In this paper, we study deep diagonal circulant neural networks, that is deep neural networks in which weight matrices are the product of diagonal and circulant ones.
 Besides making a theoretical analysis of their expressivity, we introduced principled techniques for training these models: we devise an initialization scheme and proposed a smart use of non-linearity functions in order to train deep diagonal circulant networks. 
 Furthermore, we show that these networks outperform recently introduced deep networks with other types of structured layers. We conduct a thorough experimental study to compare the performance of deep diagonal circulant networks with state of the art models based on structured matrices and with dense models. We show that our models achieve better accuracy than other structured approaches while required 2x fewer weights as the next best approach. Finally we train deep diagonal circulant networks to build a compact and accurate models on a real world video classification dataset with over 3.8 million training examples.
We train deep neural networks based on diagonal and circulant matrices, and show that this type of networks are both compact and accurate on real world applications. The authors provide a theoretical analysis of the expressive power of diagonal circulant neural networks (DCNN) and propose an initialization scheme for deep DCNNs.