Towards Understanding the Invertibility of Convolutional Neural Networks
This work provides a theoretical explanation for a phenomenon observed in CNNs, which could benefit researchers in machine learning and signal processing, though it appears incremental as it builds on existing empirical observations and models.
The authors tackled the problem of understanding the approximate invertibility of Convolutional Neural Networks (CNNs) by developing a theoretical model linking CNNs with random weights to model-based compressive sensing, and they demonstrated reasonable reconstruction results on real images.
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.