Towards Understanding the Invertibility of Convolutional Neural Networks
  Several recent works have empirically observed that Convolutional Neural Nets
(CNNs) are (approximately) invertible. To understand this approximate
invertibility phenomenon and how to leverage it more effectively, we focus on a
theoretical explanation and develop a mathematical model of sparse signal
recovery that is consistent with CNNs with random weights. We give an exact
connection to a particular model of model-based compressive sensing (and its
recovery algorithms) and random-weight CNNs. We show empirically that several
learned networks are consistent with our mathematical analysis and then
demonstrate that with such a simple theoretical framework, we can obtain
reasonable re- construction results on real images. We also discuss gaps
between our model assumptions and the CNN trained for classification in
practical scenarios.
