Equivalent Scanning Network of Unpadded CNNs

This letter presents a theory of scanning a signal with a sliding window, where the window's mapping function is built upon a convolutional neural network (CNN). When using a CNN as the sliding window, we show that the resultant feature maps are equivalent to the maps obtained by applying another CNN (called EQ-ScanNet) to the whole signal. The EQ-ScanNet can be established by reconfiguring the original CNN with dilated (i.e., sparse kernel) convolutions. We clarify that, this property is originated from the noble identity (i.e., the swapping equivalence of downsample and FIR filter), and extend the property to the generalized convolution that subsumes CNN's window-sliding operations. We further show that an unpadded CNN is a necessary condition for formulating the EQ-ScanNet.