GFlowNet隐式学习最优传输计划，可高效求解大规模图上的运输问题。
Your GFlowNet Secretly Learns an Optimal Transport Plan
- 将非无环GFlowNet与最优传输理论结合，用图最短路径定义成本
- 最小流设置下，目标等价于Kantorovich运输问题，学习到的策略即最优传输方案
- 适用于大规模图结构，支持神经网络参数化，适合需要高效采样的场景
生成流网络（GFlowNets）通过有向图中的随机轨迹来采样结构化对象。本文建立非无环GFlowNets与最优传输（OT）之间的理论联系。我们证明，在最小流GFlowNet中固定初始流分布后，其目标等价于以图诱导的最短路径成本为代价的Kantorovich OT问题。在最优解处，学习到的GFlowNet策略编码了从源分布到目标分布的最优传输计划：从最小流GFlowNet中采样轨迹可恢复对应的最优耦合。该公式使GFlowNet学习框架能通过边流和神经参数化应用于大规模图上的OT问题。实验验证了与精确OT求解器的一致性，并表明GFlowNets可学习高质量传输计划。
原文摘要 · Abstract (English)
Generative Flow Networks (GFlowNets) are a framework for sampling structured objects via stochastic trajectories in a directed graph. In this work, we establish a theoretical connection between non-acyclic GFlowNets and optimal transport (OT). We show that fixing the initial flow distribution in a minimum-flow GFlowNet reduces its objective to a Kantorovich OT problem with graph-induced shortest path costs. At the optimum, the learned GFlowNet policy therefore encodes an optimal transport plan from the source distribution to the target distribution: we show that sampling trajectories from the minimum-flow GFlowNet recovers the corresponding optimal coupling. Our formulation enables applying the GFlowNet learning framework to OT problems on large graphs via edge flows and neural parameterization. Experiments confirm agreement with exact OT solvers and demonstrate that GFlowNets can learn high-quality transport plans.
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