Convolutional Arithmetic Guide - [Deep Learning Paper]

Dumoulin and Visin (2016), researchers at University of Montreal and Polytechnic University of Milan, published a paper in Arvix explaining the arithmetic of deep convolutional neural networks.

I learned about this paper in a deep learning course that I'm auditing at Udacity. Their aim with the paper is twofold:

"1. Explain the relationship between convolutional layers and transposed convolutional
layers.

2. Provide an intuitive understanding of the relationship between input shape,
kernel shape, zero padding, strides and output shape in convolutional,
pooling and transposed convolutional layers." [source]

Convolutional neural networks are heavily used in deep learning projects with image dataset and two of the core concepts of DNN are padding and unit strides. This papers goes into the arithmetic of such, discussing all combinations:

no zero padding, unit strides
zero padding, unit strides
no zero padding, non-unit strides
zero padding, non-unit strides

They also go into the details of simple pooling and transposed pooling convolutional arithmetic:

"Pooling operations reduce the size of feature maps by using some function to summarize subregions, such as taking
the average or the maximum value." [source]

It would be relatively hard, even for researchers and practitioners, to understand these concepts without the aided graphics, which I would say is a strong point of the paper and its reason of being cited by further research in the field.

Spoiler alert: This paper is heavy on math and unless you're really into the field or you want to achieve a 'deep' comprehension of deep convolutions (which is not necessarily required for practical purposes), I would say pass. But if you are (the geek), this is a very good read (take time to explore the papers cited in its bibliography as well):

Convolutional Arithmetic Guide - [Deep Learning Paper]

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Cristi Vlad Self-Experimenter and Author