用深度学习快速预测图间最优传输方案，速度提升百倍以上。
Unsupervised Learning for Optimal Transport plan prediction between unbalanced graphs
- 设计带交叉注意力的神经网络，根据超参数动态生成传输计划。
- 在合成与真实脑图数据上，速度比传统方法快100倍，损失相当。
- 输出可微分，支持后续优化，适合需要高效图对齐的研究者。
基于格罗莫夫-沃瑟斯坦等扩展的图间最优传输是对比和对齐图结构的强大工具。然而，求解相关的非凸优化问题计算成本高，限制了其在大规模图上的应用。本文提出无监督最优传输学习（ULOT），一种通过最小化融合非平衡格罗莫夫-沃瑟斯坦（FUGW）损失训练的深度学习方法，用于预测两图间的最优传输计划。我们设计了一种新颖的神经架构，结合交叉注意力机制，并以FUGW权衡超参数为条件输入。在合成随机块模型（SBM）图及来自fMRI的真实皮层表面数据上评估，ULOT在保持竞争性损失的同时，速度比经典求解器快两个数量级。此外，预测的传输计划可作为经典求解器的热启动，加速收敛。最后，该计划对图输入和FUGW超参数完全可微，支持对函数式目标进行优化。
原文摘要 · Abstract (English)
Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally expensive, which limits the scalability of these methods to large graphs. In this work, we present Unbalanced Learning of Optimal Transport (ULOT), a deep learning method that predicts optimal transport plans between two graphs. Our method is trained by minimizing the fused unbalanced Gromov-Wasserstein (FUGW) loss. We propose a novel neural architecture with cross-attention that is conditioned on the FUGW tradeoff hyperparameters. We evaluate ULOT on synthetic stochastic block model (SBM) graphs and on real cortical surface data obtained from fMRI. ULOT predicts transport plans with competitive loss up to two orders of magnitude faster than classical solvers. Furthermore, the predicted plan can be used as a warm start for classical solvers to accelerate their convergence. Finally, the predicted transport plan is fully differentiable with respect to the graph inputs and FUGW hyperparameters, enabling the optimization of functionals of the ULOT plan.
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