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

TL;DR

This paper introduces a mathematically grounded framework for AI agent memory, utilizing information geometry, stochastic dynamics, and sheaf theory to improve retrieval, lifecycle management, and contradiction detection, with significant empirical gains.

Contribution

It presents the first formal foundations for AI memory systems using information geometry, stochastic dynamics, and sheaf theory, replacing heuristic methods with principled approaches.

Findings

Achieved +12.7 percentage points over baselines on LoCoMo benchmark.

Developed a retrieval architecture with 75% accuracy, reaching 87.7% with cloud augmentation.

Established formal mathematical foundations for memory retrieval, lifecycle, and contradiction detection.

Abstract

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.