alt Hacker NewsADAM is related if your second derivative matrix happens to be diagonal.
Of course, it takes about 5 minutes to show that any DNN is going to have very very high magnitude off-diagonal terms by the way it's constructed, so pretending that a diagonal approximation is close enough is crazy.
Adam doesn't use the second derivatives matrix, it uses second moments of the gradient, which is the diagonal of the uncentered covariance matrix, but neither of them are directly related to SVD or singular values anyway.
There is a slight connection where Adam approximates full-matrix Adagrad which computes inverse square root of the convariance matrix, which you usually do using eigendecomposition, but on the covariance matrix SVD and eigendecomposition are equivalent (can easily be converted to each other), so you could use SVD to compute the inverse square root.