Year: 2019
Type: preprint
Abstract: Encoder-decoder networks using convolutional neural network (CNN) architecture have been extensively used in deep learning literatures thanks to its excellent performance for various inverse problems. However, it is still difficult to obtain coherent geometric view why such an architecture gives the desired performance. Inspired by recent theoretical understanding on generalizability, expressivity and optimization landscape of neural networks, as well as the theory of convolutional framelets, here we provide a unified theoretical framework that leads to a better understanding of geometry of encoder-decoder CNNs. Our unified mathematical framework shows that encoder-decoder CNN architecture is closely related to nonlinear basis representation using combinatorial convolution frames, whose expressibility increases exponentially with the network depth. We also demonstrate the importance of skipped connection in terms of expressibility, and optimization landscape.
Source: arXiv (Cornell University)
Authors: Ye, Jong Chul, Sung, Woon Kyoung
Institution: Korea Advanced Institute of Science and Technology
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
Funder: National Research Foundation
Award: G5282103969
OpenAlex ID: W2912265583