(Also: I don’t Believe the Idea of “very low effective parameterisation†seriously captures what’s taking place below, but for the reason you point out by yourself.)
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I concur this arguably could be mildly deceptive. As an example, the correspondence amongst SGD and Bayesian sampling only definitely holds for some initialisation distributions. In case you deterministically initialise your neural network on the origin (i.
Mix that with the fact that empirically we get fantastic generalization and we get the thing you mentioned.
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I believe Chris has now current the In the direction of Data Science blog site publish to generally be a lot more clear, based upon the conversation you experienced, but I'll make some clarifications listed here in addition, for the good íŒŒì›Œë³¼ë¶„ì„ thing about others:
It is really correct that we do not have a arduous mathematical evidence for "why" simple features must have larger sized volumes in parameter-space, but I may give an intuitive argument for why I think it would make sense to count on this to get the case.
The Levin sure does not implement on to neural networks, as it assumes that P is finite and discrete, but it surely presents some excess backing to the instinct above.
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I'd have an interest to listen to your tackle this remark above, which is referring to compressibility, which to me appears like kolmogorov complexity.
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This does not seem like a special residence of neural nets. Â It just seems like a result of assigning a normed vector space framework to the inputs, and preferring features that "use" the composition within their labeling rule.
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