KAConvNet: Kolmogorov-Arnold Convolutional Networks for Vision Recognition

2026-04-25

AI Summary

This work proposes KAConvNet, a novel architecture that deeply integrates convolutional operations with Kolmogorov–Arnold Networks (KANs) while preserving the theoretical foundations of the Kolmogorov–Arnold representation theorem. In contrast to existing approaches that naively replace activation functions and rely on computationally inefficient, overfitting-prone B-splines, KAConvNet introduces learnable edge-wise activation mechanisms, dedicated convolutional layers, and a lightweight design to eliminate dependence on B-splines. This integration enhances both model interpretability and computational efficiency. Extensive experiments demonstrate that KAConvNet significantly outperforms prior fusion methods and achieves performance on par with state-of-the-art CNNs and Vision Transformers across multiple visual recognition tasks.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

The Convolutional Neural Networks (CNNs) have been the dominant and effective approach for general computer vision tasks. Recently, Kolmogorov-Arnold neural networks (KANs), based on the Kolmogorov-Arnold representation theorem, have shown potential to replace Multi-Layer Perceptrons (MLPs) in deep learning. KANs, which use learnable nonlinear activations on edges and simple summation on nodes, offer fewer parameters and greater explainability compared to MLPs. However, there has been limited exploration of integrating the Kolmogorov-Arnold representation theorem with convolutional methods for computer vision tasks. Existing attempts have merely replaced learnable activation functions with weights, undermining KANs' theoretical foundation and limiting their potential effectiveness. Additionally, the B-spline curves used in KANs suffer from computational inefficiency and a tendency to overfit. In this paper, we propose a novel Kolmogorov-Arnold Convolutional Layer that deeply integrates the Kolmogorov-Arnold representation theorem with convolution. This layer provides stronger method interpretability because it is based on established mathematical theorems and its design has theoretical alignment. Building on the Kolmogorov-Arnold Convolutional Layer, we design an efficient network architecture called KAConvNet, which outperforms existing methods combining KAN and convolution, and achieves competitive performance compared to mainstream ViTs and CNNs. We believe that our work offers valuable insight into the field of artificial intelligence and will inspire the development of more innovative CNNs in the 2020s. The code is publicly available at https://github.com/UnicomAI/KAConvNet.

Problem

• Kolmogorov-Arnold representation
• convolutional neural networks
• KANs
• computer vision
• interpretability

Innovation

• Kolmogorov-Arnold representation
• convolutional neural networks
• interpretable deep learning
• KAConvNet
• learnable activation functions