Primarily, we care about NN generalization on problems where by the enter House is ongoing, typically R^n. Â The authors argue that the finite-set results are applicable to these issues, since one can always discretize R^n to get a finite established. Â I don't think this captures the kinds of perform complexity we treatment about for NNs.
A method that SGD could vary from random sampling is usually that SGD will ordinarily only get to the boundary of a region with zero instruction error, whereas random sampling will sample uniformly in the area.
Given that truly functioning rejection sampling for a dataset would acquire _way_ a lot of time, the authors approximate it employing a Gaussian Process. This is understood to become a very good approximation in the large width routine.
Merge that with The truth that empirically we get good generalization and we obtain the point you said.
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There's been some modern investigate which (I believe) sheds some light on this concern. I wish to simply call awareness to this blog post: