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Image Classification using Fuzzy Pooling in Convolutional Kolmogorov-Arnold Networks

Ayan Igali, Pakizar Shamoi

TL;DR

The paper addresses the need for interpretable yet accurate image classifiers by integrating a Kolmogorov-Arnold Network (KAN) head with a Type-1 Fuzzy Pooling layer into CNNs. KAN provides interpretable activations through spline-based univariate components, while the fuzzy pooling layer handles uncertainty in feature maps via fuzzification, fuzzy aggregation, and defuzzification, enabling a more transparent and potentially memory-efficient model. The method is evaluated on CIFAR-10, MNIST, and FashionMNIST using LeNet as the backbone and compared against MLP heads with standard pooling. Results show the proposed approach achieves comparable or higher accuracy (e.g., 67.06% on CIFAR-10, 98.91% on MNIST, 89.88% on FashionMNIST) and improves interpretability, suggesting practical benefits for interpretable AI; future work includes scaling to larger datasets and exploring alternative fuzzy formulations.

Abstract

Nowadays, deep learning models are increasingly required to be both interpretable and highly accurate. We present an approach that integrates Kolmogorov-Arnold Network (KAN) classification heads and Fuzzy Pooling into convolutional neural networks (CNNs). By utilizing the interpretability of KAN and the uncertainty handling capabilities of fuzzy logic, the integration shows potential for improved performance in image classification tasks. Our comparative analysis demonstrates that the modified CNN architecture with KAN and Fuzzy Pooling achieves comparable or higher accuracy than traditional models. The findings highlight the effectiveness of combining fuzzy logic and KAN to develop more interpretable and efficient deep learning models. Future work will aim to expand this approach across larger datasets.

Image Classification using Fuzzy Pooling in Convolutional Kolmogorov-Arnold Networks

TL;DR

The paper addresses the need for interpretable yet accurate image classifiers by integrating a Kolmogorov-Arnold Network (KAN) head with a Type-1 Fuzzy Pooling layer into CNNs. KAN provides interpretable activations through spline-based univariate components, while the fuzzy pooling layer handles uncertainty in feature maps via fuzzification, fuzzy aggregation, and defuzzification, enabling a more transparent and potentially memory-efficient model. The method is evaluated on CIFAR-10, MNIST, and FashionMNIST using LeNet as the backbone and compared against MLP heads with standard pooling. Results show the proposed approach achieves comparable or higher accuracy (e.g., 67.06% on CIFAR-10, 98.91% on MNIST, 89.88% on FashionMNIST) and improves interpretability, suggesting practical benefits for interpretable AI; future work includes scaling to larger datasets and exploring alternative fuzzy formulations.

Abstract

Nowadays, deep learning models are increasingly required to be both interpretable and highly accurate. We present an approach that integrates Kolmogorov-Arnold Network (KAN) classification heads and Fuzzy Pooling into convolutional neural networks (CNNs). By utilizing the interpretability of KAN and the uncertainty handling capabilities of fuzzy logic, the integration shows potential for improved performance in image classification tasks. Our comparative analysis demonstrates that the modified CNN architecture with KAN and Fuzzy Pooling achieves comparable or higher accuracy than traditional models. The findings highlight the effectiveness of combining fuzzy logic and KAN to develop more interpretable and efficient deep learning models. Future work will aim to expand this approach across larger datasets.
Paper Structure (17 sections, 17 equations, 4 figures, 2 tables, 1 algorithm)

This paper contains 17 sections, 17 equations, 4 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Works
  3. MLP architecture and their limitations.
  4. Kolmogorov-Arnold Networks
  5. Fuzzy Logic in Neural Networks/Deep Learning
  6. Methods
  7. Data
  8. CIFAR-10
  9. MNIST
  10. FashionMNIST
  11. KAN Layer
  12. Fuzzy Pooling Layer
  13. Proposed Approach
  14. Results
  15. Experiment Setup
  16. ...and 2 more sections

Figures (4)

  • Figure 1: Example of images from datasets.
  • Figure 2: Schematic representation of the proposed architecture
  • Figure 3: Accruacy of models over epochs with KAN on the last layer of CNN with different pooling layers.
  • Figure 4: The multiclass confusion matrix of testing results for models with KAN on the last layer using different pooling methods over CIFAR-10, MNIST, and FashionMNIST datasets.