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.

The application of graph representation learning techniques to the area of financial risk management (FRM) has attracted significant attention recently. However, directly modeling transaction networks using graph neural models remains challenging: Firstly, transaction networks are directed multigraphs by nature, which could not be properly handled with most of the current off-the-shelf graph neural networks (GNN). Secondly, a crucial problem in FRM scenarios like anti-money laundering (AML) is to identify risky transactions and is most naturally cast into an edge classification problem with rich edgelevel features, which are not fully exploited by the prevailing GNN design that follows node-centric message passing protocols. In this paper, we present a systematic investigation of design aspects of neural models over directed multigraphs and develop a novel GNN protocol that overcomes the above challenges via efficiently incorporating directional information, as well as proposing an enhancement that targets edge-related tasks using a novel message passing scheme over an extension of edge-to-node dual graph. A concrete GNN architecture called GRANDE is derived using the proposed protocol, with several further improvements and generalizations to temporal dynamic graphs. We apply the GRANDE model to both a real-world anti-money laundering task and public datasets. Experimental evaluations show the superiority of the proposed GRANDE architecture over recent state-of-the-art models on dynamic graph modeling and directed graph modeling.