Typically, we treatment about NN generalization on troubles where by the enter Room is ongoing, generally R^n. Â The authors argue which the finite-set results are pertinent to these difficulties, since one can always discretize R^n to obtain a finite established. Â I do not Feel this captures the types of operate complexity we care about for NNs.
The rest of the remark is about stuff which i didn't have a solid impression on, so I'll depart it for Zach to reply if he wants.
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I do think this makes sense for clarifying the quotation, as this Portion of the post clarifies the relatively traditional arguments that neural networks generalize pretty well, are not likely constrained in terms of input/output relations, nevertheless most enter/output relations will never generalize the right way to new details. So there needs to be something a lot more right here.
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I'm not sure if accounting for your floating-point implementation is informative or not in this case.
For example, in case you look at Figure 6 while in the write-up I hyperlink, you may see that distinctive variations of SGD do provide a slightly distinct inductive bias. Nevertheless, this result is apparently pretty compact relative to what's provided by the "prior".
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