We investigate the role of learning rate grafting and the staleness of the preconditioner in Shampoo by decoupling the updates of the eigenvalues and eigenbasis of its preconditioner.

The utility of mechanisms where bidders compete for their favorite item give a $\Theta(1 + \log{n/m})$-approximation to social welfare.

We study the approximation and generalization abilities of score-based neural network generative models