Towards Root Memory: Benchmarking and Enhancing Implicit Logical Memory Retrieval for Personalized LLMs

Abstract

Memory systems are essential for personalized Large Language Models (LLMs). However, retrieval within these systems primarily relies on semantic similarity, potentially missing logically critical memories with limited semantic overlap. We refer to this failure as semantic deflection, which remains insufficiently evaluated by existing benchmarks. To address this gap, we construct IMLogic, a benchmark for implicit logical memory retrieval in long dialogues. Each question is designed around the divergence between semantic and logical relevance, with diagnostic response options that probe semantic deflection, hallucination, and lack of personalization. To help systems utilize associations that are difficult to discover through semantic matching, we introduce root memory, a structured representation that distills reusable, response-guiding logic from user histories through LLM reasoning and grounds it in supporting evidence. We further develop RootMem, a plug-and-play framework that constructs and routes root memories to complement semantic retrieval. Extensive experiments reveal persistent challenges across retrieval methods and memory systems, including substantial preference-driven errors even under full-memory access. RootMem consistently improves performance, demonstrating the potential of structured personalized logic while leaving considerable challenges unresolved. Our benchmark and code are available at https://github.com/ThisIsCosine/IMLogic.