Information propagation dynamics in Deep Graph Networks

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.

Dynamic graph neural networks (DGNNs) that operate on snapshot sequences typically fall into one of two categories. \emph{Temporal-first} approaches build per-node temporal embeddings and only afterward perform spatial aggregation, whereas \emph{Spatial-first} approaches invert this order, feeding the output of a graph convolution into a downstream temporal module. In either case, the rigid sequencing forces the second stage to consume an already-compressed summary produced by the first, ruling out joint reasoning over topology and evolution; effectively, the message-passing operator never gets to weight a neighbor's contribution by that neighbor's \emph{past} trajectory. This paper introduces \textbf{SiST-GNN} (\textbf{Si}multaneous \textbf{S}patial-\textbf{T}emporal \textbf{GNN}), which fuses the two signals inside a single message-passing operation rather than chaining them. At each snapshot, we maintain a recurrent hidden state per node that summarises its history, pairs it with the node's current feature vector, and treats the pair as two nodes joined by a cross-time edge; running a standard graph convolution on this temporally augmented graph yields the updated representation. We compare against fourteen link-prediction baselines under both the fixed-split and live-update evaluation regimes, and eleven baselines on node classification. Across the public benchmarks, SiST-GNN improves on the strongest prior method in link prediction by 1-18% in the fixed-split setting, and is the leading learned method on five of six datasets in the live-update setting, improving on the strongest prior method by 1-158% there. We additionally derive three dynamic node-classification tasks by discretizing the underlying continuous-time event streams; here SiST-GNN beats the leading discrete-time (DTDG) baseline by 7-23% and matches continuous-time (CTDG) methods that consume the raw events directly.

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.