Edge Sparsification via Temporal Forman-Ricci Curvature for Dynamic Graph Learning

We propose a novel framework for learning time-varying graphs from spatiotemporal measurements. Given an appropriate prior on the temporal behavior of signals, our proposed method can estimate time-varying graphs from a small number of available measurements. To achieve this, we introduce three regularization terms in convex optimization problems that constrain the sparseness of temporal variations of the time-varying networks. Moreover, a computationally scalable algorithm is introduced to solve the optimization problem efficiently. The experimental results with synthetic and real datasets (point cloud, temperature, and EEG data) demonstrate that our proposed method outperforms state-of-the-art methods.

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.

Predicting links in sparse, continuously evolving networks is a central challenge in network science. Conventional heuristic methods and deep learning models, including Graph Neural Networks (GNNs), are typically designed for static graphs and thus struggle to capture temporal dependencies. Snapshot-based techniques partially address this issue but often encounter data sparsity and class imbalance, particularly in networks with transient interactions such as telecommunication call detail records (CDRs). Temporal Graph Networks (TGNs) model dynamic graphs by updating node embeddings over time; however, their predictive accuracy under sparse conditions remains limited. In this study, we improve the TGN framework by extracting enclosing subgraphs around candidate links, enabling the model to jointly learn structural and temporal information. Experiments on a sparse CDR, email, message dataset show that our approach increases average precision by at least 2% over standard TGNs, demonstrating the advantages of integrating local topology for robust link prediction in dynamic networks.