Fast Walsh-Hadamard Transform and Smooth-Thresholding Based Binary Layers in Deep Neural Networks

• URL: http://arxiv.org/abs/2104.07085v1
• Date: Wed, 14 Apr 2021 19:23:36 GMT
• Title: Fast Walsh-Hadamard Transform and Smooth-Thresholding Based Binary Layers in Deep Neural Networks
• Authors: Hongyi Pan, Diaa Dabawi and Ahmet Enis Cetin
• Abstract summary: We propose a layer based on fast Walsh-Hadamard transform (WHT) and smooth-thresholding to replace $1times 1$ convolution layers in deep neural networks. Using these two types of layers, we replace the bottleneck layers in MobileNet-V2 to reduce the network's number of parameters with a slight loss in accuracy.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we propose a novel layer based on fast Walsh-Hadamard transform (WHT) and smooth-thresholding to replace $1\times 1$ convolution layers in deep neural networks. In the WHT domain, we denoise the transform domain coefficients using the new smooth-thresholding non-linearity, a smoothed version of the well-known soft-thresholding operator. We also introduce a family of multiplication-free operators from the basic 2$\times$2 Hadamard transform to implement $3\times 3$ depthwise separable convolution layers. Using these two types of layers, we replace the bottleneck layers in MobileNet-V2 to reduce the network's number of parameters with a slight loss in accuracy. For example, by replacing the final third bottleneck layers, we reduce the number of parameters from 2.270M to 947K. This reduces the accuracy from 95.21\% to 92.88\% on the CIFAR-10 dataset. Our approach significantly improves the speed of data processing. The fast Walsh-Hadamard transform has a computational complexity of $O(m\log_2 m)$. As a result, it is computationally more efficient than the $1\times1$ convolution layer. The fast Walsh-Hadamard layer processes a tensor in $\mathbb{R}^{10\times32\times32\times1024}$ about 2 times faster than $1\times1$ convolution layer on NVIDIA Jetson Nano computer board.

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