Compressing deep quaternion neural networks with targeted regularization

In recent years, hyper-complex deep networks (e.g., quaternion-based) have received increasing interest with applications ranging from image reconstruction to 3D audio processing. Similarly to their real-valued counterparts, quaternion neural networks might require custom regularization strategies to avoid overfitting. In addition, for many real-world applications and embedded implementations there is the need of designing sufficiently compact networks, with as few weights and units as possible. However, the problem of how to regularize and/or sparsify quaternion-valued networks has not been properly addressed in the literature as of now. In this paper we show how to address both problems by designing targeted regularization strategies, able to minimize the number of connections and neurons of the network during training. To this end, we investigate two extensions of $\ell_1$ and structured regularization to the quaternion domain. In our experimental evaluation, we show that these tailored strategies significantly outperform classical (real-valued) regularization strategies, resulting in small networks especially suitable for low-power and real-time applications.