Dynamic Universal Approximation Theory: The Basic Theory for Deep Learning-Based Computer Vision Models

TL;DR

This paper develops a theoretical foundation for deep learning models in computer vision using the Universal Approximation Theorem, addressing fundamental questions about CNNs and Transformers' design and generalization.

Contribution

It introduces a universal approximation framework for CNNs and Transformers, providing new insights into their effectiveness and design principles in computer vision.

Findings

Theoretical explanation for why deep CNNs are effective.

Insights into the generalization ability of CNNs and Transformers.

Understanding the success of residual networks and pruning techniques.

Abstract

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.