  We prove the existence of an upper bound on critical volume of a large class
of toric Sasaki-Einstein manifolds with respect to the first Chern class of the
resolutions of the Gorenstein singularities in the corresponding toric
Calabi-Yau varieties. We examine the canonical metrics obtained by the Delzant
construction on these varieties and characterise cases when the bound is
attained. We comment on computational tools used in the investigation, in
particular Neural Networks and the gradient saliency method.
