Interesting analogy. I think of one of your examples the opposite, way, though!
When you examine a small subset of a network, that’s more like a quotient of the set of inputs—it’s some simple filter that can get applied to lots of stimuli. And when you make a broad, high-level model of a network, that’s like a subset on inputs—the subset is the domain of validity of your high-level model, because of course such models only work within a domain of validity.
Interesting analogy. I think of one of your examples the opposite, way, though!
When you examine a small subset of a network, that’s more like a quotient of the set of inputs—it’s some simple filter that can get applied to lots of stimuli. And when you make a broad, high-level model of a network, that’s like a subset on inputs—the subset is the domain of validity of your high-level model, because of course such models only work within a domain of validity.