Interpretable graph neural networks (XGNNs ) are widely adopted in various scientific applications involving graph-structured data. Existing XGNNs predominantly adopt the attention-based mechanism to learn edge or node importance for extracting and making predictions with the interpretable subgraph. However, the representational properties and limitations of these methods remain inadequately explored. In this work, we present a theoretical framework that formulates interpretable subgraph learning with the multilinear extension of the subgraph distribution, coined as subgraph multilinear extension (SubMT). Extracting the desired interpretable subgraph requires an accurate approximation of SubMT, yet we find that the existing XGNNs can have a huge gap in fitting SubMT. Consequently, the SubMT approximation failure will lead to the degenerated interpretability of the extracted subgraphs. To mitigate the issue, we design a new XGNN architecture called Graph Multilinear neT (GMT), which is provably more powerful in approximating SubMT. We empirically validate our theoretical findings on a number of graph classification benchmarks. The results demonstrate that GMT outperforms the state-of-the-art up to 10% in terms of both interpretability and generalizability across 12 regular and geometric graph benchmarks.

翻译：可解释图神经网络（XGNNs）广泛应用于涉及图结构数据的各类科学场景。现有XGNNs主要采用基于注意力机制的方法学习边或节点的重要性，以提取可解释子图并进行预测。然而，这些方法的表征特性与局限性尚未得到充分探索。本文提出一个理论框架，通过子图分布的多线性扩展（称为子图多线性扩展，SubMT）来形式化可解释子图学习。提取理想的可解释子图需要对SubMT进行精确近似，但我们发现现有XGNNs在拟合SubMT时可能存在巨大差距。SubMT近似失败会导致所提取子图的解释性退化。为解决此问题，我们设计了一种名为图多线性网络（GMT）的新型XGNN架构，该架构在理论上具备更强的SubMT近似能力。我们在多个图分类基准上对理论发现进行了实证验证。结果表明，在12个常规与几何图基准上，GMT在解释性和泛化性方面均以最高10%的优势超越现有最优方法。