Mathematical Foundations of Deep Learning Architectures for Image Recognition

We present a rigorous mathematical analysis of fundamental properties underlying deep learning architectures, particularly convolutional neural networks used in image recognition. Our work establishes theoretical guarantees for approximation capabilities, stability under perturbations, and generalization bounds. By employing tools from functional analysis and statistical mechanics, we provide insights into why deep networks are so effective and offer guidelines for designing more robust and interpretable AI systems for computer vision applications in fields like autonomous driving and medical diagnostics.