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AI Memory, specifically how models organizes and retrieves historical messages, becomes increasingly valuable to Large Language Models (LLMs), yet existing methods (RAG and Graph-RAG) primarily retrieve memory through similarity-based mechanisms. While efficient, such System-1-style retrieval struggles with scenarios that require global reasoning or comprehensive coverage of all relevant information. In this work, We propose Mnemis, a novel memory framework that integrates System-1 similarity search with a complementary System-2 mechanism, termed Global Selection. Mnemis organizes memory into a base graph for similarity retrieval and a hierarchical graph that enables top-down, deliberate traversal over semantic hierarchies. By combining the complementary strength from both retrieval routes, Mnemis retrieves memory items that are both semantically and structurally relevant. Mnemis achieves state-of-the-art performance across all compared methods on long-term memory benchmarks, scoring 93.9 on LoCoMo and 91.6 on LongMemEval-S using GPT-4.1-mini.