I have a physics/mathematics background and am learning about NNs.
The 'pooling' operation applied to layers of CNNs seems to me to very closely resemble 'blocking' (eg decimation or 'majority rule') in Statistical Physics (eg the Ising model on a lattice).
There we impose it analytically to relate the parameters of the finer- and coarser-resolution theories, and obtain a renormalisation group equation that roughly says that we are indifferent to fine (short-wavelength) details and care about larger-scale behaviour.
In CNNs we seem to impose it numerically for a fixed number of iterations (layers) after a predefined convolution with a filter whose weights we will adapt through training.
My question is: is there any analogy between these two operations, besides the obvious one? Is it possible for CNN pooling to lead to RG-type flow, perhaps representing microscale (resolution)-invariance and macroscale (angular distance)-invariance? [my made-up terminology, probably poor].