HoT-SSM:Higher-order Temporal Knowledge Graph Reasoning with State Space Models for Health Care

Learning from Electronic Health Records (EHRs) has gained significant attention due to its potential to improve clinical prediction. However, effective learning remains challenging because EHRs encode heterogeneous, temporally ordered clinical interactions. In particular, EHRs contain: (i) heterogeneous clinical entities, including patients, visits, diagnoses, prescriptions, and procedures, together with their heterogeneous interactions, (ii) longitudinal patient trajectories across hospital visits and (iii) shared statistical dependencies across related clinical prediction tasks. Existing EHR learning methods capture only a subset of these properties. To bridge this gap, we propose Multi-task Graph transformer for Heterogeneous Temporal EHRs (MiGHT-EHR), which jointly models all three within a unified representation learning method. MiGHT-EHR constructs a heterogeneous graph from EHRs in which nodes represent clinical entities and edges connect statistically associated entities identified via normalized point-wise mutual information. Across MIMIC-III and MIMIC-IV datasets, MiGHT-EHR outperforms state-of-the-art methods on average across four tasks: drug recommendation, prediction of length-of-stay, mortality, and readmission, with particularly strong improvements in mortality and readmission prediction. Furthermore, a post-hoc analysis of the learned representations reveals that patient neighborhoods are organized by clinical outcomes, salient medical concepts are recoverable as linear directions in the representation space, and task probabilities are well calibrated. Collectively, these findings demonstrate that MiGHT-EHR representations support diverse prediction tasks while preserving clinically interpretable structure.

Continuous-time dynamic graphs (CTDGs) provide a richer framework to capture fine-grained temporal patterns in evolving relational data. Long-range information propagation is a key challenge while learning representations, wherein it is important to retain and update information over long temporal horizons. Existing approaches restrict models to capture one-hop or local temporal neighborhoods and fail to capture multi-hop or global structural patterns. To mitigate this, we derive a parameter-efficient state-space modeling framework for continuous-time dynamic graphs (CTDG-SSM) from first principles. We first introduce continuous-time Topology-Aware higher order polynomial projection operator (CTT-HiPPO), a novel memory-based reformulation of HiPPO to jointly encode temporal dynamics and graph structure. The solution from CTT-HiPPO is obtained by projecting the classical HiPPO solution through a polynomial of the Laplacian matrix, yielding topology-aware memory updates that admit an equivalent state-space formulation for CTDGs (CTDG-SSM). Then a computationally efficient discrete formulation is obtained using the zero-order hold approach for model implementation. Across benchmarks on dynamic link prediction, dynamic node classification, and sequence classification, CTDG-SSM achieves state-of-the-art performance. Notably, it achieves large performance gains on datasets that require long range temporal (LRT) and spatial reasoning.

Clinical irregular multivariate time series are shaped not only by physiological dynamics but also by the measurement process that determines when and what to observe. In event-centric models, however, co-timestamp structure can be flattened too early: measurements acquired at the same timestamp are embedded as isolated nodes, leaving local patient-state context unavailable until later message-passing layers. We study this pre-propagation representation bottleneck and address it by restoring co-timestamp context before message passing begins. We propose MissHyper, a missingness-guided hypergraph forecasting model with pre-propagation synchronicity restoration. MissHyper augments each event with a local support-density cue, aggregates co-timestamp records to recover patient-state context, and uses a missingness-guided gate to adaptively fuse node-specific evidence with the recovered context. Across PhysioNet 2012, MIMIC-III, and MIMIC-IV, MissHyper achieves consistent gains in multi-step forecasting and outperforms a strong hypergraph baseline. These results suggest that improving event initialization can benefit sparse clinical forecasting without requiring a redesigned downstream propagation architecture. Ablations indicate that snapshot restoration, adaptive fusion, and support-density encoding all contribute, pointing to event initialization as a critical design axis for sparse clinical forecasting.