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

arXiv: https://arxiv.org/abs/2407.17480 · HTML: https://mlsanity.com/paper/2407.17480/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 30 of its 42 references that are in the map.
- First posted on arXiv 2 Jul 2024.

## Builds on (most cited first, 30 of 30)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [An Image is Worth 16x16 Words: Transformers for Image Recognition at Scale](https://mlsanity.com/paper/2010.11929/) (2020)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Swin Transformer: Hierarchical Vision Transformer using Shifted Windows](https://mlsanity.com/paper/2103.14030/) (2021)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- [Going Deeper with Convolutions](https://mlsanity.com/paper/1409.4842/) (2014)
- [Aggregated Residual Transformations for Deep Neural Networks](https://mlsanity.com/paper/1611.05431/) (2016)
- [Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2001.05566/) (2020)
- [DETRs Beat YOLOs on Real-time Object Detection](https://mlsanity.com/paper/2304.08069/) (2023)
- [EDVR: Video Restoration with Enhanced Deformable Convolutional Networks](https://mlsanity.com/paper/1905.02716/) (2019)
- [Res2Net: A New Multi-scale Backbone Architecture](https://mlsanity.com/paper/1904.01169/) (2019)
- [Video-to-Video Synthesis](https://mlsanity.com/paper/1808.06601/) (2018)
- [Residual Attention Network for Image Classification](https://mlsanity.com/paper/1704.06904/) (2017)
- [How Do Vision Transformers Work?](https://mlsanity.com/paper/2202.06709/) (2022)
- [A Fourier Perspective on Model Robustness in Computer Vision](https://mlsanity.com/paper/1906.08988/) (2019)
- [Few-shot Video-to-Video Synthesis](https://mlsanity.com/paper/1910.12713/) (2019)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Training behavior of deep neural network in frequency domain](https://mlsanity.com/paper/1807.01251/) (2018)
- [Medical Image Segmentation Using Deep Learning: A Survey](https://mlsanity.com/paper/2009.13120/) (2020)
- [RepViT: Revisiting Mobile CNN From ViT Perspective](https://mlsanity.com/paper/2307.09283/) (2023)
- [Improving Vision Transformers by Revisiting High-frequency Components](https://mlsanity.com/paper/2204.00993/) (2022)
- [TransNeXt: Robust Foveal Visual Perception for Vision Transformers](https://mlsanity.com/paper/2311.17132/) (2023)
- [Selective Convolutional Descriptor Aggregation for Fine-Grained Image Retrieval](https://mlsanity.com/paper/1604.04994/) (2016)
- [Salience DETR: Enhancing Detection Transformer with Hierarchical Salience Filtering Refinement](https://mlsanity.com/paper/2403.16131/) (2024)
- [Learning Correlation Structures for Vision Transformers](https://mlsanity.com/paper/2404.03924/) (2024)
- [On the rates of convergence for learning with convolutional neural networks](https://mlsanity.com/paper/2403.16459/) (2024)
- [Are Large Kernels Better Teachers than Transformers for ConvNets?](https://mlsanity.com/paper/2305.19412/) (2023)
- [On the Universal Approximation Property of Deep Fully Convolutional Neural Networks](https://mlsanity.com/paper/2211.14047/) (2022)

## Abstract (arXiv)

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.