Knowledge Graph Completion (KGC) has garnered massive research interest recently, and most existing methods are designed following a transductive setting where all entities are observed during training. Despite the great progress on the transductive KGC, these methods struggle to conduct reasoning on emerging KGs involving unseen entities. Thus, inductive KGC, which aims to deduce missing links among unseen entities, has become a new trend. Many existing studies transform inductive KGC as a graph classification problem by extracting enclosing subgraphs surrounding each candidate triple. Unfortunately, they still face certain challenges, such as the expensive time consumption caused by the repeat extraction of enclosing subgraphs, and the deficiency of entity-independent feature learning. To address these issues, we propose a global-local anchor representation (GLAR) learning method for inductive KGC. Unlike previous methods that utilize enclosing subgraphs, we extract a shared opening subgraph for all candidates and perform reasoning on it, enabling the model to perform reasoning more efficiently. Moreover, we design some transferable global and local anchors to learn rich entity-independent features for emerging entities. Finally, a global-local graph reasoning model is applied on the opening subgraph to rank all candidates. Extensive experiments show that our GLAR outperforms most existing state-of-the-art methods.

Designing algorithms to solve math word problems (MWPs) is an important research topic in natural language processing and smart education domains. The task of solving MWPs involves transforming math problem texts into math equations. Although recent Graph2Tree-based models, which adopt homogeneous graph encoders to learn quantity representations, have obtained very promising results in generating math equations, they do not consider the heterogeneous issue and the long-distance dependencies of heterogeneous nodes. In this paper, we propose a novel hierarchical heterogeneous graph encoding called HGEN for MWPs. Specifically, HGEN first introduces a heterogeneous graph consisting of a node-level attention layer and a type-aware attention layer to learn the heterogeneous node embedding. HGEN then captures the long-distance dependent information by propagating the multi-hop nodes in a hierarchical manner. We conduct extensive experiments on two popular MWP datasets. Our empirical results show that HGEN significantly outperforms the state-of-the-art Graph2Tree-based models in the literature.