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In recent years, hyper‐complex deep networks (such as complex‐valued and quaternion‐valued neural networks – QVNNs) have received a renewed interest in the literature. They find applications in multiple fields, ranging from image reconstruction to 3D audio processing. Similar to their real‐valued counterparts, quaternion neural networks require custom regularisation strategies to avoid overfitting. In addition, for many real‐world applications and embedded implementations, there is the need of designing sufficiently compact networks, with few weights and neurons. However, the problem of regularising and/or sparsifying QVNNs has not been properly addressed in the literature as of now. In this study, the authors show how to address both problems by designing targeted regularisation strategies, which can minimise the number of connections and neurons of the network during training. To this end, they investigate two extensions of    ℓ  1    and structured regularisations to the quaternion domain. In the authors’ experimental evaluation, they show that these tailored strategies significantly outperform classical (real‐valued) regularisation approaches, resulting in small networks especially suitable for low‐power and real‐time applications.

Compressing deep‐quaternion neural networks with targeted regularisation