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This argument just doesn’t audio really powerful to me. It also can be placed on virtually any machine learning algorithm; I don’t see why this is certain to neural nets. If This can be just intended to clarify why it is actually all right to overparameterize neural nets, then which makes extra feeling to me, though then I’d say a little something like “with overparameterized neural nets, a variety of parameterizations instantiate the exact same function, and Hence the ‘successful parameterization’ is reduced than You may have assumedâ€, as opposed to stating just about anything about Kolmogorov complexity.
This Portion of the argument is certainly very typical, however it’s not vacuous. For your argument to use you need it to get the case that the operate space is overparameterised, that the parameter-function map has small complexity relative into the features while in the operate Room, and that parameter-perform map is biased in some way. This will not be the case for all Studying algorithms.
I believe the ideal theoretical result would be to indicate that SGD on neural nets is undoubtedly an approximation of Solomonoff Induction (or anything like SI), along with the approximation will get much better because the NNs get even larger and deeper. But I have nonetheless to find out any principle that connects neural nets/ SGD to one thing like shorter plans.
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Beyond that, approximating the random sampling chance having a Gaussian approach is a reasonably delicate affair and I have concerns regarding the applicability to real neural networks.
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Ok, I do think a confusion right here is the fact I (and the OP AFAIK) Really don't mention the exact same items as you need to do when using the term "functionality". Solomonoff induction is about systems (commonly Turing devices) and from the comment it seems like the perception of capabilities you take. But functions 파워볼 as I am working with listed here (and I'm pretty positive this is the this means while in the quote) is simply an input/output relation.
The 파워볼 common standard, however, you chop it right into a trillion items about the x axis, and translate the pieces to arbitrary places in R
Even though correlation is not perfect around all scales, it tends to further improve given that the frequency of your functionality raises. Particularly, the very best handful of almost certainly functions tend to have hugely correlated probabilities underneath the two generation mechanisms.
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