论文标题
最佳传输图神经网络
Optimal Transport Graph Neural Networks
论文作者
论文摘要
当前的图形神经网络（GNN）将嵌入到汇总的图表表示中 - 可能会丢失结构或语义信息，将嵌入的平均平均值或总和节点嵌入。我们在这里介绍了OT-GNN，该模型使用参数原型计算图形嵌入，突出了不同图形方面的关键方面。为了实现这一目标，我们成功地将最佳传输（OT）与参数图模型相结合。图表是从gnn节点嵌入和``Prototype''点云作为自由参数之间的wasserstein距离获得的。从理论上讲，与传统的总和汇总不同，点云上的函数类别满足了基本的通用近似定理。从经验上讲，我们通过提出噪声对比的正规器来引导模型真正利用OT几何形状来解决固有的崩溃优化问题。最后，在表现出更平滑的图表表示时，我们在几个分子属性预测任务上胜过流行方法。
Current graph neural network (GNN) architectures naively average or sum node embeddings into an aggregated graph representation -- potentially losing structural or semantic information. We here introduce OT-GNN, a model that computes graph embeddings using parametric prototypes that highlight key facets of different graph aspects. Towards this goal, we successfully combine optimal transport (OT) with parametric graph models. Graph representations are obtained from Wasserstein distances between the set of GNN node embeddings and ``prototype'' point clouds as free parameters. We theoretically prove that, unlike traditional sum aggregation, our function class on point clouds satisfies a fundamental universal approximation theorem. Empirically, we address an inherent collapse optimization issue by proposing a noise contrastive regularizer to steer the model towards truly exploiting the OT geometry. Finally, we outperform popular methods on several molecular property prediction tasks, while exhibiting smoother graph representations.
