An event sequence generated by a temporal point process is often associated with a hidden and structured event branching process that captures the triggering relations between its historical and current events. In this study, we design a new plug-and-play module based on the Bregman ADMM (BADMM) algorithm, which infers event branches associated with event sequences in the maximum likelihood estimation framework of temporal point processes (TPPs). Specifically, we formulate the inference of event branches as an optimization problem of event transition matrix under sparse and low-rank constraints, which is embedded in existing TPP models or their learning paradigms. We can implement this optimization problem based on subspace clustering and sparse group-lasso, respectively, and solve it using the Bregman ADMM algorithm, whose unrolling leads to the proposed BADMM module. When learning a classic TPP (e.g., Hawkes process) by the expectation-maximization algorithm, the BADMM module helps derive structured responsibility matrices in the E-step. Similarly, the BADMM module helps derive low-rank and sparse attention maps for the neural TPPs with self-attention layers. The structured responsibility matrices and attention maps, which work as learned event transition matrices, indicate event branches, e.g., inferring isolated events and those key events triggering many subsequent events. Experiments on both synthetic and real-world data show that plugging our BADMM module into existing TPP models and learning paradigms can improve model performance and provide us with interpretable structured event branches.

We propose TPP-SD, a novel approach that accelerates Transformer temporal point process (TPP) sampling by adapting speculative decoding (SD) techniques from language models. By identifying the structural similarities between thinning algorithms for TPPs and speculative decoding for language models, we develop an efficient sampling framework that leverages a smaller draft model to generate multiple candidate events, which are then verified by the larger target model. TPP-SD maintains the same output distribution as autoregressive sampling while achieving significant acceleration. Experiments on both synthetic and real datasets demonstrate that our approach produces samples from identical distributions as standard methods, but with 2-6$\times$ speedup. Our ablation studies analyze the impact of hyperparameters such as draft length and draft model size on sampling efficiency. TPP-SD bridges the gap between powerful Transformer TPP models and the practical need for rapid sequence generation.

Graph neural networks (GNNs) have achieved remarkable success in various domains but typically rely on centralized, static graphs, which limits their applicability in distributed, evolving environments. To address this limitation, we define the task of Federated Continual Graph Learning (FCGL), a paradigm for incremental learning on dynamic graphs distributed across decentralized clients. Existing methods, however, neither preserve graph topology during task transitions nor mitigate parameter conflicts in server‐side aggregation. To overcome these challenges, we introduce **MOTION**, a generalizable FCGL framework that integrates two complementary modules: the Graph Topology‐preserving Multi‐Sculpt Coarsening (G‐TMSC) module, which maintains the structural integrity of past graphs through a multi‐expert, similarity‐guided fusion process, and the Graph‐Aware Evolving Parameter Adaptive Engine (G‐EPAE) module, which refines global model updates by leveraging a topology‐sensitive compatibility matrix. Extensive experiments on real‐world datasets show that our approach improves average accuracy (AA) by an average of 30\% $\uparrow$ over the FedAvg baseline across five datasets while maintaining a negative $\downarrow$ average forgetting (AF) rate, significantly enhancing generalization and robustness under FCGL settings. The code is available for anonymous access at https://anonymous.4open.science/r/MOTION.