Let's assume I want to teach a CNN some physics. Starting with a U-Net, I input images A
and B
as separate channels. I know that my target (produced by a very slow Monte-Carlo code) represents a signal such as f(g(A) * h(B))
, where f
, g
and h
are fairly "convolutional" operations -- meaning, involving mostly blurring and rescaling operations.
I feel safe to state that this problem would not be too difficult for the case of f(g(A) + h(B))
-- but what about f(g(A) * h(B))
? Can I expect a basic CNN such as the U-Net to be able to represent the *
(multiplication) operation?
Or should I expect to be forced to include a Multiply
layer in my network, somewhere where I expect that the part before can learn the g
and h
parts, and the part after can learn the f
part?