Convolution in Convolution for Network in Network

Network in Netwrok (NiN) is an effective instance and an important extension of Convolutional Neural Network (CNN) 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 rate. However, MLP itself consists of fully connected layers which 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 CiC. Experimental results on the CIFAR10 dataset, augmented CIFAR10 dataset, and CIFAR100 dataset demonstrate the effectiveness of the proposed CiC method.

Cascaded Subpatch Networks for Effective CNNs

Conventional Convolutional Neural Networks (CNNs) use either a linear or non-linear filter to extract features from an image patch (region) of spatial size $ H\times W $ (Typically, $ H $ is small and is equal to $ W$, e.g., $ H $ is 5 or 7). Generally, the size of the filter is equal to the size $ H\times W $ of the input patch. We argue that the representation ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size $ h\times w $ is smaller than $ H\times W $. The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size $ h\times w $ and is aimed at extracting features from spatial domain. The second one is of spatial size $ 1\times 1 $ and is used for strengthening the connection between different input feature channels and for reducing the number of parameters. The subpatch filter convolves with the input patch and the resulting network is called a subpatch network. Taking the output of one subpatch network as input, we further repeat constructing subpatch networks until the output contains only one neuron in spatial domain. These subpatch networks form a new network called Cascaded Subpatch Network (CSNet). The feature layer generated by CSNet is called csconv layer. For the whole input image, we construct a deep neural network by stacking a sequence of csconv layers. Experimental results on four benchmark datasets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of $ 5.68\% $ on the CIFAR10 dataset without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 dataset.