Graph neural networks are prominent models for representation learning over graphs, where the idea is to iteratively compute representations of nodes of an input graph through a series of transformations in such a way that the learned graph function is isomorphism invariant on graphs, which makes the learned representations graph invariants. On the other hand, it is well-known that graph invariants learned by these class of models are incomplete: there are pairs of non-isomorphic graphs which cannot be distinguished by standard graph neural networks. This is unsurprising given the computational difficulty of graph isomorphism testing on general graphs, but the situation begs to differ for special graph classes, for which efficient graph isomorphism testing algorithms are known, such as planar graphs. The goal of this work is to design architectures for efficiently learning complete invariants of planar graphs. Inspired by the classical planar graph isomorphism algorithm of Hopcroft and Tarjan, we propose PlanE as a framework for planar representation learning. PlanE includes architectures which can learn complete invariants over planar graphs while remaining practically scalable. We empirically validate the strong performance of the resulting model architectures on well-known planar graph benchmarks, achieving multiple state-of-the-art results.

翻译：图神经网络是图表示学习的突出模型，其核心思想是通过一系列变换迭代计算输入图中节点的表示，使得学习到的图函数具有同构不变性，从而令学习到的表示成为图不变量。然而，众所周知，这类模型学习到的图不变量是不完备的：存在非非同构的图对，标准图神经网络无法区分。鉴于一般图上的同构测试在计算上的难度，这一结果不足为奇，但对于特殊图类（如平面图）而言，情况有所不同——已知存在高效的平面图同构测试算法。本文旨在设计能高效学习平面图完备不变量的架构。受Hopcroft和Tarjan经典平面图同构算法的启发，我们提出了平面表示学习框架PlanE。PlanE包含的架构既能学习平面图的完备不变量，又保持了实际可扩展性。我们通过在知名平面图基准上的实验验证了所得模型架构的强性能，取得了多项最先进的结果。