  Sequential interaction networks (SIN) have been commonly adopted in many
applications such as recommendation systems, search engines and social networks
to describe the mutual influence between users and items/products. Efforts on
representing SIN are mainly focused on capturing the dynamics of networks in
Euclidean space, and recently plenty of work has extended to hyperbolic
geometry for implicit hierarchical learning. Previous approaches which learn
the embedding trajectories of users and items achieve promising results.
However, there are still a range of fundamental issues remaining open. For
example, is it appropriate to place user and item nodes in one identical space
regardless of their inherent discrepancy? Instead of residing in a single fixed
curvature space, how will the representation spaces evolve when new interaction
occurs? To explore these issues for sequential interaction networks, we propose
SINCERE, a novel method representing Sequential Interaction Networks on
Co-Evolving RiEmannian manifolds. SIN- CERE not only takes the user and item
embedding trajectories in respective spaces into account, but also emphasizes
on the space evolvement that how curvature changes over time. Specifically, we
introduce a fresh cross-geometry aggregation which allows us to propagate
information across different Riemannian manifolds without breaking conformal
invariance, and a curvature estimator which is delicately designed to predict
global curvatures effectively according to current local Ricci curvatures.
Extensive experiments on several real-world datasets demonstrate the promising
performance of SINCERE over the state-of-the-art sequential interaction
prediction methods.
