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.

翻译：连续图学习在多种实际应用中扮演着常规角色，这些应用中不同任务的图数据按顺序呈现。尽管先前的研究已取得一定成功，但仍面临巨大挑战。一方面，现有方法基于零曲率欧几里得空间运作，在很大程度上忽略了曲率会随图序列变化的事实。另一方面，文献中的连续学习者依赖于丰富的标签，但在实践中，为图数据标注标签尤为困难，尤其是针对持续出现的动态图。为解决上述挑战，我们提出探索一个具有挑战性且实用的问题——自适应黎曼空间中的自监督连续图学习。本文提出一种新型自监督黎曼图连续学习器（RieGrace）。在RieGrace中，我们首先设计了一种自适应黎曼图卷积网络（AdaRGCN），这是一种与神经曲率适配器耦合的统一图卷积网络，使得黎曼空间可根据每个图的学习曲率进行塑造。随后，我们提出了一种无标签洛伦兹蒸馏方法，其中为图序列创建了教师-学生AdaRGCN模型。学生模型依次执行自蒸馏（从自身）和交叉蒸馏（从教师），从而在不发生灾难性遗忘的情况下巩固知识。特别地，我们提出了一种理论支撑的广义洛伦兹投影，用于黎曼空间中的对比蒸馏。在基准数据集上的大量实验表明RieGrace具有优越性，此外，我们还研究了曲率随图序列的变化规律。