Medication recommendation (MR) is critical for clinical decision support. While existing MR methods are mostly designed for single-center learning, where only one independent hospital is involved, multi-center MR with hospitals of different scales has become increasingly demanding in practice. In multi center settings, abundant data from large medical centers can improve recommendation performance for low-resource centers. Despite a few preliminary attempts on this task, two critical gaps remain. Gap 1: Existing multi-center methods fail to disentangle transferable cross-hospital clinical experience from hospital-specific prescribing patterns, limiting clinical feasibility and physician acceptance. Gap 2: They commonly overlook multi label safety constraints of MR, including drug-drug interaction risks and local formulary feasibility, which are essential for safe real-world deployment. To address these gaps, we propose HEM-Med, a novel hierarchical agentic memory framework for multi-center MR. To address Gap 1, we design a disentangled hierarchical memory module that builds patient-level medication context attribution records and disentangles them into cross hospital experience memory and hospital-specific residual memory. To address Gap 2, we introduce a safety-aware medication set generation module, which integrates dual-level experience retrieval with safety-aware set decoding to produce clinically relevant, safer, and locally adaptive medication recommendations. Experiments on a real-world multi-center eICU dataset show that HEM-Med outperforms representative transfer learning, LLM-based, and MR baselines in terms of both recommendation accuracy and safety.

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