I was watching some videos online about convolutional networks, and the speaker was discussing the concept of running a filter over an image.  He said, and it is also shown in the image below, that Depth = Semantic representation.This sounds nice, but I'm not sure exactly what is so special about reducing the spatial dimension of the image in favor of increased depth? What makes depth more important than any other dimension? A dimension is just dimension, right?  EDIT: I have a hunch that the reason is going to have something to do with translation independence...
Why does Depth = Semantic representation in convolutional neural networks?
neural network;dimensionality reduction;convnet