论文标题
Weisfeiler和Leman Go Infinite：光谱和组合预彩色
Weisfeiler and Leman Go Infinite: Spectral and Combinatorial Pre-Colorings
论文作者
论文摘要
通常通过比较图形不变剂进行图形同构测试。在表达能力和计算效率之间提供良好权衡的两种流行替代方案是组合（即，通过Weisfeiler-Leman（WL）测试获得）和光谱不变性。虽然后者的确切功能仍然是一个悬而未决的问题，但使用统一的预涂层标准配置时，前者经常因其有限的能力而受到批评。这种缺点阻碍了消息传递图神经网络（MPGNN）的适用性，其表达能力在WL测试中限制。放松统一的预彩的假设，我们表明可以增加WL测试AD Infinitum的表达能力。在此之后，我们提出了一个基于光谱特征的有效的预彩，可证明可以提高香草WL检验的表达能力。以上主张伴随着广泛的合成和真实数据实验。重现我们的实验的代码可从https://github.com/tpfi22/spectral-and-combinatorial获得
Graph isomorphism testing is usually approached via the comparison of graph invariants. Two popular alternatives that offer a good trade-off between expressive power and computational efficiency are combinatorial (i.e., obtained via the Weisfeiler-Leman (WL) test) and spectral invariants. While the exact power of the latter is still an open question, the former is regularly criticized for its limited power, when a standard configuration of uniform pre-coloring is used. This drawback hinders the applicability of Message Passing Graph Neural Networks (MPGNNs), whose expressive power is upper bounded by the WL test. Relaxing the assumption of uniform pre-coloring, we show that one can increase the expressive power of the WL test ad infinitum. Following that, we propose an efficient pre-coloring based on spectral features that provably increase the expressive power of the vanilla WL test. The above claims are accompanied by extensive synthetic and real data experiments. The code to reproduce our experiments is available at https://github.com/TPFI22/Spectral-and-Combinatorial
