6. Examples with genuinely infinite-dimensional inputs
This chapter is Section 7 of the manuscript together with Appendix E. A function f on H
is cylindrical if f=\widetilde f\circ L for a finite-rank linear map L; all examples are
non-cylindrical, so finite width is never obtained by truncating the input. We write
\phi_v for the centred one-dimensional Gaussian density of variance v>0, with
\phi_0=\delta_0, and \Phi(u)=e^{-u^2/2} for the Gaussian activation.