  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.
