Representation learning on dynamic graphs requires capturing complex dependencies that evolve across both time and structure. Existing approaches typically adopt fixed temporal decay schemes or predetermined structural propagation depths, limiting their ability to generalize across graphs with diverse interaction frequencies and topological characteristics. We propose Dual-Scale Retentive Dynamics (DSRD), a unified framework that maintains a retentive representation state encoding both temporal memory and structural context. DSRD introduces two key components: (i) a retentive state with dual-scale adaptation that jointly models temporal dynamics and structural propagation within a single recurrent formulation, and (ii) adaptive decay kernels with learnable time-sensitivity parameters that automatically balance short-term responsiveness and long-term retention based on the underlying interaction patterns. We provide theoretical analysis establishing the equivalence between event-wise parallel aggregation and efficient recurrent state updates, as well as stability and boundedness guarantees for the learned dynamics. Extensive experiments on 14 real-world benchmarks demonstrate that DSRD consistently achieves state-of-the-art performance on both link prediction and node classification tasks, with strong generalization across transductive and inductive settings.
Dynamic graphs are widely used to model time-evolving relational systems in real-world applications. Dynamic graph neural networks provide an effective framework for capturing both structural dependencies and temporal dynamics in such data. However, they typically intertwine temporal graph propagation with every optimization epoch and often maintain large trainable representations for each node-time pair. This design repeatedly recomputes largely unchanged historical structures, leading to substantial training and parameter overhead. To address this critical issue, we propose CacheDyG, a Cache-refine framework for efficient Dynamic Graph learning. Specifically, it decouples temporal propagation from routine parameter updates by constructing a time-ordered temporal dependency cache that stores graph-aware node-time representations in non-trainable buffers. During standard training epochs, CacheDyG reads from the cache and updates only a lightweight cache refiner, an adaptive residual gate, and the link predictor. Selective cache refresh further keeps cached representations aligned with the supervised objective while avoiding epoch-wise sparse propagation. Experiments on five dynamic graph benchmarks show that CacheDyG adopts substantially fewer trainable parameters and lower runtime to obtain more competitive predictive performance than baselines. These results demonstrate that cache-based decoupling provides an effective principle for scalable dynamic graph learning.
The rich information underlying graphs has inspired further investigation of unsupervised graph representation. Existing studies mainly depend on node features and topological properties within static graphs to create self-supervised signals, neglecting the temporal components carried by real-world graph data, such as timestamps of edges. To overcome this limitation, this paper explores how to model temporal evolution on dynamic graphs elegantly. Specifically, we introduce a new inductive bias, namely temporal translation invariance, which illustrates the tendency of the identical node to keep similar labels across different timespans. Based on this assumption, we develop a dynamic graph representation framework CLDG that encourages the node to maintain locally consistent temporal translation invariance through contrastive learning on different timespans. Except for standard CLDG which only considers explicit topological links, our further proposed CLDG++ additionally employs graph diffusion to uncover global contextual correlations between nodes, and designs a multi-scale contrastive learning objective composed of local-local, local-global, and global-global contrasts to enhance representation capabilities. Interestingly, by measuring the consistency between different timespans to shape anomaly indicators, CLDG and CLDG++ are seamlessly integrated with the task of spotting anomalies on dynamic graphs, which has broad applications in many high-impact domains, such as finance, cybersecurity, and healthcare. Experiments demonstrate that CLDG and CLDG++ both exhibit desirable performance in downstream tasks including node classification and dynamic graph anomaly detection. Moreover, CLDG significantly reduces time and space complexity by implicitly exploiting temporal cues instead of complicated sequence models.
Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs (CTDG-SSM) from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator (CTT-HiPPO), a novel memory-based reformulation of HiPPO to jointly encode temporal dynamics and graph structure. The solution from CTT-HiPPO is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs (CTDG-SSM). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation. Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, CTDG-SSM achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.