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Can KAN Work? Exploring the Potential of Kolmogorov-Arnold Networks in Computer Vision

Yueyang Cang, Yu hang liu, Li Shi

TL;DR

This study analyzes the potential of KAN in computer vision tasks, evaluating the performance of KAN and its convolutional variants in image classification and semantic segmentation and proposes a smoothness regularization method and introduces a Segment Deactivation technique.

Abstract

Kolmogorov-Arnold Networks(KANs), as a theoretically efficient neural network architecture, have garnered attention for their potential in capturing complex patterns. However, their application in computer vision remains relatively unexplored. This study first analyzes the potential of KAN in computer vision tasks, evaluating the performance of KAN and its convolutional variants in image classification and semantic segmentation. The focus is placed on examining their characteristics across varying data scales and noise levels. Results indicate that while KAN exhibits stronger fitting capabilities, it is highly sensitive to noise, limiting its robustness. To address this challenge, we propose a smoothness regularization method and introduce a Segment Deactivation technique. Both approaches enhance KAN's stability and generalization, demonstrating its potential in handling complex visual data tasks.

Can KAN Work? Exploring the Potential of Kolmogorov-Arnold Networks in Computer Vision

TL;DR

This study analyzes the potential of KAN in computer vision tasks, evaluating the performance of KAN and its convolutional variants in image classification and semantic segmentation and proposes a smoothness regularization method and introduces a Segment Deactivation technique.

Abstract

Kolmogorov-Arnold Networks(KANs), as a theoretically efficient neural network architecture, have garnered attention for their potential in capturing complex patterns. However, their application in computer vision remains relatively unexplored. This study first analyzes the potential of KAN in computer vision tasks, evaluating the performance of KAN and its convolutional variants in image classification and semantic segmentation. The focus is placed on examining their characteristics across varying data scales and noise levels. Results indicate that while KAN exhibits stronger fitting capabilities, it is highly sensitive to noise, limiting its robustness. To address this challenge, we propose a smoothness regularization method and introduce a Segment Deactivation technique. Both approaches enhance KAN's stability and generalization, demonstrating its potential in handling complex visual data tasks.

Paper Structure

This paper contains 13 sections, 4 equations, 2 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Related Work
  3. Method
  4. Kolmogorov-Arnold Networks (KAN)
  5. Convolutional KAN (CKAN)
  6. The Potential of KAN in Computer Vision
  7. Experiments
  8. Experiment 0: Preliminary Evaluation of KAN and CKAN on Core Vision Tasks
  9. Experiment 1: Effect of Dataset Size on KAN Performance
  10. Experiment 2:
  11. Experiment 3: Impact of Regularization on the Generalization of KAN and CKAN
  12. Experiment 4: Enhanced Regularization and Segment Deactivation for Improved KAN Generalization
  13. Conclusions

Figures (2)

  • Figure 1: Illustration of KAN’s Potential in Edge Detection. This figure presents an example comparing the edge detection capabilities of KAN and a traditional MLP. The MLP successfully detects the left edge pattern but struggles with the right edge, while KAN accurately identifies both patterns due to its nonlinear fitting capacity.
  • Figure 2: Illustration of Segment Deactivation Technique. This figure demonstrates the simplification process where the entire spline function between its start and end points is replaced with a linear connection (shown in red) with a certain probability $p$. This technique reduces complexity in noisy segments, enhancing generalization.