Cascaded Subpatch Networks for Effective CNNs
Conventional convolutional neural networks use either a linear or a nonlinear filter to extract features from an image patch (region) of spatial size <inline-formula> <tex-math notation="LaTeX">$ H\times W $ </tex-math></inline-formula> (typically, <inline-formula> <tex-math notation="LaTeX">$ H $ </tex-math></inline-formula> is small and is equal to <inline-formula> <tex-math notation="LaTeX">$ W$ </tex-math></inline-formula>, e.g., <inline-formula> <tex-math notation="LaTeX">$ H $ </tex-math></inline-formula> is 5 or 7). Generally, the size of the filter is equal to the size <inline-formula> <tex-math notation="LaTeX">$ H\times W $ </tex-math></inline-formula> of the input patch. We argue that the representational ability of equal-size strategy is not strong enough. To overcome the drawback, we propose to use subpatch filter whose spatial size <inline-formula> <tex-math notation="LaTeX">$ h\times w $ </tex-math></inline-formula> is smaller than <inline-formula> <tex-math notation="LaTeX">$ H\times W $ </tex-math></inline-formula>. The proposed subpatch filter consists of two subsequent filters. The first one is a linear filter of spatial size <inline-formula> <tex-math notation="LaTeX">$ h\times w $ </tex-math></inline-formula> and is aimed at extracting features from spatial domain. The second one is of spatial size <inline-formula> <tex-math notation="LaTeX">$ 1\times 1 $ </tex-math></inline-formula> 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 the cascaded subpatch network (CSNet). The feature layer generated by CSNet is called the <italic>csconv</italic> layer. For the whole input image, we construct a deep neural network by stacking a sequence of <italic>csconv</italic> layers. Experimental results on five benchmark data sets demonstrate the effectiveness and compactness of the proposed CSNet. For example, our CSNet reaches a test error of 5.68% on the CIFAR10 data set without model averaging. To the best of our knowledge, this is the best result ever obtained on the CIFAR10 data set.