We investigate novel random graph embeddings that can be computed in expected polynomial time and that are able to distinguish all non-isomorphic graphs in expectation. Previous graph embeddings have limited expressiveness and either cannot distinguish all graphs or cannot be computed efficiently for every graph. To be able to approximate arbitrary functions on graphs, we are interested in efficient alternatives that become arbitrarily expressive with increasing resources. Our approach is based on Lov\'asz' characterisation of graph isomorphism through an infinite dimensional vector of homomorphism counts. Our empirical evaluation shows competitive results on several benchmark graph learning tasks.

翻译：我们研究了新型随机图嵌入方法，这些方法可在期望多项式时间内计算，并能够在期望意义上区分所有非同构图。现有图嵌入方法的表现力有限，要么无法区分所有图，要么无法对任意图进行高效计算。为逼近图上的任意函数，我们致力于寻找随着资源增加而渐进具有任意表达力的高效替代方案。本研究基于Lovász通过无限维同态计数向量刻画图同构的理论框架。实验评估表明，该方法在多个基准图学习任务中取得了有竞争力的结果。