# Towards Understanding the Invertibility of Convolutional Neural Networks

arXiv: https://arxiv.org/abs/1705.08664 · HTML: https://mlsanity.com/paper/1705.08664/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 May 2017.

## Built on by (most cited first, 10 of 10)

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## Abstract (arXiv)

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.