  Knowledge graph embedding research has mainly focused on the two smallest
normed division algebras, $\mathbb{R}$ and $\mathbb{C}$. Recent results suggest
that trilinear products of quaternion-valued embeddings can be a more effective
means to tackle link prediction. In addition, models based on convolutions on
real-valued embeddings often yield state-of-the-art results for link
prediction. In this paper, we investigate a composition of convolution
operations with hypercomplex multiplications. We propose the four approaches
QMult, OMult, ConvQ and ConvO to tackle the link prediction problem. QMult and
OMult can be considered as quaternion and octonion extensions of previous
state-of-the-art approaches, including DistMult and ComplEx. ConvQ and ConvO
build upon QMult and OMult by including convolution operations in a way
inspired by the residual learning framework. We evaluated our approaches on
seven link prediction datasets including WN18RR, FB15K-237 and YAGO3-10.
Experimental results suggest that the benefits of learning hypercomplex-valued
vector representations become more apparent as the size and complexity of the
knowledge graph grows. ConvO outperforms state-of-the-art approaches on
FB15K-237 in MRR, Hit@1 and Hit@3, while QMult, OMult, ConvQ and ConvO
outperform state-of-the-approaches on YAGO3-10 in all metrics. Results also
suggest that link prediction performances can be further improved via
prediction averaging. To foster reproducible research, we provide an
open-source implementation of approaches, including training and evaluation
scripts as well as pretrained models.
