Exponential expressivity of neural networks on Gevrey classes with point singularities
We analyze deep Neural Network emulation rates of smooth functions with point singularities in bounded, polytopal domains , . We prove exponential emulation rates in Sobolev spaces in terms of the number of neurons and in terms of the number of nonzero coefficients for Gevrey-regular solution classes defined in terms of weighted Sobolev scales in , comprising the countably-normed spaces of I. M. Babuška and B. Q. Guo. As intermediate result, we prove that continuous, piecewise polynomial high...