Understanding Geometry of Encoder-Decoder CNNs

Understand

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.