Convolution in Convolution for Network in Network
Network in network (NiN) is an effective instance and an important extension of deep convolutional neural network consisting of alternating convolutional layers and pooling layers. Instead of using a linear filter for convolution, NiN utilizes shallow multilayer perceptron (MLP), a nonlinear function, to replace the linear filter. Because of the powerfulness of MLP and  $ 1\times 1 $  convolutions in spatial domain, NiN has stronger ability of feature representation and hence results in better recognition performance. However, MLP itself consists of fully connected layers that give rise to a large number of parameters. In this paper, we propose to replace dense shallow MLP with sparse shallow MLP. One or more layers of the sparse shallow MLP are sparely connected in the channel dimension or channel–spatial domain. The proposed method is implemented by applying unshared convolution across the channel dimension and applying shared convolution across the spatial dimension in some computational layers. The proposed method is called convolution in convolution (CiC). The experimental results on the CIFAR10 data set, augmented CIFAR10 data set, and CIFAR100 data set demonstrate the effectiveness of the proposed CiC method.