Provable Non-Acceleration of Standard Strang Splittings of Kinetic Langevin Dynamics

What the math gives to ML

The paper reduces several kinetic Langevin Strang splittings to an exact noisy heavy-ball position recursion and proves a sharp obstruction: fixed step size and friction cannot uniformly obtain accelerated square-root-condition-number mixing over smooth strongly convex potentials. The transferable asset is not the MCMC sampler itself, but the explicit connection between momentum recursions, slow linear modes, and attracting periodic orbits caused by fixed hyperparameter choices. This suggests an optimizer safeguard that monitors local two-step dynamics for oscillatory or periodic behavior and changes momentum or step size before the optimizer enters a long-lived cycle. The proposed intervention is falsifiable on ill-conditioned quadratic losses and smooth nonquadratic objectives, where it should reduce stagnation without sacrificing the fast regime.