提出新方法，显著提升对数凹分布采样效率。
Parallel Simulation for Log-concave Sampling and Score-based Diffusion Models
- 基于科学计算中的并行模拟思想，设计可并行的采样算法。
- 将适应性复杂度从约 log²d 降低到 logd，逼近理论最优。
- 适合需要高效高维采样的研究者，如生成模型方向。
高维概率分布采样是机器学习与统计学的基础问题。随着数据集规模扩大，计算效率愈发关键，尤其体现在降低自适应复杂度——即采样算法所需的串行轮次数量上。尽管已有研究提出多种可并行化技术，但其收敛速率常不理想，仍显著弱于对数凹采样最新的理论下界。为此，本文提出一种新型并行采样方法，将适应性复杂度关于维度 d 的依赖从 ∼O(log²d) 降至 ∼O(logd)，在特定条件下达到对数凹采样理论最优。该方法借鉴科学计算中的并行模拟技术。
原文摘要 · Abstract (English)
Sampling from high-dimensional probability distributions is fundamental in machine learning and statistics. As datasets grow larger, computational efficiency becomes increasingly important, particularly in reducing adaptive complexity, namely the number of sequential rounds required for sampling algorithms. While recent works have introduced several parallelizable techniques, they often exhibit suboptimal convergence rates and remain significantly weaker than the latest lower bounds for log-concave sampling. To address this, we propose a novel parallel sampling method that improves adaptive complexity dependence on dimension $d$ reducing it from $\widetilde{\mathcal{O}}(\log^2 d)$ to $\widetilde{\mathcal{O}}(\log d)$. which is even optimal for log-concave sampling with some specific adaptive complexity. Our approach builds on parallel simulation techniques from scientific computing.
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