Your identity function f is indistiguishable from the function g that rounds to the even number below, leaving the parity bit to zero — or, indeed, to any function equal to f after restricting the input domain to the even integers, as represented with parity bit = 0. (1/n)
Generalizing outside a space is exactly what convolution is designed to do, for translation invariance. We just need a more general solution, like the one toddlers use in acquiring language.https://twitter.com/lostanlen/status/948551656593125376 …
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Right. Which is why people are totally different; I address your objection at length in The Algebraic Mind, chapter 3.
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Isn’t that generalizing ability (Eg toddler language acquisition) likely to be ‘structural’? Hence the common grammar across all languages. Ie the more general solution of Deep Learning is actually the problem?
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Ie in order for an optimizing system to generalize it must have much more data than degrees of freedom. Our brains generalize better precisely bc they have fewer deg’s of freedom bc evolution structurally built a system which disallows deg’s of freedom not useful in real world.
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