用几何与拓扑理论构建零大模型企业级记忆系统，提升一致性与合规性。
SuperLocalMemory V3: Information-Geometric Foundations for Zero-LLM Enterprise Agent Memory
- 基于费雪信息几何设计高效检索度量，支持快速计算与统计不变性。
- 引入黎曼随机动力学管理记忆生命周期，确保稳定收敛，替代人工衰减。
- 通过上同调理论检测记忆矛盾，适合对数据主权和逻辑一致性要求高的场景。
持久记忆是智能体的核心能力，但其检索、生命周期管理和一致性机制尚无数学基础。现有系统依赖余弦相似度检索、启发式衰减机制，且缺乏形式化矛盾检测。本文通过三项贡献建立信息几何基础：第一，基于对角高斯族的费雪信息结构，提出满足黎曼度量公理、在充分统计量下不变、计算复杂度为O(d)的检索度量；第二，将记忆生命周期建模为黎曼朗之万动力学，利用福克-普朗克方程证明平稳分布的存在与唯一性，取代人工调参的衰减策略；第三，采用细胞层叠模型，非平凡的一阶上同调类恰好对应跨上下文不可调和的矛盾。在LoCoMo基准上，该数学框架在六轮对话中相较工程基线提升12.7个百分点，最挑战对话达19.9个百分点。四通道检索架构实现75%准确率且无需云端依赖，云增强后达87.7%。零大模型配置通过架构设计满足欧盟人工智能法案的数据主权要求。据我们所知，这是首个建立信息几何、层叠理论与随机动力学基础的智能体记忆系统。
原文摘要 · Abstract (English)
Persistent memory is a central capability for AI agents, yet the mathematical foundations of memory retrieval, lifecycle management, and consistency remain unexplored. Current systems employ cosine similarity for retrieval, heuristic decay for salience, and provide no formal contradiction detection. We establish information-geometric foundations through three contributions. First, a retrieval metric derived from the Fisher information structure of diagonal Gaussian families, satisfying Riemannian metric axioms, invariant under sufficient statistics, and computable in O(d) time. Second, memory lifecycle formulated as Riemannian Langevin dynamics with proven existence and uniqueness of the stationary distribution via the Fokker-Planck equation, replacing hand-tuned decay with principled convergence guarantees. Third, a cellular sheaf model where non-trivial first cohomology classes correspond precisely to irreconcilable contradictions across memory contexts. On the LoCoMo benchmark, the mathematical layers yield +12.7 percentage points over engineering baselines across six conversations, reaching +19.9 pp on the most challenging dialogues. A four-channel retrieval architecture achieves 75% accuracy without cloud dependency. Cloud-augmented results reach 87.7%. A zero-LLM configuration satisfies EU AI Act data sovereignty requirements by architectural design. To our knowledge, this is the first work establishing information-geometric, sheaf-theoretic, and stochastic-dynamical foundations for AI agent memory systems.
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