  Few-shot knowledge graph (KG) completion task aims to perform inductive
reasoning over the KG: given only a few support triplets of a new relation
$\bowtie$ (e.g., (chop,$\bowtie$,kitchen), (read,$\bowtie$,library), the goal
is to predict the query triplets of the same unseen relation $\bowtie$, e.g.,
(sleep,$\bowtie$,?). Current approaches cast the problem in a meta-learning
framework, where the model needs to be first jointly trained over many training
few-shot tasks, each being defined by its own relation, so that
learning/prediction on the target few-shot task can be effective. However, in
real-world KGs, curating many training tasks is a challenging ad hoc process.
Here we propose Connection Subgraph Reasoner (CSR), which can make predictions
for the target few-shot task directly without the need for pre-training on the
human curated set of training tasks. The key to CSR is that we explicitly model
a shared connection subgraph between support and query triplets, as inspired by
the principle of eliminative induction. To adapt to specific KG, we design a
corresponding self-supervised pretraining scheme with the objective of
reconstructing automatically sampled connection subgraphs. Our pretrained model
can then be directly applied to target few-shot tasks on without the need for
training few-shot tasks. Extensive experiments on real KGs, including NELL,
FB15K-237, and ConceptNet, demonstrate the effectiveness of our framework: we
show that even a learning-free implementation of CSR can already perform
competitively to existing methods on target few-shot tasks; with pretraining,
CSR can achieve significant gains of up to 52% on the more challenging
inductive few-shot tasks where the entities are also unseen during
(pre)training.
