AI evidence extraction

A Geometric Analysis of Small-sized Language Model Hallucinations

Emanuele Ricco, E. Onofri, Lorenzo Cima, Stefano Cresci, Roberto Di Pietro · ArXiv.org · 2026

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9/10

Relevance

1/4

Quality (LMQS)

Evidence

Citations

0.00

FWCI

Methodology & findings

Study design

Empirical computational analysis using: (1) dataset generation from 10 small-sized LLMs (7-32B parameters) generating 150 responses each for 200 time-sensitive prompts; (2) LLM-as-a-judge evaluation using Claude 4.5 Sonnet to label responses as genuine (G), hallucinated (H), or unknown (U); (3) structural analysis of embedded responses using Wasserstein distance comparisons and Fisher Discriminant Analysis; (4) supervised label propagation framework using point-to-cluster distance distributions in Fisher space; (5) manual validation of 1,000 instances (≈0.4% of dataset) by two PhD students with Cohen's κ = 0.86 agreement..

Primary method

Empirical design science; structural analysis-driven framework development; validation through cross-model and cross-prompt evaluation

Main result

The study demonstrates that "genuine and hallucinated responses exhibit systematically different geometric properties in embedding space, with hallucinated responses displaying reduced semantic cohesion relative to genuine ones." The analysis reveals that "inter-class distances (blue boxplots) are often entangled with both D_GG and D_HH, especially in the presence of class imbalance," yet after Fisher projection, "separability increases consistently across all considered models, with an average amplification factor of 7.26×."

Research paradigm

Empirical-analytical (positivist); geometric/structural analysis of language model behavior

Author conclusions

The authors conclude: "We have shown that hallucinations in small-sized LLMs are strongly linked to structural patterns in the embedding space rather than purely to missing knowledge. Indeed, genuine responses exhibit higher semantic cohesion, while hallucinated ones form distinct distributions, with inter-versus intra-class distance ratios increasing on average from 1.13 in the original embedding space to 7.26 along the Fisher discriminant direction." They further state that their "results suggest that the embedding-space geometry provides both a diagnostic and a practical tool for scalable hallucination detection, complementing existing knowledge-centric or single-response evaluation paradigms."

Risk of bias

LLM-as-a-judge bias: reliance on Claude 4.5 Sonnet as oracle for labeling; human validation only on 1,000/250,000 instances (~0.4%); Selection bias: time-sensitive questions may not represent all hallucination types; base models only (no instruction-tuned variants); Dataset composition: 100 repetitive events from 2020-2022, may not generalize to other domains or temporal ranges; Annotation bias: manual validation by two PhD students with adjudication; potential for expert bias; Embedding bias: single embedding model (all-MiniLM-L6-v2) may encode specific representational biases; Selection bias: Only time-sensitive factual questions were used; may not generalize to other hallucination types; Dependency on LLM-as-judge: Claude 4.5 Sonnet used as external oracle; potential bias in how it evaluates factual correctness; Base model variants only: All models are pretrained without instruction/alignment fine-tuning; results may not transfer to fine-tuned models; Limited prompt diversity: Only 100 repetitive events across 2020 and 2022; temporal scope may be narrow; Manual annotation limited: Only 0.4% of dataset manually validated; Embedding choice: Analysis dependent on all-MiniLM-L6-v2 sentence encoder; results may not generalize to other embeddings; Selection bias: Analysis restricted to time-sensitive factual questions; smaller models may be more susceptible to hallucination on these question types; LLM-as-judge bias: Uses proprietary Claude 4.5 Sonnet as oracle; potential systematic biases in Claude's evaluation; Annotator bias: Only 1,000 instances (≈0.4% of full dataset) manually validated; potential inconsistency in remaining 99.6%; Dataset bias: All base model variants (no instruction fine-tuning), limiting generalizability to aligned models; Embedding bias: Results dependent on specific sentence embedding model (all-MiniLM-L6-v2); generalization to other embeddings unstudied in main analysis

Limitations

The authors note that "the present study focuses on prompt-local structural analysis and does not explore the coherence of discriminative directions across prompts or tasks
While this choice allows for controlled and interpretable comparisons, it does not address the extent to which discriminative directions or geometric signatures align across different prompts, domains, or tasks." Additionally, "our analysis is grounded in a specific embedding choice and in factual, time-sensitive queries, which offer a convenient testbed but capture only a subset of hallucination phenomena."

Open questions raised

Coherence of discriminative directions across prompts or tasks
Transferability of geometric signatures across different prompts, domains, or tasks
Extension to other embedding spaces beyond all-MiniLM-L6-v2
Generalization beyond factual, time-sensitive queries to other hallucination categories
Integration with alternative judging protocols, prompt conditioning strategies, and multi-prompt aggregation schemes
Lack of coherence analysis across prompts and tasks: 'Understanding whether Fisher projections exhibit coherence or transferability across prompts and models represents an important next step'

Data: The authors state: "We release a fully labeled dataset of repeated responses (150 generations for 200 prompts across 10 small-sized LLMs) to support structural analyses of hallucinations." Specific URL for dataset access not provided in text.; The authors state they "release a fully labeled dataset of repeated responses (150 generations for 200 prompts across 10 small-sized LLMs) to support structural analyses of hallucinations." However, no specific URL or repository link is provided in the paper.; Fully labeled dataset of repeated responses (150 generations for 200 prompts across 10 small-sized LLMs) - stated as released but no URL providedCode: No code repositories explicitly mentioned with URLs in the paper; Not mentioned in the documentExtracted from: pdfAgreement 51%

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