SuperLocalMemory V3: Information-Geometric Foundations for Zero-LLM Enterprise Agent Memory

The AI agent memory landscape lacks mathematical foundations. Every major system — from commercial platforms to recent open-source contributions — retrieves memories via cosine similarity, manages lifecycle through heuristic decay, and provides no formal mechanism for detecting contradictions. As agent deployments scale to enterprise workloads under emerging regulations like the EU AI Act (Regulation 2024/1689), this mathematical poverty becomes a reliability risk.

 

This paper introduces the first information-geometric framework for agent memory systems, drawing on three branches of mathematics not previously connected to this domain. We replace cosine similarity with a metric derived from Fisher information theory — the only Riemannian metric invariant under sufficient statistics (Čencov's theorem). We formulate memory lifecycle as Riemannian Langevin dynamics with proven convergence to a unique stationary distribution, eliminating hand-tuned decay functions. We detect contradictions across memory contexts via sheaf cohomology, where non-trivial first cohomology classes correspond precisely to irreconcilable inconsistencies — the first algebraic consistency guarantee for agent memory.

 

Empirical results on the LoCoMo benchmark (10,407 scored questions): the mathematical layers contribute +12.7 percentage points over engineering baselines, with gains reaching +19.9pp on the most challenging conversations. The four-channel retrieval architecture achieves 75% retrieval quality without any cloud and LLM dependency. A cloud-LLM-augmented configuration reaches 87.7% with 100% accuracy on multi-hop reasoning. A zero-LLM configuration — the first reported for any memory system — satisfies EU AI Act data sovereignty requirements by architectural design. 

 

Related publications: SuperLocalMemory V2 (arXiv:2603.02240), AgentAssay (arXiv:2603.02601), SkillFortify (arXiv:2603.00195), Agent Behavioral Contracts (arXiv:2602.22302).