  Graphs are typical non-Euclidean data of complex structures. In recent years,
Riemannian graph representation learning has emerged as an exciting alternative
to Euclidean ones. However, Riemannian methods are still in an early stage:
most of them present a single curvature (radius) regardless of structural
complexity, suffer from numerical instability due to the
exponential/logarithmic map, and lack the ability to capture motif regularity.
In light of the issues above, we propose the problem of \emph{Motif-aware
Riemannian Graph Representation Learning}, seeking a numerically stable encoder
to capture motif regularity in a diverse-curvature manifold without labels. To
this end, we present a novel Motif-aware Riemannian model with
Generative-Contrastive learning (MotifRGC), which conducts a minmax game in
Riemannian manifold in a self-supervised manner. First, we propose a new type
of Riemannian GCN (D-GCN), in which we construct a diverse-curvature manifold
by a product layer with the diversified factor, and replace the
exponential/logarithmic map by a stable kernel layer. Second, we introduce a
motif-aware Riemannian generative-contrastive learning to capture motif
regularity in the constructed manifold and learn motif-aware node
representation without external labels. Empirical results show the superiority
of MofitRGC.
