Noise thresholds and topology drift in planar memory graphs

Research Question

In a two-dimensional (2D) planar memory graph, what threshold of contextual noise causes a bounded entity-extraction schema to stop suppressing Large Language Model (LLM)-driven predicate hallucinations, and how does the resulting topological drift affect the agent's ability to perform spatial-relational reasoning over the graph?

Findings

(Populated from §6 Synthesis above.)

Executive Summary

No source in the 2023-2026 GraphRAG, agent-memory, or spatial-reasoning literature reports a numeric contextual-noise threshold at which a bounded entity-extraction schema stops suppressing Large Language Model (LLM)-driven predicate hallucinations in a planar memory graph. No source uses "planar memory graph" as an established architecture at all. The evidence instead supports two usable proxy-metric families for detecting the drift the research question describes. A structural-stability family is built on community-detection modularity, where a value below roughly Q equals 0.3 signals eroding community boundaries. A task-outcome family is built on multi-hop path-query accuracy and community-report factual distortion under injected noise. A bounded extraction schema suppresses out-of-vocabulary predicate hallucinations but does not verify whether an in-vocabulary predicate instance is actually supported by source text. Schema boundedness alone therefore cannot suppress all hallucination-driven drift regardless of how tightly the schema is drawn. Every system in the evidence base shown to remain usable under noise achieves that robustness through an active, post-extraction repair mechanism rather than through extraction-schema rigidity alone. This indicates that a planar memory graph needs a repair loop to remain a stable long-horizon substrate. Spatial path-finding degradation under uncorrected structural inconsistency is directly evidenced in an incrementally-constructed topological navigation graph, where a version-controlled repair framework significantly improved map correctness in scenarios with entangled or chained inconsistencies.

Key Findings

1. No paper in the reviewed 2023-2026 literature uses "planar memory graph" as a named agent-memory architecture, and a 2026 survey of graph-based agent memory does not identify layout planarity as a distinct architectural category, so no planarity-specific robustness claim exists in the surveyed literature.
2. Standard Graph Retrieval-Augmented Generation's default entity-merge step performs no semantic entity resolution and matches only identical title-and-type strings, so alias duplication is structurally expected to survive into any graph built with the default pipeline.
3. Schema-free extraction is documented to fragment entity and relation labelling for the same underlying concept into inconsistent representations, establishing one concrete mechanism by which unbounded extraction generates topology drift.
4. LLM-constructed knowledge graphs exhibit two recurring issue modes, spurious noise that induces retrieval drift toward plausible but unsupported triples, and incomplete information that forces continuation through under-supported structure, and a constraint-based retriever addressing both remains measurably more stable under controlled knowledge-graph issue injection across three multi-hop benchmarks than retrievers that assume a structurally sound graph.
5. A bounded, schema-constrained extraction pipeline suppresses predicate types outside its defined vocabulary but provides no mechanism to verify that an in-vocabulary predicate instance is actually supported by the underlying source text, so schema boundedness alone leaves an evidentiary gap that a query-time sufficiency check is needed to close.
6. A production agent-memory system's entity-resolution merge cutoff, a weighted score of name similarity, co-occurrence overlap, and temporal recency with a merge threshold at 0.6, is the only concrete numeric duplicate-suppression proxy located in the evidence base for this specific error class.
7. Community-detection modularity above a value of roughly Q equals 0.3 is an established proxy for stable graph community structure, but the Leiden algorithm used in reference GraphRAG pipelines guarantees only internal connectivity of a community, not the semantic correctness of the nodes and edges inside it, so high modularity can coexist with undetected noise-driven topology drift.
8. A companion repository item on macro-level hallucination in standard GraphRAG independently concludes that no located study measures how community-report distortion scales with injected duplicate or falsely-associated node counts, corroborating this item's own finding that the structural-stability and task-outcome proxy-metric families remain uncalibrated against one another.
9. GraphRAG-Bench was constructed specifically because GraphRAG frequently underperforms plain Retrieval-Augmented Generation on real-world tasks, and its four-level difficulty gradient isolates the point at which multi-hop graph traversal begins to fail under structural degradation, a task treated here as the closest available proxy for spatial path-finding.
10. A version-controlled repair framework for incrementally-constructed topological navigation graphs, using an Edge Impact Score to prioritise repairs by structural reachability, path usage, and conflict propagation, significantly improves map correctness and robustness in scenarios with entangled or chained inconsistencies, directly evidencing that active repair rather than extraction-time schema rigidity restores spatial path-finding capability after drift.

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Assumptions

The item's own architecture, a two-dimensional planar memory graph, is treated as functionally equivalent to an incrementally-constructed topological navigation graph for the purpose of this investigation. This assumption is justified because no closer published match was located, and the nearest evidence-backed system shares the defining property of building spatial structure from stepwise observations.

A production entity-resolution merge cutoff (0.6, on a weighted name-similarity/co-occurrence/recency score) is treated as a workable proxy for a duplicate-suppression threshold rather than as a validated information-theoretic optimum. This assumption is justified because it is the only concrete, numeric merge criterion located in the evidence base for this specific error class.

A modularity value below roughly Q equals 0.3 is treated as a usable proxy signal for the onset of topology drift, rather than as a measured drift threshold. This assumption is justified because the Q equals 0.3 figure is validated for general community-structure stability, not for extraction-noise-driven drift specifically, so its application here is an extrapolation across domains.

Analysis

The research question asks for a numeric threshold, but the strongest-supported conclusion is that no such single number exists in the current evidence base. The item's own Scope constraint anticipated this outcome by directing that proxy metrics and threshold-estimation methods substitute for an invented figure. A plausible rival position holds that a sufficiently narrow bounded schema alone could suppress hallucination-driven drift without any repair mechanism. This position is addressed and rejected by the evidence. The TBox-versus-ABox comparison shows a narrow, predefined schema losing accuracy faster than a schema-free approach as corpus noise rises, and the constraint-based retriever paper explicitly targets the residual in-vocabulary gap that a schema cannot close on its own. The structural-stability proxy (modularity) and the task-outcome proxy (path-query accuracy, community-report distortion) measure different things. Neither is shown anywhere in the evidence base to move together with the other, so a system could pass one and fail the other. This is treated as a genuine uncalibrated gap rather than resolved in either direction. The clearest single piece of direct evidence for the second half of the research question, the effect of uncorrected topology drift on spatial-relational reasoning, comes from the graph-rectification paper's finding that a version-controlled repair mechanism specifically improved correctness in scenarios with entangled or chained inconsistencies. This is the closest available direct test of drift's effect on path-finding in a spatially-laid-out graph.

Risks, Gaps, and Uncertainties

• No source directly measures topology drift in a graph memory system that is explicitly planar or 2D-laid-out as opposed to a general-purpose knowledge graph; every quantitative finding in this item is extrapolated from general GraphRAG or spatial-navigation-graph research rather than from a study of planar memory graphs specifically.
• No source calibrates the modularity-based structural-stability proxy against the task-outcome proxy (path-query accuracy or community-report distortion) in a single experiment, so it is unknown whether the two proxies would agree on where a real system's drift threshold lies.
• The entity-resolution merge-cutoff figure (0.6) comes from a single vendor engineering blog post rather than a peer-reviewed or independently replicated source, so it should not be read as a validated threshold for any system beyond the one it describes.
• The Edge Impact Score repair framework's reported improvement is stated qualitatively in its own abstract ("significantly improves map correctness and robustness") without a specific effect-size figure independently verified in this investigation, so the magnitude of the improvement, as opposed to its direction, remains unconfirmed here.

Open Questions

• Would a controlled noise-injection experiment run directly on a planar or explicitly 2D-laid-out agent-memory graph reproduce the same repair-versus-prevention pattern found in general GraphRAG and spatial-navigation-graph research, or does planarity introduce a distinct failure mode not captured by non-planar studies?
• Can the structural-stability (modularity) and task-outcome (path-query accuracy, community-report distortion) proxy-metric families be calibrated against one another in a single experiment to produce a joint, empirically-grounded drift threshold?

sources

• [x] GitHub issue #651: Multiple research questions: canonical statement of the research request and open-question linkage
• [x] TBox-driven vs ABox-emergent ontology approaches in GraphRAG systems: closest prior repository item on schema-guided versus emergent graph construction
• [x] Knowledge Representation for Agent Context: prior repository item on graph-based context representations, cited for the multi-hop task-proxy justification in §3
• [x] Domain Emergence in Semantic Networks, Cognition, and Organizational Structure: prior repository item on threshold effects in semantic graph structure
• [x] Evaluation frameworks for agentic memory quality, relevance, and retrieval accuracy: prior repository item on how to measure graph-memory failure
• [x] Graph-Based Agent Memory Systems: A Survey (2026): arXiv preprint surveying graph-based agent memory architectures; no planarity-specific category identified
• [x] Graph Retrieval-Augmented Generation: A Survey (2024): original GraphRAG survey establishing default construction and community-detection pipeline
• [x] Zhang & Soh Extract, Define, Canonicalize: An LLM-based Framework for Knowledge Graph Construction (2024): arXiv preprint and ACL Anthology paper identifying inconsistent, fragmented entity/relation labelling as a core problem in schema-free extraction and proposing a post-hoc canonicalization step to resolve it
• [x] Toward Robust GraphRAG: Mitigating Retrieval Drift and Hallucination from Imperfect Knowledge Graphs (2026): arXiv preprint on spurious-noise and incomplete-information issue modes in LLM-constructed knowledge graphs, proposing the Constraint-based and Sufficiency-guided Retrieval-Augmented Generation (CS-RAG) method
• [x] GraphEval: A Knowledge-Graph-Based Framework for Hallucination Detection and Correction (2024): arXiv preprint on post-extraction knowledge-graph-based hallucination correction
• [x] Zhang et al. Constructing Coherent Spatial Memory in LLM Agents through Graph Rectification (2026): ACL (Association for Computational Linguistics) paper on version-controlled repair of incrementally-constructed topological navigation graphs using an Edge Impact Score
• [x] Microsoft GraphRAG Default Dataflow Documentation: official documentation confirming default entity-merge matches only identical title/type strings
• [x] Vectorize/Hindsight Entity Resolution for Agent Memory (2026): vendor engineering blog describing a weighted-score entity-merge cutoff of 0.6
• [x] Girvan & Newman Community Structure in Social and Biological Networks / Modularity Threshold (PNAS): PNAS (Proceedings of the National Academy of Sciences) paper establishing modularity Q>0.3 as a proxy for stable community structure
• [x] From Louvain to Leiden: Guaranteeing Well-Connected Communities (Nature Scientific Reports): Nature Scientific Reports paper on the Leiden algorithm's internal-connectivity guarantee
• [x] GraphRAG macro-level hallucination from unresolved duplicate entities: companion repository item from the same issue cluster, cited directly for the uncalibrated-proxy-metrics finding
• [x] Albert, Jeong & Barabási Error and Attack Tolerance of Complex Networks (Nature, 2000): primary source for percolation-threshold and giant-component network-robustness framing used only as an orientation concept in §5