  Computer vision (CV) is one of the most crucial fields in artificial
intelligence. In recent years, a variety of deep learning models based on
convolutional neural networks (CNNs) and Transformers have been designed to
tackle diverse problems in CV. These algorithms have found practical
applications in areas such as robotics and facial recognition. Despite the
increasing power of current CV models, several fundamental questions remain
unresolved: Why do CNNs require deep layers? What ensures the generalization
ability of CNNs? Why do residual-based networks outperform fully convolutional
networks like VGG? What is the fundamental difference between residual-based
CNNs and Transformer-based networks? Why can CNNs utilize LoRA and pruning
techniques? The root cause of these questions lies in the lack of a robust
theoretical foundation for deep learning models in CV. To address these
critical issues and techniques, we employ the Universal Approximation Theorem
(UAT) to provide a theoretical basis for convolution- and Transformer-based
models in CV. By doing so, we aim to elucidate these questions from a
theoretical perspective.
