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Towards Understanding the Invertibility of Convolutional Neural Networks
Anna C. Gilbert, Yi Zhang, Kibok Lee, Yuting Zhang, Honglak Lee
Nov 04, 2016 (modified: Jan 16, 2017)ICLR 2017 conference submissionreaders: everyone
Abstract: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:Deep learning, Theory
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