Organizations: Key Laboratory of Computational Intelligence and Chinese Information Processing of Ministry of Education, School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi 030006, China. · Department of System Engineering and Engineering Management, City University of Hong Kong, Kowloon 999077, Hong Kong, China. · Key Laboratory of Complex Systems and Data Science of Ministry of Education, Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, China.
Graph neural Ordinary Differential Equations (ODE) combine neural ODE with the message passing mechanism of Graph Neural Networks (GNN), providing a continuous-time modeling method for graph representation learning. However, in dynamic graph scenarios, existing graph neural ODEs typically employ a unified message passing mechanism, assuming that inter-node interactions share the same message passing function at any time, which makes it challenging to capture the diversity and time-varying nature of inter-node interaction patterns. To address this, we propose Time-varying Interaction Graph Ordinary Differential Equations (TI-ODE). The core idea of TI-ODE is to decompose the evolution function of a graph ODE into a set of learnable interaction basis functions, where each basis function corresponds to a distinct type of inter-node interaction. These basis functions are dynamically combined through time-dependent learnable weights, enabling inter-node interaction patterns to adaptively evolve over time. Experimental results on six dynamic graph datasets demonstrate that TI-ODE consistently outperforms existing methods and achieves state-of-the-art performance on attribute prediction tasks, and experiments on the \textit{Covid} dataset further verify the interpretability and generalizability of our TI-ODE. Furthermore, we demonstrate both theoretically and empirically that TI-ODE exhibits superior robustness compared to models utilizing a unified message-passing mechanism.
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.
Graph neural ordinary differential equations (Graph ODEs) extend graph learning from discrete message-passing layers to continuous-time representation flows. While it supports adaptive long-range propagation, we show that Graph ODEs with strictly positive irreducible mixing operators face an inherent \emph{monostability trap}: in the long-time regime, information leakage is unavoidable and the dynamics converge to a single global consensus attractor. We propose the \textbf{Hysteresis Graph ODE (HGODE)}, which couples feature evolution with a latent topological potential driven by a learned pairwise force. A double-well edge potential and bipolarized gate allow edge states to polarize into connected or insulated phases while preserving differentiability. We provide asymptotic analysis of the collapse mechanism and the proposed hysteretic topology dynamics, and validate HGODE on theory-driven synthetic diagnostics and real-world graph benchmarks.