Department of Mathematics

Applied Mathematics

  •  Ding-Xua Zhou, City University of Hong Kong
  •  Theory of Deep Convolutional Neural Networks; zoom link @ https://sites.google.com/view/minds-seminar/home
  •  12/03/2020
  •  3:30 AM - 4:30 AM
  •  Online (virtual meeting) (Virtual Meeting Link)
  •  Olga Turanova (turanova@msu.edu)

(Note the unusual time: 4:30pm Shanghai, 10:30am Paris.) Deep learning has been widely applied and brought breakthroughs in speech recognition, computer vision, natural language processing, and many other domains. The involved deep neural network architectures and computational issues have been well studied in machine learning. But there lacks a theoretical foundation for understanding the modelling, approximation or generalization ability of deep learning models with network architectures. Here we are interested in deep convolutional neural networks (CNNs) with convolutional structures. The convolutional architecture gives essential differences between deep CNNs and fully-connected neural networks, and the classical approximation theory for fully-connected networks developed around 30 years ago does not apply. This talk describes an approximation theory of deep CNNs associated with the rectified linear unit (ReLU) activation function. In particular, we prove the universality of deep CNNs, meaning that a deep CNN can be used to approximate any continuous function to an arbitrary accuracy when the depth of the neural network is large enough. We also show that deep CNNs perform at least as well as fully-connected neural networks for approximating general functions, and much better for approximating radial functions in high dimensions.

 

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