Fixed-point algorithms for inverse of residual rectifier neural networks

Ruhua Wang; Senjian An; Wanquan Liu; Ling Li

doi:10.3934/mfc.2020024

Article Contents

2021, Volume 4, Issue 1: 31-44. Doi: 10.3934/mfc.2020024

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Fixed-point algorithms for inverse of residual rectifier neural networks

School of Electrical Engineering, Computing and Mathematical Sciences, Curtin University, Bentley, WA, Australia

^* Corresponding author: Ruhua Wang
^* Corresponding author: Ruhua Wang

Received: July 31, 2020

Revised: August 31, 2020

Early access: October 2020

Published: February 2021

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Abstract

A deep neural network with invertible hidden layers has a nice property of preserving all the information in the feature learning stage. In this paper, we analyse the hidden layers of residual rectifier neural networks, and investigate conditions for invertibility under which the hidden layers are invertible. A new fixed-point algorithm is developed to invert the hidden layers of residual networks. The proposed inverse algorithms are capable of inverting some residual networks which cannot be inverted by existing inverting algorithms. Furthermore, a special residual rectifier network is designed and trained on MNIST so that it can achieve comparable performance with the state-of-art performance while its hidden layers are invertible.

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Mathematics Subject Classification: Primary: 68T07.

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Figure 1. The proposed residual network architecture

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Figure 2. Inverse of the rectifier linear transform: Invertible percentage of 500 cases changes along with $ \gamma $ when the dimension of $ \mathbf{x} $ is 10

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Figure 3. Inverse of the residual unit with the fully-connected layer: Invertible percentage of 500 cases changes along with $ \gamma $ when the dimension of $ \mathbf{x} $ is 10

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Figure 4. Comparison of recovered images to original digit images. The 1st row illustrates the original images, whereas the 2nd and 3rd rows show the recovered images from the proposed fixed-point method and the existing fixed-point method, respectively

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Figure 5. Relative error rates (%) of the recovered images. One hundred samples per each class, in total 1000 samples, were chosen and recovered

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