Time-Varying Graph Learning with Constraints on Graph Temporal Variation

Temporal graph learning has become essential for analyzing real-world systems whose interactions continuously evolve over time, including financial transaction networks, communication systems, and online social platforms. However, learning from large-scale temporal graphs remains computationally challenging when networks are dense and rapidly changing. To address this limitation, we propose a network-curvature-inspired edge sparsification framework for dynamic graph learning. Our proposed method, TRicci, extends classical Forman-Ricci curvature to directed weighted temporal graphs by capturing structural support, temporal recency, and local interaction competition. Experiments on 9 transaction networks and 3 temporal graph benchmark datasets demonstrate that the proposed framework preserves predictive performance across multiple graph-level prediction tasks. The results show that TRicci sparsifies temporal graphs by approximately 80% while reducing end-to-end downstream training and inference time by an average of 55.94%, without substantial degradation in predictive performance. Our findings suggest that temporal curvature can serve as a principled basis for scalable temporal graph learning by preserving predictive temporal-structural information under substantial sparsification.

Temporal graph networks suffer from irregular supervision in realworld dynamic graphs, as most minibatches contain few labeled events. The lack of labels leads to high-variance gradient updates and, consequently, slow wall-clock convergence. To constructively reduce sparsity, our Moving-Averaged Labels (MAL) assigns soft pseudo-targets based on past supervised signals using a running label distribution while leaving the loss and the model architecture unchanged. Thus, supervision gaps are replaced with informative signals independent of a temporal graph model and the message passing or memory components used. Theoretical analysis supports our insight that aggregating historical supervision into moving average targets reduces stochastic gradient variance, yielding faster convergence under mild assumptions. Experimentally, for TGNv2 and DyRepv2 (our modification of DyRep) models, MAL boosts predictive performance, establishing a new SOTA, and improves time-to-accuracy (on average 6x faster to reach the top score) for a common suite of Temporal Graph Benchmark datasets.

This work focuses on the problem of learning on temporal graphs, with particular emphasis on the task of clustering: obtaining coarse-grained representations by aggregating information from nodes, edges, and temporal dynamics - a task related to pooling in machine learning on graphs, or community detection in network science. Although graph neural networks reach state-of-the-art performance across many downstream graph tasks, their advantage over established descriptive and inferential clustering algorithms is far less settled, especially under demands of efficiency and recovery accuracy. We frame this tension through three linked perspectives: principles, connecting graph learning and community detection through shared spectral foundations and detectability thresholds in stochastic block model regimes; primitives, making spectral clustering and multislice modularity optimization tractable through GPU-accelerated temporal backends; and pooling, viewing principled community detection as a theory-grounded coarse-graining operator for temporal graphs. Our results indicate that algorithmic methods remain the appropriate tool where attributes are absent or weak - scalability rather than accuracy being the binding obstacle - while neural models are most compelling when structural, temporal, and attribute signals align. By making temporal clustering scalable, GPU-accelerated primitives suggest a route toward theory-grounded pooling, while raising a central question: when does community-based coarse-graining preserve the dynamics needed for downstream learning tasks?