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 in computer vision, medical imaging, etc. 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.
Jong Ye ("Department of Bio and Brain Engineering, KAIST, Korea")
woonkyoung Sung (KAIST)
Related Events (a corresponding poster, oral, or spotlight)
2019 Poster: Understanding Geometry of Encoder-Decoder CNNs »
Thu Jun 13th 01:30 -- 04:00 AM Room Pacific Ballroom