[論文レビュー] SuperLocalMemory V3: Information-Geometric Foundations for Zero-LLM Enterprise Agent Memory

Varun Pratap Bhardwaj|arXiv (Cornell University)|Mar 15, 2026

Topological and Geometric Data Analysis被引用数 0

ひとこと要約

One or two sentence direct-answer summary

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.

研究の動機と目的

• Identify mathematical foundations for persistent agent memory in retrieval, lifecycle, and consistency.
• Replace heuristic memory retrieval with principled, information-geometric metrics.
• Provide a formal mechanism to detect contradictions across memory contexts.
• Demonstrate scalable, zero-LLM memory operation compliant with data sovereignty requirements.

提案手法

• Introduce a four-channel retrieval architecture integrating Fisher–Rao semantic retrieval, BM25, entity-graph, and temporal channels.
• Develop a variance-weighted Fisher information metric for memory embeddings with per-dimension uncertainty.
• Model memory store as a cellular sheaf; use first cohomology to detect irreconcilable contradictions.
• Formulate memory lifecycle as Riemannian Langevin dynamics with proven existence/uniqueness of the stationary distribution.
• Provide four-channel fusion via weighted reciprocal rank fusion and neural reranking for optimization.
• Evaluate zero-LLM configuration on LoCoMo with cloud-free retrieval and report improvements over baselines.

Figure 1 : The SLM-V3 architecture. Left: Ingestion pipeline processes content through entropy gating, fact extraction, entity resolution, graph construction, and sheaf consistency checking ( $H^{1}\neq 0$ detects contradictions). Center: Four-channel retrieval with Fisher-information-weighted scori

実験結果

リサーチクエスチョン

• RQ1 What mathematical structures are appropriate for retrieval, lifecycle management, and consistency in persistent AI memory?
• RQ2 Can Fisher information-based retrieval improve over cosine similarity in high-dimensional embeddings?
• RQ3 How can memory contradictions be formally detected and diagnosed in a multi-context store?
• RQ4 Does a zero-LLM deployment with information-geometric foundations achieve competitive retrieval without cloud access?

主な発見

• Average gain of +12.7 percentage points over engineered baseline across six LoCoMo conversations (n=832) with the three mathematical layers.
• Maximum gain of +19.9 percentage points on the most challenging dialogues.
• Four-channel retrieval achieves ~75% retrieval quality without cloud dependency.
• Zero-LLM configuration reaches 75% retrieval quality, demonstrating data sovereignty viability.
• Ablation shows cross-encoder reranking is the largest contributor to performance gains.
• Cross-hop reasoning shows a +12 pp gain from mathematical layers.

Figure 2 : Competitive landscape of agent memory systems (March 2026) evaluated on LoCoMo. All systems above SLM-V3 require cloud LLM dependency. SLM-V3 Mode A Retrieval (74.8%) is the highest reported score achievable without cloud dependency during retrieval. Stars ( $\star$ ) denote zero-LLM conf