Knots Kolmogorov-Arnold Network: On the Analysis of Spline Knots and Advancing Stability](https://mlsanity.com/paper/2501.09283/) (2025)
- [HyperKAN: Kolmogorov-Arnold Networks make Hyperspectral Image Classificators Smarter](https://mlsanity.com/paper/2407.05278/) (2024)
- [Rethinking the Function of Neurons in KANs](https://mlsanity.com/paper/2407.20667/) (2024)
- [HaSPeR: An Image Repository for Hand Shadow Puppet Recognition](https://mlsanity.com/paper/2408.10360/) (2024)
- [LAR-IQA: A Lightweight, Accurate, and Robust No-Reference Image Quality Assessment Model](https://mlsanity.com/paper/2408.17057/) (2024)
- [GaRField++: Reinforced Gaussian Radiance Fields for Large-Scale 3D Scene Reconstruction](https://mlsanity.com/paper/2409.12774/) (2024)
- [Residual Kolmogorov-Arnold Network for Enhanced Deep Learning](https://mlsanity.com/paper/2410.05500/) (2024)

## Abstract (arXiv)

In this paper, we present Convolutional Kolmogorov-Arnold Networks, a novel architecture that integrates the learnable spline-based activation functions of Kolmogorov-Arnold Networks (KANs) into convolutional layers. By replacing traditional fixed-weight kernels with learnable non-linear functions, Convolutional KANs offer a significant improvement in parameter efficiency and expressive power over standard Convolutional Neural Networks (CNNs). We empirically evaluate Convolutional KANs on the Fashion-MNIST dataset, demonstrating competitive accuracy with up to 50% fewer parameters compared to baseline classic convolutions. This suggests that the KAN Convolution can effectively capture complex spatial relationships with fewer resources, offering a promising alternative for parameter-efficient deep learning models.