Dynamic Universal Approximation Theory: The Basic Theory for Deep Learning-Based Computer Vision Models
This work addresses theoretical gaps for researchers and practitioners in computer vision, but it appears incremental as it builds on existing UAT without introducing new methods or data.
The paper tackles the lack of theoretical foundation for deep learning models in computer vision by applying the Universal Approximation Theorem to convolution- and Transformer-based models, aiming to explain fundamental questions about their design and performance.
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.