> Perhaps what we want is a compromise between convnets and fcs though?
ie, either take an fc and make it a bit more sparse, and / or take an
fc and randomly link sets of weights together???

Maybe something like: each filter consists of eg 16 weights, which are
assigned randomly over all input-output pairs, such that each pair is
assign to exactly one of these shared weights, and then somehow:
- either just fix the sharing assignment, a little like how echo state
networks fix many of their weights, to keep the number of learnable
parameters down,
- or, have some way of optimizing the filters to learn the most useful
sharing assigments, eg:
   - randomly modify them, genetic-type algorithm, or
   - some kind of Dirichlet-process type sampling? :-P
   - something else?
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