Out-of-distribution (OOD) graph generalization are critical for many real-world applications. Existing methods neglect to discard spurious or noisy features of inputs, which are irrelevant to the label. Besides, they mainly conduct instance-level class-invariant graph learning and fail to utilize the structural class relationships between graph instances. In this work, we endeavor to address these issues in a unified framework, dubbed Individual and Structural Graph Information Bottlenecks (IS-GIB). To remove class spurious feature caused by distribution shifts, we propose Individual Graph Information Bottleneck (I-GIB) which discards irrelevant information by minimizing the mutual information between the input graph and its embeddings. To leverage the structural intra- and inter-domain correlations, we propose Structural Graph Information Bottleneck (S-GIB). Specifically for a batch of graphs with multiple domains, S-GIB first computes the pair-wise input-input, embedding-embedding, and label-label correlations. Then it minimizes the mutual information between input graph and embedding pairs while maximizing the mutual information between embedding and label pairs. The critical insight of S-GIB is to simultaneously discard spurious features and learn invariant features from a high-order perspective by maintaining class relationships under multiple distributional shifts. Notably, we unify the proposed I-GIB and S-GIB to form our complementary framework IS-GIB. Extensive experiments conducted on both node- and graph-level tasks consistently demonstrate the superior generalization ability of IS-GIB. The code is available at https://github.com/YangLing0818/GraphOOD.

翻译：分布外（OOD）图泛化对许多实际应用至关重要。现有方法忽略了丢弃输入中与标签无关的虚假或噪声特征。此外，它们主要进行实例级类不变图学习，未能利用图实例之间的结构类关系。在本工作中，我们致力于在一个统一框架内解决这些问题，称为个体与结构图信息瓶颈（IS-GIB）。为去除分布偏移导致的类虚假特征，我们提出个体图信息瓶颈（I-GIB），通过最小化输入图与其嵌入之间的互信息来丢弃无关信息。为利用结构性的域内和域间相关性，我们提出结构图信息瓶颈（S-GIB）。具体地，对于包含多个域的一批图，S-GIB首先计算成对的输入-输入、嵌入-嵌入和标签-标签相关性，然后最小化输入图与嵌入对之间的互信息，同时最大化嵌入与标签对之间的互信息。S-GIB的关键洞察在于通过维护多重分布偏移下的类关系，从高阶视角同时丢弃虚假特征并学习不变特征。值得注意的是，我们将所提I-GIB和S-GIB统一为互补框架IS-GIB。在节点级和图级任务上进行的广泛实验一致表明IS-GIB具有优越的泛化能力。代码可在 https://github.com/YangLing0818/GraphOOD 获取。