一句话：提出在惰性函数式概率程序中实现无限维参数空间上的梯度型 HMC 与 NUTS，并用 PACAP 分析保证梯度有限支撑。
该论文针对标准 HMC 依赖梯度和有限维参数空间的问题，利用 Haskell 惰性求值表达随机过程等隐式无限维非参数贝叶斯模型。作者提出 LazyHMC，为无限维设置给出基于惰性求值的梯度型 HMC 新表述。针对自动微分，引入“柱状解析划分下的分段解析”（PACAP）分析，证明即使程序无限维且惰性定义，似然梯度仍具有有限支撑。蒙特卡洛方面，开发多种 HMC 变体与 No-U-Turn Sampler，使其可在无限维参数空间运行，并因惰性求值保持可产出。实验包括高斯混合聚类、随机游走，以及带 Poisson 过程变点的分段常值回归。
Hamiltonian Monte Carlo (HMC) is a successful generic inference method in probabilistic programming, but in its ordinary formulation it needs gradients and finite-dimensional parameter spaces. In Haskell, lazy evaluation lets probabilistic programs express stochastic processes and other non-parametric Bayesian models over implicit infinite-dimensional spaces. This paper develops new formulations of gradient-based HMC for this infinite-dimensional setting, via lazy evaluation. For automatic differentiation, we provide an analysis based on a new notion of "piecewise analytic under cylindrical analytic partition" (PACAP), to show that even if a program is infinite-dimensional and defined lazily, the gradient of the likelihood function is finitely supported. For the Monte Carlo method itself, we develop several HMC variants and a No-U-Turn Sampler that operate over the infinite-dimensional parameter space but are still productive because of lazy evaluation. Experiments cover Gaussian mixture clustering, random walks, and piecewise-constant regression with Poisson-process changepoints.
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@article{CraciunOSS26,
title = {LazyHMC: Hamiltonian Monte Carlo Simulation for Lazy, Infinite Dimensional Probabilistic Programs},
author = {Maria-Nicoleta Crăciun and C.-H. Luke Ong and Tom Schrijvers and Sam Staton},
journal = {Proceedings of the ACM on Programming Languages},
volume = {10},
number = {ICFP},
year = {2026},
doi = {10.1145/3828696}
}