Topology-aware Embedding Memory for Learning on Expanding Graphs

Memory replay based techniques have shown great success for continual learning with incrementally accumulated Euclidean data. Directly applying them to continually expanding graphs, however, leads to the potential memory explosion problem due to the need to buffer representative nodes and their associated topological neighborhood structures. To this end, we systematically analyze the key challenges in the memory explosion problem, and present a general framework, i.e., Parameter Decoupled Graph Neural Networks (PDGNNs) with Topology-aware Embedding Memory (TEM), to tackle this issue. The proposed framework not only reduces the memory space complexity from $\mathcal{O}(nd^L)$ to $\mathcal{O}(n)$~\footnote{$n$: memory budget, $d$: average node degree, $L$: the radius of the GNN receptive field}, but also fully utilizes the topological information for memory replay. Specifically, PDGNNs decouple trainable parameters from the computation ego-subgraph via \textit{Topology-aware Embeddings} (TEs), which compress ego-subgraphs into compact vectors (i.e., TEs) to reduce the memory consumption. Based on this framework, we discover a unique \textit{pseudo-training effect} in continual learning on expanding graphs and this effect motivates us to develop a novel \textit{coverage maximization sampling} strategy that can enhance the performance with a tight memory budget. Thorough empirical studies demonstrate that, by tackling the memory explosion problem and incorporating topological information into memory replay, PDGNNs with TEM significantly outperform state-of-the-art techniques, especially in the challenging class-incremental setting.