Analytic Drift Resister for Non-Exemplar Continual Graph Learning

Lei Song; Shihan Guan; Youyong Kong

cs.LGApr 3, 2026

Analytic Drift Resister for Non-Exemplar Continual Graph Learning

Authors: Lei Song, Shihan Guan, Youyong Kong

Organizations: School of Computer Science and Engineering, Southeast University, Nanjnig 211189, China

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 & tables

Fig. 1: A schematic overview of different Continual Graph Learning paradigms.

Fig. 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.

Datasets	CS-CL	CoraFull-CL	Arxiv-CL	Reddit-CL
# nodes	18333	19793	169343	232965
# edges	163788	126842	1166243	114615892
# features	6805	8710	128	602
# all classes	15	70	40	40
# base classes	5	30	20	20
# incremental classes	10	40	20	20

TABLE I: Key statistical characteristics of four node classification benchmarks.

Methods	CS-CL		CoraFull-CL		Arxiv-CL		Reddit-CL
Methods	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)
Joint	-	88.92 $\pm$ 0.25	-	61.62 $\pm$ 0.26	-	42.11 $\pm$ 0.20	-	79.82 $\pm$ 0.69
Bare	53.24 $\pm$ 1.83	34.54 $\pm$ 6.39	17.55 $\pm$ 0.15	3.75 $\pm$ 0.90	18.16 $\pm$ 0.10	8.99 $\pm$ 0.02	40.47 $\pm$ 0.91	12.64 $\pm$ 1.97
LWF	62.59 $\pm$ 1.40	38.40 $\pm$ 2.30	18.53 $\pm$ 0.75	6.91 $\pm$ 1.17	17.64 $\pm$ 0.18	8.97 $\pm$ 0.05	37.73 $\pm$ 0.76	12.76 $\pm$ 2.45
EWC	72.76 $\pm$ 3.04	49.67 $\pm$ 5.28	20.23 $\pm$ 0.40	5.44 $\pm$ 1.92	17.01 $\pm$ 0.15	8.91 $\pm$ 0.03	40.93 $\pm$ 0.74	8.82 $\pm$ 0.04
MAS	75.22 $\pm$ 2.02	66.91 $\pm$ 2.09	19.21 $\pm$ 0.29	9.09 $\pm$ 1.83	17.68 $\pm$ 0.49	8.81 $\pm$ 0.51	53.02 $\pm$ 3.55	33.11 $\pm$ 4.24

TABLE II: Performance comparison on the four benchmarks. The best results are highlighted in bold, and the second-best results are underlined.

Variants	CS-CL		CoraFull-CL		Arxiv-CL		Reddit-CL
Variants	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)	$\mathcal{A}_{avg}$ (%)	$\mathcal{A}_{f}$ (%)
w/o HAM	52.28 $\pm$ 1.27	36.63 $\pm$ 2.92	17.36 $\pm$ 0.19	7.65 $\pm$ 0.99	20.07 $\pm$ 0.06	9.01 $\pm$ 0.02	43.83 $\pm$ 0.67	17.43 $\pm$ 1.75
w/ Simple Averaging	65.08 $\pm$ 1.31	48.79 $\pm$ 1.91	31.83 $\pm$ 0.48	24.75 $\pm$ 0.95	23.23 $\pm$ 0.20	15.17 $\pm$ 0.37	69.29 $\pm$ 2.12	48.23 $\pm$ 1.89
w/ Fisher Merging	69.07 $\pm$ 2.58	58.01 $\pm$ 5.32	27.68 $\pm$ 0.66	18.64 $\pm$ 1.39	26.06 $\pm$ 1.33	10.15 $\pm$ 0.23	68.53 $\pm$ 2.78	48.42 $\pm$ 3.25
w/ MAGMAX Merging	67.23 $\pm$ 0.78	57.34 $\pm$ 3.98	31.08 $\pm$ 1.16	21.91 $\pm$ 1.82	21.66 $\pm$ 0.24	9.64 $\pm$ 0.20	70.15 $\pm$ 1.03	50.81 $\pm$ 3.52
ADR	90.71 $\pm$ 0.22	87.21 $\pm$ 0.42	67.52 $\pm$ 0.83	60.03 $\pm$ 1.22	39.66 $\pm$ 0.43	34.74 $\pm$ 0.21	82.52 $\pm$ 0.21	75.45 $\pm$ 0.40

TABLE III: Ablation studies of HAM on the four benchmarks. The best results are highlighted in bold.

Fig. 3: Model plasticity comparison of our ADR versus existing ACL methods on the four benchmarks.

Panel of Figure 7 — Fig. 4: Feature drift visualization of EFC, DPCR, and ADR on the base task graph $\mathcal{G}_{0}$ across CS-CL and CoraFull-CL benchmarks.

Panel of Figure 8 — Fig. 5: Visualization of the grid search over hyperparameters $\alpha$ and $\gamma$ , with $\mathcal{A}_{avg}$ reported.

Fig. 6: Learning dynamics over the task streams on CS-CL, CoraFull-CL, Arxiv-CL, and Reddit-CL, with $\mathcal{A}_{t}$ reported for all tasks.

Panel of Figure 10 — Fig. 7: Left three panels: Performance matrices for ACIL, DS-AL, and ADR on the test set of Arxiv-CL. Rightmost panel: Quantification of intra-task class imbalance in the training set of Arxiv-CL.

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DRIFT: A Benchmark for Task-Free Continual Graph Learning with Continuous Distribution Shifts

Guiquan Sun, Xikun Zhang, Jingchao Ni, Dongjin Song

University of Connecticut · RMIT University · University of Houston

Distribution Shift Continual Learning

Open paper AskPDF arXiv

Continual graph learning (CGL) aims to learn from dynamically evolving graphs while mitigating catastrophic forgetting. Existing CGL approaches typically adopt a task-based formulation, where the data stream is partitioned into a sequence of discrete tasks with pre-defined boundaries. However, such assumptions rarely hold in real-world environments, where data distributions evolve continuously and task identity is often unavailable. To better reflect realistic non-stationary environments, we revisit continual graph learning from a task-free perspective. We propose a unified formulation that models the data stream as a time-varying mixture of latent task distributions, enabling continuous modeling of distribution drift. Based on this formulation, we construct DRIFT, a benchmark that spans a spectrum of transition dynamics ranging from hard task switches to smooth distributional drift through a Gaussian parameterization. We evaluate representative continual learning methods under this task-free setting and observe substantial performance degradation compared to traditional task-based protocols. Our findings indicate that many existing approaches implicitly rely on task boundary information and struggle under realistic task-free graph streams. This work highlights the importance of studying continual graph learning under realistic non-stationary conditions and provides a benchmark for future research in this direction. Our code is available at https://github.com/UConn-DSIS/DRIFT.

Abstract

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