Nazmul Shahadat

Nazmul Shahadat, Anthony S. Maida

Recently, many deep networks have introduced hypercomplex and related calculations into their architectures. In regard to convolutional networks for classification, these enhancements have been applied to the convolution operations in the frontend to enhance accuracy and/or reduce the parameter requirements while maintaining accuracy. Although these enhancements have been applied to the convolutional frontend, it has not been studied whether adding hypercomplex calculations improves performance when applied to the densely connected backend. This paper studies ResNet architectures and incorporates parameterized hypercomplex multiplication (PHM) into the backend of residual, quaternion, and vectormap convolutional neural networks to assess the effect. We show that PHM does improve classification accuracy performance on several image datasets, including small, low-resolution CIFAR 10/100 and large high-resolution ImageNet and ASL, and can achieve state-of-the-art accuracy for hypercomplex networks.

Nazmul Shahadat, Anthony S. Maida

While convolutional neural networks (CNNs) demonstrate outstanding performance on computer vision tasks, their computational costs remain high. Several techniques are used to reduce these costs, like reducing channel count, and using separable and depthwise separable convolutions. This paper reduces computational costs by introducing a novel architecture, axial CNNs, which replaces spatial 2D convolution operations with two consecutive depthwise separable 1D operations. The axial CNNs are predicated on the assumption that the dataset supports approximately separable convolution operations with little or no loss of training accuracy. Deep axial separable CNNs still suffer from gradient problems when training deep networks. We modify the construction of axial separable CNNs with residual connections to improve the performance of deep axial architectures and introduce our final novel architecture namely residual axial networks (RANs). Extensive benchmark evaluation shows that RANs achieve at least 1% higher performance with about 77%, 86%, 75%, and 34% fewer parameters and about 75%, 80%, 67%, and 26% fewer flops than ResNets, wide ResNets, MobileNets, and SqueezeNexts on CIFAR benchmarks, SVHN, and Tiny ImageNet image classification datasets. Moreover, our proposed RANs improve deep recursive residual networks performance with 94% fewer parameters on the image super-resolution dataset.

Nazmul Shahadat, Anthony S. Maida

Over the past decade, deep hypercomplex-inspired networks have enhanced feature extraction for image classification by enabling weight sharing across input channels. Recent works make it possible to improve representational capabilities by using hypercomplex-inspired networks which consume high computational costs. This paper reduces this cost by factorizing a quaternion 2D convolutional module into two consecutive vectormap 1D convolutional modules. Also, we use 5D parameterized hypercomplex multiplication based fully connected layers. Incorporating both yields our proposed hypercomplex network, a novel architecture that can be assembled to construct deep axial-hypercomplex networks (DANs) for image classifications. We conduct experiments on CIFAR benchmarks, SVHN, and Tiny ImageNet datasets and achieve better performance with fewer trainable parameters and FLOPS. Our proposed model achieves almost 2% higher performance for CIFAR and SVHN datasets, and more than 3% for the ImageNet-Tiny dataset and takes six times fewer parameters than the real-valued ResNets. Also, it shows state-of-the-art performance on CIFAR benchmarks in hypercomplex space.

Nazmul Shahadat, Anthony S. Maida

In recent years, hypercomplex-inspired neural networks (HCNNs) have been used to improve deep learning architectures due to their ability to enable channel-based weight sharing, treat colors as a single entity, and improve representational coherence within the layers. The work described herein studies the effect of replacing existing layers in an Axial Attention network with their representationally coherent variants to assess the effect on image classification. We experiment with the stem of the network, the bottleneck layers, and the fully connected backend, by replacing them with representationally coherent variants. These various modifications lead to novel architectures which all yield improved accuracy performance on the ImageNet300k classification dataset. Our baseline networks for comparison were the original real-valued ResNet, the original quaternion-valued ResNet, and the Axial Attention ResNet. Since improvement was observed regardless of which part of the network was modified, there is a promise that this technique may be generally useful in improving classification accuracy for a large class of networks.