Towards Understanding the Invertibility of Convolutional Neural Networks

05/24/2017
by   Anna C. Gilbert, et al.
0

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.

READ FULL TEXT

page 7

page 14

research
08/29/2018

Theoretical Linear Convergence of Unfolded ISTA and its Practical Weights and Thresholds

In recent years, unfolding iterative algorithms as neural networks has b...
research
04/18/2023

SO(2) and O(2) Equivariance in Image Recognition with Bessel-Convolutional Neural Networks

For many years, it has been shown how much exploiting equivariances can ...
research
05/07/2020

Compressive sensing with un-trained neural networks: Gradient descent finds the smoothest approximation

Un-trained convolutional neural networks have emerged as highly successf...
research
06/06/2019

Covariance in Physics and Convolutional Neural Networks

In this proceeding we give an overview of the idea of covariance (or equ...
research
09/06/2019

Automatic Weight Estimation of Harvested Fish from Images

Approximately 2,500 weights and corresponding images of harvested Lates ...
research
01/22/2019

Understanding Geometry of Encoder-Decoder CNNs

Encoder-decoder networks using convolutional neural network (CNN) archit...
research
04/19/2023

Generalization and Estimation Error Bounds for Model-based Neural Networks

Model-based neural networks provide unparalleled performance for various...

Please sign up or login with your details

Forgot password? Click here to reset