Over the past few years, research on deep graph learning has shifted from static graphs to temporal graphs in response to real-world complex systems that exhibit dynamic behaviors. In practice, temporal graphs are formalized as an ordered sequence of static graph snapshots observed at discrete time points. Sequence models such as RNNs or Transformers have long been the predominant backbone networks for modeling such temporal graphs. Yet, despite the promising results, RNNs struggle with long-range dependencies, while transformers are burdened by quadratic computational complexity. Recently, state space models (SSMs), which are framed as discretized representations of an underlying continuous-time linear dynamical system, have garnered substantial attention and achieved breakthrough advancements in independent sequence modeling. In this work, we undertake a principled investigation that extends SSM theory to temporal graphs by integrating structural information into the online approximation objective via the adoption of a Laplacian regularization term. The emergent continuous-time system introduces novel algorithmic challenges, thereby necessitating our development of GraphSSM, a graph state space model for modeling the dynamics of temporal graphs. Extensive experimental results demonstrate the effectiveness of our GraphSSM framework across various temporal graph benchmarks.

Graph convolutional networks (GCNs) play a critical role in improving the performance of collaborative filtering. They leverage the concept of aggregating neighbor information to capture user preferences on bipartite graphs by stacking multiple convolutional layers. However, this requirement for layer stacking often leads to a long training time for convergence, and results in indistinguishable representations with significant performance deterioration due to the problem of oversmoothing. Additionally, the noise of interactions will be amplified by the stacking of convolutional layers through message passing. To address these issues, we propose a simple, plug-and-play-Neighborhood Structure -Embedding approach, named NSE, which utilizes first-order adjacency information to construct structural embeddings. By explicitly incorporating local topologically statistical information before message passing, the embeddings propagated at GCNs have better topology-structure awareness. This leads to an improved optimization path and greater robustness against noise propagation. Experimental results demonstrate significant performance improvements by employing our proposed NSE in graph collaborative filtering models. Particularly, the NSE-enhanced LGCN shows performance gains of 5.06% and 4.86% on the Yelp and Amazon-Books datasets, respectively. The average training convergence speed is improved by 204.8%. NSE-enhanced graph collaborative filtering has also demonstrated excellent robustness against both noise and oversmoothing.