SOAR-SSM: SOBOLEV-REGULARIZED STATE SPACE MODEL WITH ARMA NEURAL NETWORKS FOR TEMPORAL HYPERGRAPH REASONING IN HEALTH CARE

Medical knowledge graphs (MKGs) provide a structured mechanism for incorporating clinical knowledge into electronic health record (EHR) modeling. However, existing MKG-based approaches remain limited in three important aspects. First, they predominantly encode pairwise relations or collapse temporal records into static graphs, thereby overlooking higher-order clinical interactions and their evolution across visits. Second, graph representations are commonly learned using message-passing operators that exhibit a strong low-frequency bias and are susceptible to oversmoothing, potentially suppressing localized and clinically salient variations distributed across different spectral regimes. Third, existing approaches often lack an explicit mechanism for preserving long-range patient history. To address these limitations, we propose SoAR-SSM, a Sobolev-regularized State Space Model with Auto Regressive Moving Average (ARMA) hypergraph neural networks for frequency-aware temporal hypergraph reasoning. SoAR-SSM represents each clinical visit as a knowledge-infused hypergraph to capture higher-order interactions among conditions, procedures, and medications. We then derive a Sobolev-regularized temporal SSM from first principles, yielding a topology-aware spectral operator that governs how structural information is injected into long-range temporal memory. To obtain a more expressive spectral realization, we approximate this operator using parallel ARMA hypergraph neural networks, whose rational responses enable the model to capture complementary information across multiple frequency regimes while mitigating oversmoothing. We evaluate SoAR-SSM on MIMIC-III and MIMIC-IV across multiple clinical prediction tasks. The results demonstrate the effectiveness of jointly modeling higher-order clinical interactions, multi-frequency structural information, and long-range temporal dependencies, while maintaining parameter-efficient EHR representation learning.