Efficient Memory Crystallization for Graph Learning under Non-Stationary Distribution Shifts

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.

Pre-trained foundation models have demonstrated remarkable success in many domains, enabling a unified backbone to generalize across diverse downstream tasks. However, extending this paradigm to graph learning remains challenging due to the intrinsic mismatch between graph data and fixed architectural designs. In this work, we show that this limitation can be overcome via recurrent graph models. To achieve this, we conduct a systematic theoretical analysis, rigorously deriving step dependence as a necessary and sufficient condition for an adaptively convergent recurrent process. Building on this foundation, we propose AdaR, an Adaptive Recurrent graph model, empowering flexible test-time computing on various downstream tasks without changing model parameters. To enable adaptive inference, AdaR explicitly encodes normalized step information and representation-target relations into the recurrent updates. To ensure convergence of the recurrent process, AdaR employs gradient-based supervision signals that guide representation updates throughout the recurrence. Empirical results demonstrate that AdaR consistently outperforms strong baselines in both inductive and transductive settings.

This paper addresses domain adaptation in graph-structured data under chronological splits. We consider transductive semi-supervised node classification (SSNC), in which labels of historical nodes are used to predict labels of more recent nodes. Temporal dependencies in graph connectivity induce distribution shifts across time, often degrading the performance of models trained on past nodes. Despite its practical relevance, domain adaptation under chronological graph splits remains relatively underexplored. We propose Symmetric Temporal Averaging Message Passing (STAMP), a timestamp-balanced operator that replaces standard neighborhood aggregation with temporally aligned propagation. We call its specialized variant for the heterogeneous ogbn-mag dataset STAMP-mag, reserving STAMP for the general formulation. By balancing messages across timestamps, STAMP enforces first-moment invariance across temporal domains while remaining scalable and easy to implement. Unlike many existing domain adaptation methods, whose assumptions are difficult to verify on graphs, STAMP relies on transparent, practically checkable conditions and is supported by theoretical analysis. Empirically, STAMP and STAMP-mag improve accuracy across all evaluated temporal graph benchmarks. STAMP achieves state-of-the-art performance on ogbn-arxiv, while STAMP-mag does so on ogbn-mag. For temporal-split Pokec, where no established benchmark exists, applying STAMP to the state-of-the-art model for the original dataset consistently improves performance under our chronological split. These results demonstrate that timestamp-balanced propagation is an effective and practical approach to mitigating temporal distribution shift in graph learning.