  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.
