$E[ \lVert \nabla f(x)\rVert^2_{\nabla^2 f(x) ^{-1}}]$
This is explained as a norm of gradient and a measure of its magnitude under the hessian.
I have no idea what it means and would appreciate any changes to the question or explanation.
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1If A is a positive definite matrix and x is a real vector then $| x |_A=(x^T A x)^{1/2}$. – Ian Jul 14 '17 at 17:10
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Is there a name for this operator? if I had to search for this – knk Jul 15 '17 at 01:48
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The (vector) norm induced by A. – Ian Jul 15 '17 at 04:23