Temporal point processes offer a powerful framework for sampling from discrete distributions, yet they remain underutilized in existing literature. We show how to construct, for any target multivariate count distribution with downward-closed support, a multivariate temporal point process whose event-count vector in a fixed-length sliding window converges in distribution to the target as time tends to infinity. Structured as a system of potentially coupled infinite-server queues with deterministic service times, the sampler exhibits a discrete form of momentum that suppresses random-walk behaviour. The admissible families of processes permit both reversible and non-reversible dynamics. As an application, we derive a recurrent stochastic neural network whose dynamics implement sampling-based computation and exhibit some biologically plausible features, including relative refractory periods and oscillations. The introduction of auxiliary randomness reduces the sampler to a birth-death process, establishing the latter as a degenerate case with the same limiting distribution. In simulations on 63 target distributions, our sampler always outperforms these birth-death processes and frequently outperforms Zanella processes in multivariate effective sample size, with further gains when normalized by CPU time.

翻译：时序点过程为从离散分布中采样提供了强大的框架，然而在现有文献中，这一方法尚未得到充分利用。我们展示了如何针对任意具备向下封闭支撑集的多变量计数分布，构造一个多变量时序点过程，使得其在固定长度滑动窗口内的事件计数向量在时间趋于无穷时依分布收敛于目标分布。该采样器结构上是一个由可能耦合的无限服务器队列组成的系统，并具有确定性服务时间，呈现出一种离散形式的动量，能够抑制随机游走行为。所允许的过程族同时支持可逆与非可逆动力学。作为应用，我们推导出一种循环随机神经网络，其动力学实现了基于采样的计算，并展现出一些生物合理性特征，包括相对不应期与振荡。引入辅助随机性后，该采样器简化为生灭过程，从而将后者确立为具有相同极限分布的退化情形。在针对63个目标分布的仿真中，我们的采样器在多变量有效样本量上始终优于这些生灭过程，并经常优于Zanella过程；按CPU时间归一化后，优势进一步扩大。