The task of inductive link prediction in discrete attributed multigraphs (e.g., knowledge graphs, multilayer networks, heterogeneous networks, etc.) generally focuses on test predictions with solely new nodes but not both new nodes and new relation types. In this work, we formally define the task of predicting (completely) new nodes and new relation types in test as a doubly inductive link prediction task and introduce a theoretical framework for the solution. We start by defining the concept of double permutation-equivariant representations that are equivariant to permutations of both node identities and edge relation types. We then propose a general blueprint to design neural architectures that impose a structural representation of relations that can inductively generalize from training nodes and relations to arbitrarily new test nodes and relations without the need for adaptation, side information, or retraining. We also introduce the concept of distributionally double equivariant positional embeddings designed to perform the same task. Finally, we empirically demonstrate the capability of the two proposed models on a set of novel real-world benchmarks, showcasing average relative performance gains of $39.65\%$ on predicting new relations types compared to baselines.

翻译：离散属性多图（如知识图谱、多层网络、异质网络等）中的归纳式链接预测任务通常仅关注仅包含新节点的测试预测，而无法同时处理新节点与新关系类型。本文正式将测试中预测（全新）节点与新关系类型的任务定义为双重归纳链接预测，并提出相应理论框架。我们首先定义双置换等变表示的概念，该表示对节点身份与边关系类型的置换均具有等变性。随后提出通用蓝图，用于设计神经网络架构：通过强制关系结构表示，使其能够从训练节点与关系归纳泛化至任意新测试节点与关系，无需自适应调整、侧信息或重新训练。同时引入分布双等变位置嵌入的概念以完成相同任务。最终，我们在一组新型真实世界基准上实证展示了两种模型的性能，相较于基线模型，在新关系类型预测中平均相对性能提升达$39.65\%$。