Primarily, we care about NN generalization on problems in which the input Place is constant, usually R^n. Â The authors argue the finite-set results are suitable to those problems, since one can always discretize R^n to secure a finite established. Â I do not Believe this captures the kinds of functionality complexity we treatment about for NNs.
A technique that SGD could vary from random sampling is the fact that SGD will usually only get to the boundary of a area with zero training error, Whilst random sampling will sample uniformly within the area.
--The stuff joined In this particular publish hypothesizes that straightforward functions love greater quantity in parameter-Room, i.e. you will find a lot more attainable mixtures of neuron weights that add as much as a simple function than a complex just one.
I feel The best theoretical result might be to indicate that SGD on neural nets is undoubtedly an approximation of Solomonoff Induction (or one thing like SI), as well as approximation gets better as the NNs get more substantial and further. But I have but to discover any concept that connects neural nets/ SGD to a thing like limited systems.
We do have empirical facts which exhibits which the neural network "prior" is biased in the direction of low-complexity capabilities, and a few arguments for why it would make sense to assume this to become the case -- see this new web site submit, and my comment right here.
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From there, the natural future dilemma is what precisely generality is retained/missing, and whether or not the lack of generality essentially issues for points in the true entire world.
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This option makes sense if A, B are truly unstructured collections of objects with no intrinsic this means.
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Crucial point listed here: the appropriate notion of "uncomplicated" isn't "small Kolmogorov complexity"; It really is extra like smoothness. A bias toward "very simple" functions, for this Idea of "easy", would generally make interpolation function nicely, not automatically other prediction problems.
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