  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.
