SuperLocalMemory V3：面向零样本大模型企业级代理记忆的信息几何基础
SuperLocalMemory V3: Information-Geometric Foundations for Zero-LLM Enterprise Agent Memory
March 15, 2026
作者: Varun Pratap Bhardwaj
cs.AI
摘要
持久记忆是智能代理的核心能力，然而记忆检索、生命周期管理与一致性的数学基础尚未得到探索。现有系统采用余弦相似度进行检索，使用启发式衰减衡量显著性，且缺乏形式化的矛盾检测机制。
我们通过三项贡献建立了信息几何基础框架：首先提出基于对角高斯族费舍尔信息结构的检索度量，满足黎曼度量公理，具有充分统计量不变性，并可在O(d)时间内计算；其次将记忆生命周期建模为黎曼流形上的朗之万动力学，通过福克-普朗克方程证明稳态分布的存在唯一性，以理论支撑的收敛保证替代人工调参的衰减机制；最后建立细胞层模模型，其非平凡第一上同调类精确对应记忆语境间不可调和的矛盾。
在LoCoMo基准测试中，数学基础层在六组对话任务上较工程基线提升12.7个百分点，在最具挑战性对话中提升达19.9个百分点。四通道检索架构在无云依赖条件下实现75%准确率，云端增强结果达87.7%。零大语言模型配置通过架构设计满足欧盟《人工智能法案》数据主权要求。本研究首次为智能代理记忆系统建立了信息几何、层论及随机动力学的理论基础。
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.