Many downstream inference tasks for knowledge graphs, such as relation prediction, have been handled successfully by knowledge graph embedding techniques in the transductive setting. To address the inductive setting wherein new entities are introduced into the knowledge graph at inference time, more recent work opts for models which learn implicit representations of the knowledge graph through a complex function of a network's subgraph structure, often parametrized by graph neural network architectures. These come at the cost of increased parametrization, reduced interpretability and limited generalization to other downstream inference tasks. In this work, we bridge the gap between traditional transductive knowledge graph embedding approaches and more recent inductive relation prediction models by introducing a generalized form of harmonic extension which leverages representations learned through transductive embedding methods to infer representations of new entities introduced at inference time as in the inductive setting. This harmonic extension technique provides the best such approximation, can be implemented via an efficient iterative scheme, and can be employed to answer a family of conjunctive logical queries over the knowledge graph, further expanding the capabilities of transductive embedding methods. In experiments on a number of large-scale knowledge graph embedding benchmarks, we find that this approach for extending the functionality of transductive knowledge graph embedding models to perform knowledge graph completion and answer logical queries in the inductive setting is competitive with--and in some scenarios outperforms--several state-of-the-art models derived explicitly for such inductive tasks.

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