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arXiv · 2603.09089

Sampling on Discrete Spaces with Temporal Point Processes

Cameron A. Stewart·Maneesh Sahani
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Abstract

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.

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BibTeXRIS

Cameron A. Stewart, Maneesh Sahani. 2026-05-17. Sampling on Discrete Spaces with Temporal Point Processes. https://arxiv.org/abs/2603.09089

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