Analytic Drift Resister for Non-Exemplar Continual Graph Learning

Abstract

Non-Exemplar Continual Graph Learning (NECGL) seeks to eliminate the privacy risks intrinsic to rehearsal-based paradigms by retaining solely class-level prototype representations rather than raw graph examples for mitigating catastrophic forgetting. However, this design choice inevitably precipitates feature drift. As a nascent alternative, Analytic Continual Learning (ACL) capitalizes on the intrinsic generalization properties of frozen pre-trained models to bolster continual learning performance. Nonetheless, a key drawback resides in the pronounced attenuation of model plasticity. To surmount these challenges, we propose Analytic Drift Resister (ADR), a novel and theoretically grounded NECGL framework. ADR exploits iterative backpropagation to break free from the frozen pre-trained constraint, adapting to evolving task graph distributions and fortifying model plasticity. Since parameter updates trigger feature drift, we further propose Hierarchical Analytic Merging (HAM), performing layer-wise merging of linear transformations in Graph Neural Networks (GNNs) via ridge regression, thereby ensuring absolute resistance to feature drift. On this basis, Analytic Classifier Reconstruction (ACR) enables theoretically zero-forgetting class-incremental learning. Empirical evaluation on four node classification benchmarks demonstrates that ADR maintains strong competitiveness against existing state-of-the-art methods.

Figures (7)

• Figure 1: A schematic overview of different Continual Graph Learning paradigms.
• Figure 2: The overall pipeline of the proposed ADR. (a) Upon the arrival of a new task $\mathcal{T}_t$, the model adapts freely to the corresponding graph distribution via iterative BP without any imposed regularization. (b) HAM performs analytic merging of the layer-wise linear transformations of all historical task encoders, unifying their latent representation spaces. (c) ACR exploits the merged encoder to derive linear classifier weights, enabling robust class-incremental learning.
• Figure 3: Model plasticity comparison of our ADR versus existing ACL methods on the four benchmarks.
• Figure 4: Feature drift visualization of EFC, DPCR, and ADR on the base task graph $\mathcal{G}_0$ across CS-CL and CoraFull-CL benchmarks.
• Figure 5: Visualization of the grid search over hyperparameters $\alpha$ and $\gamma$, with $\mathcal{A}_{avg}$ reported.