Towards Understanding the Invertibility of Convolutional Neural Networks

Towards Understanding the Invertibility of Convolutional Neural Networks

Anna Gilbert, Yi Zhang, Kibok Lee, Yuting Zhang, Honglak Lee

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 1703-1710. https://doi.org/10.24963/ijcai.2017/236

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 reconstruction results on real images. We also discuss gaps between our model assumptions and the CNN trained for classification in practical scenarios.
Keywords:
Machine Learning: Neural Networks
Machine Learning: Deep Learning