用随机交换样本索引模拟多边缘最优传输，高效处理高维数据。
Collision-based Dynamics for Multi-Marginal Optimal Transport
- 基于碰撞机制设计随机交换算法，模拟多边缘最优传输过程。
- 计算复杂度与内存使用随样本数线性增长，适合高维场景。
- 相比前沿方法更快，适用于大规模样本的优化传输任务。
受玻尔兹曼动力学启发，我们提出一种基于碰撞的动力学模型，并配合蒙特卡洛求解算法，通过随机配对交换样本索引来近似求解多边缘最优传输问题。该方法的计算复杂度和内存占用均随样本数量呈线性增长，因此在高维设置下极具优势。在多个实验中，我们展示了该方法相较当前最先进方法的高效性。
原文摘要 · Abstract (English)
Inspired by the Boltzmann kinetics, we propose a collision-based dynamics with a Monte Carlo solution algorithm that approximates the solution of the multi-marginal optimal transport problem via randomized pairwise swapping of sample indices. The computational complexity and memory usage of the proposed method scale linearly with the number of samples, making it highly attractive for high-dimensional settings. In several examples, we demonstrate the efficiency of the proposed method compared to the state-of-the-art methods.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。