Persistence Pays: Square-root condition-number dependence for Metropolis-adjusted kinetic Langevin Monte Carlo with a non-reversibly updated accept/reject uniform

We prove accelerated mixing for a Metropolis-adjusted kinetic Langevin sampler: the OBABO splitting with friction $2\sqrt m$, adjusted with Neal's non-reversibly updated uniform, which is redrawn after every epoch of $E$ steps. For targets $e^{-U}$ on $\mathbb{R}^d$ with $mI\preceq\nabla^2U\preceq L