Accelerated Mixing Time of Randomized Hamiltonian Monte Carlo

What the math gives to ML

The paper provides a randomized Hamiltonian sampler whose refresh-and-trajectory mechanism exploits second-order dynamics rather than diffusive position updates. For an alpha-strongly log-concave target, choosing random trajectory durations with mean proportional to alpha^{-1/2} yields a total simulated-time guarantee of O(alpha^{-1/2} log(epsilon^{-1})), improving the characteristic alpha^{-1} dependence of first-order Langevin mixing. The most credible neural-network transfer is Bayesian inference for a strongly log-concave neural subproblem, such as a regularized convex last layer or Gaussian local posterior, rather than unconstrained full-network weight sampling. Randomized durations are useful because they avoid resonant fixed-length Hamiltonian trajectories while retaining an explicit mixing-time target.