Over the past decade, deep learning has revolutionized the field of computer vision, with convolutional neural network (CNN) models proving highly effective for image classification benchmarks. However, a fundamental theoretical question remains unanswered: why can they solve discrete image classification tasks involving feature extraction? This paper addresses this question by introducing a novel mathematical model for image classification based on feature extraction, capable of generating images resembling real-world datasets. We demonstrate that convolutional neural network classifiers can solve these image classification tasks with zero error. In our proof, we construct piecewise linear functions that detect the presence of features and show that they can be realized by a convolutional network.
Blogger's Review: This paper delves into the mathematical foundations of why CNNs excel at feature extraction, providing theoretical backing that enhances our understanding of deep learning's effectiveness in image classification. The use of piecewise linear functions is particularly insightful and lays the groundwork for building more efficient network architectures.