SuperLocalMemory V3: Information-Geometric Foundations for Zero-LLM Enterprise Agent Memory
Organizations: Independent Researcher, Solution Architect India
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.
Figures & tables
| # | Component | Signal | Foundation | Weight |
| Core Channels (parallel, fused via WRRF) | ||||
| 1 | Semantic (Fisher–Rao) | Embedding uncertainty | Amari [ 4 ] | 1.2 |
| 2 | BM25 Keyword | Term frequency–inverse doc | Robertson [ 43 ] | 1.0 |
| 3 | Entity Graph | Spreading activation | Novel (this work) | 1.3 |
| 4 | Temporal Reasoning | Date proximity + validity | Novel (this work) | 1.0 |
| Supplementary Stages (sequential, post-fusion) | ||||
| Mode | Embeddings | LLM | EU AI Act | LoCoMo |
|---|---|---|---|---|
| A: Zero-LLM | nomic-embed-v1.5 (768d) | None | Full compliance | – |
| B: Local-LLM | nomic-embed-v1.5 (768d) | Local (Ollama) | Full compliance | – |
| C: Cloud-Augmented | text-embedding-3-large (3072d) | Cloud API | Partial | – |
| System | Single | Multi | Temporal | Open | Aggregate |
|---|---|---|---|---|---|
| EverMemOS | 96.1 | 91.1 | 89.7 | 70.8 | 92.3 |
| Hindsight | 86.2 | 70.8 | 95.1 | 83.8 | 89.6 |
| Zep v3 | 90.8 | 81.9 | 77.3 | 75.0 | 85.2 |
| SLM-V3 Mode C | 64.0 | 100.0 | — | 86.0 | 87.7 |
| MemOS v2 | 85.4 | 79.4 | 75.1 | 64.6 | 80.8 |
| SLM-V3 Mode A (Ret.) | 72.0 | 70.3 | 80.0 | 85.0 | 74.8 |
| Configuration | LoCoMo (%) | (pp) |
|---|---|---|
| SLM-V3 (full system) | 60.4 | — |
| Fisher metric ( fisher_off ) | 49.6 | |
| Sheaf consistency ( sheaf_off ) | 58.7 | |
| All math layers ( all_math_off ) | 52.8 | |
| BM25 channel ( bm25_off ) | 53.9 | |
| Entity graph ( entity_off ) | 59.4 |
| Conversation | With Math (%) | Without Math (%) | (pp) |
|---|---|---|---|
| conv-26 | 78.5 | 71.2 | |
| conv-30 | 77.5 | 66.7 | |
| conv-42 | 60.8 | 47.3 | |
| conv-43 | 64.3 | 58.3 | |
| conv-44 | 64.2 | 44.3 | |
| conv-49 | 84.7 | 65.9 |
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
| Component | Parameters | Notes |
| Channel weights | 4 per-channel, query-type-dependent | Grid-search optimized |
| RRF fusion | Fusion constant | Standard range per literature [ 12 ] |
| Cross-encoder blend | Query-type-dependent | Higher for single-hop (Eq. 12 ) |
| BM25 | , | Standard Okapi defaults |
| Fisher-information | Temperature, access threshold | Controls cosine Fisher transition |
| Sheaf consistency | Contradiction threshold | Coboundary norm based |
| Conversation | Questions | Accuracy (%) | Status |
|---|---|---|---|
| conv-26 | 152 | 58.6 | Done |
| conv-30 | 81 | 63.0 | Done |
| conv-41 | 134 | 62.7 | Partial |
| conv-42 | 149 | 55.7 | Partial |
| conv-43 | 161 | 65.2 | Partial |
| conv-44 | 123 | 64.2 | Done |
| Category | Count | Mode C (%) | CE off (%) | |
|---|---|---|---|---|
| Single-hop | 11 | 64.0 | 55.0 | |
| Multi-hop | 26 | 100.0 | 100.0 | |
| Open-domain | 44 | 86.0 | 93.0 | |
| Aggregate | 81 | 87.7 | 90.1 |
| Conversation | Accuracy (%) | Questions |
|---|---|---|
| conv-26 | 50.0 | 152 |
| conv-30 | 56.8 | 81 |
| conv-41 | 66.4 | 152 |
| conv-42 | 58.8 | 199 |
| conv-43 | 58.4 | 178 |
| conv-44 | 56.1 | 123 |
Agent Memory
Agent memory lets AI systems retain, update, and use facts, experiences, and skills across sessions and long-horizon tasks.
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