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

Abstract

In this paper, we propose a novel layer based on fast Walsh-Hadamard transform (WHT) and smooth-thresholding to replace 1 × 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 2×2 Hadamard transform to implement 3 × 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 <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> m). As a result, it is computationally more efficient than the 1 × 1 convolution layer. The fast Walsh-Hadamard layer processes a tensor in ℝ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10×32×32×1024</sup> about 2 times faster than 1 × 1 convolution layer on NVIDIA Jetson Nano computer board.