This is the 2nd post in our series on equivariant neural nets. It explains conventional CNNs from a representation theoretic viewpoint and clarifies the mutual relationship between equivariance and spatial weight sharing.ÔÇŽ ­čĹçTL;DR­čžÁ

CNNs are often understood as neural nets which share weights (kernel/bias/...) between different spatial locations. Depending on the application, it may be sensible to enforce a local connectivity, however, this is not strictly necessary for the network to be convolutional. [2/N]

Imagine to shift the input of a CNN layer. As the neural connectivity is the same everywhere, shifted patterns will evoke exactly the same responses, however, at correspondingly shifted locations. [3/N]