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A Geometric Taxonomy of Hallucinations in LLMs

Javier Marín · Jan 26, 2026 · Citations: 0

Automatic Metrics
Open arXiv Find Implementation RSS feed Shortlist (0)

Data freshness

Extraction: Fresh

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Metadata refreshed

Mar 7, 2026, 9:13 AM

Recent

Extraction refreshed

Mar 14, 2026, 5:03 AM

Fresh

Extraction source

Persisted extraction

Confidence 0.45

Abstract

The term "hallucination" converge different failure modes with specific geometric signatures in embedding space. We propose a taxonomy identifying three types: unfaithfulness (Type I: ignoring provided context), confabulation (Type II: inventing semantically foreign content), and factual error (Type III: wrong details within correct conceptual frames). We introduce two detection methods grounded in this taxonomy: the Semantic Grounding Index (SGI) for Type I, which measures whether a response moves toward provided context on the unit hypersphere, and the Directional Grounding Index (DGI) for Type II, which measures displacement geometry in context-free settings. DGI achieves AUROC=0.958 on human-crafted confabulations with 3.8% cross-domain degradation. External validation on three independently collected human-annotated benchmarks -WikiBio GPT-3, FELM, and ExpertQA- yields domain-specific AUROC 0.581-0.695, with DGI outperforming an NLI CrossEncoder baseline on expert-domain data, where surface entailment operates at chance. On LLM-generated benchmarks, detection is domain-local. We examine the Type III boundary through TruthfulQA, where apparent classifier signal (Logistic Regression with AUROC 0.731) is traced to a stylistic annotation confound: false answers are geometrically closer to queries than truthful ones, a pattern incompatible with factual-error detection. This identifies a theoretical constraint from a methodological limitation.

Low-signal caution for protocol decisions

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  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.45 (below strong-reference threshold).
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HFEPX Relevance Assessment

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

A benchmark-and-metrics comparison anchor.

Main weakness

Extraction flags indicate low-signal or possible false-positive protocol mapping.

Trust level

Low

Eval-Fit Score

5/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Detected

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

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Field Provenance & Confidence

Each key protocol field shows extraction state, confidence band, and data source so you can decide whether to trust it directly or validate from full text.

Human Feedback Types

missing

None explicit

Confidence: Low Source: Persisted extraction missing

No explicit feedback protocol extracted.

Evidence snippet: The term "hallucination" converge different failure modes with specific geometric signatures in embedding space.

Evaluation Modes

partial

Automatic Metrics

Confidence: Low Source: Persisted extraction evidenced

Includes extracted eval setup.

Evidence snippet: The term "hallucination" converge different failure modes with specific geometric signatures in embedding space.

Quality Controls

missing

Not reported

Confidence: Low Source: Persisted extraction missing

No explicit QC controls found.

Evidence snippet: The term "hallucination" converge different failure modes with specific geometric signatures in embedding space.

Benchmarks / Datasets

partial

TruthfulQA

Confidence: Low Source: Persisted extraction evidenced

Useful for quick benchmark comparison.

Evidence snippet: We examine the Type III boundary through TruthfulQA, where apparent classifier signal (Logistic Regression with AUROC 0.731) is traced to a stylistic annotation confound: false answers are geometrically closer to queries than truthful ones, a pattern incompatible with factual-error detection.

Reported Metrics

partial

Auroc

Confidence: Low Source: Persisted extraction evidenced

Useful for evaluation criteria comparison.

Evidence snippet: DGI achieves AUROC=0.958 on human-crafted confabulations with 3.8% cross-domain degradation.

Rater Population

partial

Domain Experts

Confidence: Low Source: Persisted extraction evidenced

Helpful for staffing comparability.

Evidence snippet: External validation on three independently collected human-annotated benchmarks -WikiBio GPT-3, FELM, and ExpertQA- yields domain-specific AUROC 0.581-0.695, with DGI outperforming an NLI CrossEncoder baseline on expert-domain data, where surface entailment operates at chance.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Domain Experts
  • Unit of annotation: Unknown
  • Expertise required: General
  • Extraction source: Persisted extraction

Evaluation Lens

  • Evaluation modes: Automatic Metrics
  • Agentic eval: None
  • Quality controls: Not reported
  • Confidence: 0.45
  • Flags: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

TruthfulQA

Reported Metrics

auroc

Research Brief

Deterministic synthesis

We propose a taxonomy identifying three types: unfaithfulness (Type I: ignoring provided context), confabulation (Type II: inventing semantically foreign content), and factual error (Type III: wrong details within correct conceptual… HFEPX signals include Automatic Metrics with confidence 0.45. Updated from current HFEPX corpus.

Generated Mar 14, 2026, 5:03 AM · Grounded in abstract + metadata only

Key Takeaways

  • We propose a taxonomy identifying three types: unfaithfulness (Type I: ignoring provided context), confabulation (Type II: inventing semantically foreign content), and factual…
  • We introduce two detection methods grounded in this taxonomy: the Semantic Grounding Index (SGI) for Type I, which measures whether a response moves toward provided context on the…
  • DGI achieves AUROC=0.958 on human-crafted confabulations with 3.8% cross-domain degradation.

Researcher Actions

  • Treat this as method context, then pivot to protocol-specific HFEPX hubs.
  • Cross-check benchmark overlap: TruthfulQA.
  • Validate metric comparability (auroc).

Caveats

  • Generated from title, abstract, and extracted metadata only; full-paper implementation details are not parsed.
  • Low-signal flag detected: protocol relevance may be indirect.

Research Summary

Contribution Summary

  • We propose a taxonomy identifying three types: unfaithfulness (Type I: ignoring provided context), confabulation (Type II: inventing semantically foreign content), and factual error (Type III: wrong details within correct conceptual…
  • We introduce two detection methods grounded in this taxonomy: the Semantic Grounding Index (SGI) for Type I, which measures whether a response moves toward provided context on the unit hypersphere, and the Directional Grounding Index (DGI)…
  • DGI achieves AUROC=0.958 on human-crafted confabulations with 3.8% cross-domain degradation.

Why It Matters For Eval

  • DGI achieves AUROC=0.958 on human-crafted confabulations with 3.8% cross-domain degradation.
  • External validation on three independently collected human-annotated benchmarks -WikiBio GPT-3, FELM, and ExpertQA- yields domain-specific AUROC 0.581-0.695, with DGI outperforming an NLI CrossEncoder baseline on expert-domain data, where…

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Pass: Evaluation mode is explicit

    Detected: Automatic Metrics

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Pass: Benchmark or dataset anchors are present

    Detected: TruthfulQA

  • Pass: Metric reporting is present

    Detected: auroc

Category-Adjacent Papers (Broader Context)

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