Abstract
The field of deep learning has seen significant advancement in recent years.
However, much of the existing work has been focused on real-valued numbers.
Recent work has shown that a deep learning system using the complex numbers can
be deeper for a fixed parameter budget compared to its real-valued counterpart.
In this work, we explore the benefits of generalizing one step further into the
hyper-complex numbers, quaternions specifically, and provide the architecture
components needed to build deep quaternion networks. We go over quaternion
convolutions, present a quaternion weight initialization scheme, and present
algorithms for quaternion batch-normalization. These pieces are tested in a
classification model by end-to-end training on the CIFAR-10 and CIFAR-100 data
sets and a segmentation model by end-to-end training on the KITTI Road
Segmentation data set. The quaternion networks show improved convergence
compared to real-valued and complex-valued networks, especially on the
segmentation task.
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