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.

翻译：超复数神经网络在深度学习领域正引起越来越多的关注。对超复数模型的关注源于多个方面，涵盖从纯粹的理论数学特性到与传统网络相比轻量模型的实用优势，以及它们捕捉全局和局部关系的独特能力。特别是，这些架构中的一个分支，参数化超复数神经网络（PHNNs），因其在众多应用领域的通用性而广受欢迎。然而，仅有少数尝试旨在解释或阐明其复杂性。在本文中，我们提出了一种内在可解释的PHNNs和类四元数网络，从而无需任何事后解释方法。为实现这一目标，我们在参数化超复数域内定义了一种余弦相似度变换。这种PHB-cos变换能使权重与相关输入特征对齐，并允许将模型简化为单一线性变换，使其可直接解释。在本工作中，我们开始深入探索这一独特神经模型分支的运行机制。我们观察到，超复数网络除了关注目标物体的形状外，还倾向于关注主要目标周围的轮廓。我们提供了全面分析，研究了不同层的单个神经元，并将其与实值网络的学习方式进行了比较。本文代码可在https://github.com/ispamm/HxAI获取。