  Memory replay based techniques have shown great success for continual
learning with incrementally accumulated Euclidean data. Directly applying them
to continually expanding networks, 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, \textit{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-subnetwork via
\textit{Topology-aware Embeddings} (TEs), which compress ego-subnetworks into
compact vectors (\textit{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 networks 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.
