  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.
