aiqbench analysis
This research establishes a theoretical link between non-acyclic Generative Flow Networks and optimal transport, demonstrating that GFlowNets can implicitly learn high-quality transport plans on large graphs. By framing the learning objective as a Kantorovich problem, the approach enables neural parameterization of optimal couplings that align with exact solvers. This finding expands the applicability of GFlowNets beyond simple sampling to solving complex distributional matching problems efficiently.
Your GFlowNet Secretly Learns an Optimal Transport Plan
arXiv:2606.06272v1 Announce Type: cross Abstract: 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.
Abstract: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.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
arXiv:2606.06272 [cs.LG]
(or arXiv:2606.06272v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2606.06272 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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Full text under the publisher's open licence · 226 words
