Despite the remarkable success of Graph Neural Networks (GNNs), the common belief is that their representation power is limited and that they are at most as expressive as the Weisfeiler-Lehman (WL) algorithm. In this paper, we argue the opposite and show that standard GNNs, with anonymous inputs, produce more discriminative representations than the WL algorithm. Our novel analysis employs linear algebraic tools and characterizes the representation power of GNNs with respect to the eigenvalue decomposition of the graph operators. We prove that GNNs are able to generate distinctive outputs from white uninformative inputs, for, at least, all graphs that have different eigenvalues. We also show that simple convolutional architectures with white inputs, produce equivariant features that count the closed paths in the graph and are provably more expressive than the WL representations. Thorough experimental analysis on graph isomorphism and graph classification datasets corroborates our theoretical results and demonstrates the effectiveness of the proposed approach.

翻译：尽管图神经网络（GNN）取得了显著成功，但普遍认为其表示能力有限，至多与Weisfeiler-Lehman（WL）算法具有同等的表达力。本文提出相反观点，证明标准GNN在匿名输入下能生成比WL算法更具区分性的表示。我们采用线性代数工具进行创新性分析，基于图算子的特征值分解刻画了GNN的表示能力。我们证明，对于至少所有具有不同特征值的图，GNN能够从无信息的白色输入中生成具有区分性的输出。我们还表明，采用白色输入的简单卷积架构可生成等变特征，这些特征能够计数图中的闭合路径，且已被证明具有比WL表示更强的表达力。在图同构与图分类数据集上的全面实验分析验证了我们的理论结果，并展示了所提方法的有效性。