Invariant Structural Distillation via Graph Condensation for History-Aware Graph Continual Learning

Graph Continual Learning (GCL) tackles the stability-plasticity dilemma: models must retain historical knowledge while rapidly adapting to evolving graph distributions under restricted observability. Recent graph condensation methods improve stability by compressing past task data into compact, high-fidelity memory. We show that fidelity-focused condensation can lead to Temporally Illusory Invariance: memories that overfit task-specific spurious motifs, which appear stable within a task but fail to transfer as the graph structure evolves. Meanwhile, real-world graph streams often remain structurally connected across tasks. Current-task nodes may still interact with locally observable but unlabeled historical neighbors, even when raw historical graphs and labels are no longer accessible. We formalize this realistic setting as history-aware restricted observability. Exposing historical neighbors creates a tension: it may provide additional context, but it also introduces cross-task neighborhood mixing, which can blur class boundaries and amplify the brittleness of shortcut-based decision rules, ultimately propagating bias and degrading model robustness. To address these challenges, we propose ISD-GC (Invariant Structure Distillation for Graph Condensation), which reframes the memory buffer as a transferable structural prior rather than a fidelity-optimized snapshot, following a Connect-then-Condense principle. First, ISD-GC performs memory-grounded context disambiguation through Virtual Soft Edges, which construct relative evidence between historical memory prototypes and current-task anchors. A calibrated context discriminator further identifies historical candidates and distinguishes beneficial, irrelevant, and harmful context for selective message passing. Second, ISD-GC condenses each task into structure-invariant prototypes by distilling cross-view consistent structural information across complementary graph views and stochastic structural perturbations. This approach suppresses brittle motif reliance and improves transferability under structural drift. Extensive experiments on multiple class-incremental GCL benchmarks, supported by a controlled Motif Trap diagnostic, demonstrate that ISD-GC significantly enhances long-term retention, robustness, and memory-budget efficiency under strict memory budgets, particularly in realistic history-aware settings.