用神经最优传输生成图上分布，支持连续数据建模。
Generative Modeling on Metric Graphs via Neural Optimal Transport
- 将图嵌入光滑空间，用神经网络求解熵正则最优传输
- 在曼哈顿一百万个网约车点上训练，效果优于传统离散方法
- 适用于城市交通等连续图结构数据，可扩展性强
我们提出首个针对紧致度量图上连续概率分布的深度生成建模框架。给定度量图上的源与目标分布，该方法将图嵌入光滑环境空间，通过神经半对偶参数化求解熵正则的Kantorovich问题，并将生成样本投影回原图。研究了两种嵌入几何：外嵌欧氏实现与内嵌热带阿贝尔-雅可比嵌入到雅可比环面。两种情况下生成器均天然支持图结构。理论证明，在神经网络表达能力趋于无限、联合极限下，学习到的生成器弱收敛于原始图分布间的有效传输耦合。实验表明，在多种几何不同的图上，本方法性能匹配或超越基于离散图最优传输的启发式基线，且扩展性更优。最后，我们在纽约曼哈顿的一百万个Uber接客点数据上验证了模型可扩展性。
原文摘要 · Abstract (English)
We introduce, to our knowledge, the first deep generative modeling framework for probability distributions continuously supported on compact metric graphs. Given source and target measures on a metric graph, our method embeds the graph into a smooth ambient space, solves an entropic Kantorovich problem via a neural semidual parameterization, and projects generated samples back onto the original graph. We study two embedded geometries: an extrinsic Euclidean realization and the intrinsic tropical Abel--Jacobi embedding into the Jacobian torus. In both cases, the resulting generator is graph-supported by construction. We prove that, in the joint limit of increasing neural expressivity, the learned generator converges weakly to a valid transport coupling between the original graph measures. Empirically, across a range of geometrically distinct graphs, our method matches or improves upon heuristic transport baselines based on discrete graph OT, while scaling more favorably. Finally, we demonstrate scalability on real-world urban mobility data by training our model on one million Uber pickup locations in Manhattan, New York City.
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