> I don't know, nor does anyone else.

We don't know the details. But it's pretty implausible that the process of learning wouldn't involve the brain having some representation of the thing it's learning, or wouldn't involve repeatedly "copying" that representation. Every way we know of processing data works like that. (OK, there are theoretical notions of reversible computation - but it's more complex and less effective than the regular kind, so it seems very unlikely the brain would operate that way)

And a human who has learned to perform a task has certainly "derived a function that takes some input and produces an output".