[nickhuh]

So I'm not an expert in the mathematics they're using specifically, but my high level understanding is that convolutional neural nets are able to extract features because they satisfy certain invariance properties. For example, a face is still a face even if it's shifted to the right, made a little smaller, or tilted a bit. Therefore, the feature of faces should be invariant to these transformations. This paper develops the mathematical framework to better help understand when such invariance properties pop up in a wider class of deep neural net architectures, and thereby when these architectures can identify broader classes of features.