Universality of deep convolutional neural networks |
| |
Institution: | 1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2. Department of Mathematical Sciences, Middle Tennessee State University, Murfreesboro, TN 37132, USA;3. School of Data Science and Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong, China;1. Laboratory for Information and Inference Systems, École Polytechnique Fédérale de Lausanne, CH1015 Lausanne, Switzerland;2. INRIA, Sierra project-team, 75012 Paris, France;3. Département Informatique - École Normale Supérieure, Paris, France;4. University of Genova, 16146 Genova, Italy;5. LCSL, Massachusetts Institute of Technology, United States of America;6. Italian Institute of Technology, Italy;1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2. School of Data Science and Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong |
| |
Abstract: | Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, and many other domains. Deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the approximation or generalization ability of deep learning methods generated by the network architectures such as deep convolutional neural networks. Here we show that a deep convolutional neural network (CNN) is universal, meaning that it can be used to approximate any continuous function to an arbitrary accuracy when the depth of the neural network is large enough. This answers an open question in learning theory. Our quantitative estimate, given tightly in terms of the number of free parameters to be computed, verifies the efficiency of deep CNNs in dealing with large dimensional data. Our study also demonstrates the role of convolutions in deep CNNs. |
| |
Keywords: | Deep learning Convolutional neural network Universality Approximation theory |
本文献已被 ScienceDirect 等数据库收录! |
|