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Convolutional networks are large linear systems divided into layers andconnected by non-linear units. These units are the "articulations" that allowthe network to adapt to the input. To understand how a network manages to solvea problem we must look at the articulated decisions in entirety. If we couldcapture the actions of non-linear units for a particular input, we would beable to replay the whole system back and forth as if it was always linear. Itwould also reveal the actions of non-linearities because the resulting linearsystem, a Linear Interpreter, depends on the input image. We introduce ahooking layer, called a LinearScope, which allows us to run the network and thelinear interpreter in parallel. Its implementation is simple, flexible andefficient. From here we can make many curious inquiries: how do these linearsystems look like? When the rows and columns of the transformation matrix areimages, how do they look like? What type of basis do these lineartransformations rely on? The answers depend on the problems presented, throughwhich we take a tour to some popular architectures used for classification,super-resolution (SR) and image-to-image translation (I2I). For classificationwe observe that popular networks use a pixel-wise vote per class strategy andheavily rely on bias parameters. For SR and I2I we find that CNNs usewavelet-type basis similar to the human visual system. For I2I we revealcopy-move and template-creation strategies to generate outputs.

A Tour of Convolutional Networks Guided by Linear Interpreters