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Dependant on that description, it ought to be simple to generalize the Levin certain to neural networks. The primary move will be to exchange the Huffman code using a turbocode (or some other near-Shannon-sure code), at which issue the compressibility is largely just like the log probability density, and we may take the limit to steady perform space without any trouble.
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As for why most functions will likely not generalize effectively, it's almost certainly due to the fact there's a lot more Erroneous responses than appropriate ones for every new datapoint, in general.
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From there, the pure upcoming problem is what exactly generality is held/missing, and if the lack of generality essentially issues for points in the true planet.
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The point that uncomplicated features just take up a larger quantity in parameter Place looks clearly legitimate to me and I am unable to truly envision anyone disagreeing with that section (while I'm nonetheless pretty glad to have genuine analysis to back again that up).
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I'm sure the toy design definitions of Those people phrases (connecting dots vs. drawing a line off absent from your dots) but Exactly what does it mean in authentic lifestyle challenges? It seems like a fuzzy/graded distinction to me, at most effective.
Do you do have a good reference for your Levin certain? My makes an attempt at getting a applicable paper all failed.
(Even when you are discussing the overparameterized scenario, in which this argument isn't vacuous in addition to applies principally to neural nets rather than other ML designs, I do not uncover this argument really compelling a priori, while I agree that according to empirical proof it might be mostly accurate.)