Neural Non-Equilibrium Hamiltonian Monte Carlo for Corrected Boltzmann Sampling

What the math gives to ML

The paper's transferable contribution is a train-then-correct sampler: a neural finite-time transport can make global moves without requiring the learned dynamics to preserve the target exactly, because the complete proposal path records a computable probability correction. The key asset is path-space correction rather than endpoint-only correction: minimizing expected generalized work trains the proposal toward a reverse-compatible path law, while the same work yields importance weights, free-energy estimates, and an exact independent Metropolis correction. This suggests neural samplers for multimodal targets that can diagnose proposal failure through work variance, effective sample size, and acceptance rather than silently producing biased samples. The most practical transfers are a learned stochastic Hamiltonian bridge and path-level importance or Metropolis correction.