Sampling on Discrete Spaces with Temporal Point Processes

2026-03-09

AI Summary

This work addresses the problem of efficiently sampling from discrete multivariate count distributions with downward-closed support. To this end, the authors propose a novel sampler based on temporal point processes, which approximates the target distribution through vectors of event counts observed within a fixed-length sliding window. Sampling is realized via a coupled infinite-server queueing system, and the method incorporates a discrete momentum mechanism that accommodates both reversible and non-reversible dynamics. Notably, its architecture aligns with biological neural mechanisms, enabling seamless integration into stochastic recurrent neural networks. Theoretical analysis and empirical evaluation across 63 target distributions demonstrate that the proposed approach consistently outperforms classical birth–death processes in terms of multivariate effective sample size, and typically surpasses the Zanella process as well; these advantages become even more pronounced after normalization by CPU time.

Technology Category

• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Reasoning under Uncertainty: Stochastic Optimization
• Machine Learning: Probabilistic Circuits and Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Models for Web evolution

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 oscillatory dynamics. 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.

Problem

• discrete sampling
• temporal point processes
• multivariate count distribution
• downward-closed support
• stochastic sampling

Innovation

• temporal point processes
• discrete sampling
• infinite-server queues
• stochastic neural networks
• non-reversible dynamics