  Continual graph learning routinely finds its role in a variety of real-world
applications where the graph data with different tasks come sequentially.
Despite the success of prior works, it still faces great challenges. On the one
hand, existing methods work with the zero-curvature Euclidean space, and
largely ignore the fact that curvature varies over the coming graph sequence.
On the other hand, continual learners in the literature rely on abundant
labels, but labeling graph in practice is particularly hard especially for the
continuously emerging graphs on-the-fly. To address the aforementioned
challenges, we propose to explore a challenging yet practical problem, the
self-supervised continual graph learning in adaptive Riemannian spaces. In this
paper, we propose a novel self-supervised Riemannian Graph Continual Learner
(RieGrace). In RieGrace, we first design an Adaptive Riemannian GCN (AdaRGCN),
a unified GCN coupled with a neural curvature adapter, so that Riemannian space
is shaped by the learnt curvature adaptive to each graph. Then, we present a
Label-free Lorentz Distillation approach, in which we create teacher-student
AdaRGCN for the graph sequence. The student successively performs
intra-distillation from itself and inter-distillation from the teacher so as to
consolidate knowledge without catastrophic forgetting. In particular, we
propose a theoretically grounded Generalized Lorentz Projection for the
contrastive distillation in Riemannian space. Extensive experiments on the
benchmark datasets show the superiority of RieGrace, and additionally, we
investigate on how curvature changes over the graph sequence.
