  Hypercomplex neural networks are gaining increasing interest in the deep
learning community. The attention directed towards hypercomplex models
originates from several aspects, spanning from purely theoretical and
mathematical characteristics to the practical advantage of lightweight models
over conventional networks, and their unique properties to capture both global
and local relations. In particular, a branch of these architectures,
parameterized hypercomplex neural networks (PHNNs), has also gained popularity
due to their versatility across a multitude of application domains.
Nonetheless, only few attempts have been made to explain or interpret their
intricacies. In this paper, we propose inherently interpretable PHNNs and
quaternion-like networks, thus without the need for any post-hoc method. To
achieve this, we define a type of cosine-similarity transform within the
parameterized hypercomplex domain. This PHB-cos transform induces weight
alignment with relevant input features and allows to reduce the model into a
single linear transform, rendering it directly interpretable. In this work, we
start to draw insights into how this unique branch of neural models operates.
We observe that hypercomplex networks exhibit a tendency to concentrate on the
shape around the main object of interest, in addition to the shape of the
object itself. We provide a thorough analysis, studying single neurons of
different layers and comparing them against how real-valued networks learn. The
code of the paper is available at https://github.com/ispamm/HxAI.
