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[D] Modern applications of statistical learning theory?

I was reading about concentration of measure related stuff recently and was curious whether anyone knows whether this material is still applicable to ‘deep learning’ models. By statistical learning theory I mean stuff like VC / Rademacher bounds etc.

If it is, can anyone point to any research papers on this topic?

From my naive understanding, because these bounds relate to the worst-case scenario the union bound may be excessively pessimistic in terms of the number of training examples required.

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