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Hallucination is a Consequence of Space-Optimality: A Rate-Distortion Theorem for Membership Testing

Anxin Guo, Jingwei Li · Jan 31, 2026 · Citations: 0

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How to use this paper page

Coverage: Stale

Use this page to decide whether the paper is strong enough to influence an eval design. It summarizes the abstract plus available structured metadata. If the signal is thin, use it as background context and compare it against stronger hub pages before making protocol choices.

Best use

Background context only

Metadata: Stale

Trust level

Low

Signals: Stale

What still needs checking

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

Signal confidence: 0.15

Abstract

Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns. We formalize the memorization of such facts as a membership testing problem, unifying the discrete error metrics of Bloom filters with the continuous log-loss of LLMs. By analyzing this problem in the regime where facts are sparse in the universe of plausible claims, we establish a rate-distortion theorem: the optimal memory efficiency is characterized by the minimum KL divergence between score distributions on facts and non-facts. This theoretical framework provides a distinctive explanation for hallucination: even with optimal training, perfect data, and a simplified "closed world" setting, the information-theoretically optimal strategy under limited capacity is not to abstain or forget, but to assign high confidence to some non-facts, resulting in hallucination. We validate this theory empirically on synthetic data, showing that hallucinations persist as a natural consequence of lossy compression.

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Use this page for context, then validate protocol choices against stronger HFEPX references before implementation decisions.

  • Extraction flags indicate low-signal or possible false-positive protocol mapping.
  • Extraction confidence is 0.15 (below strong-reference threshold).
  • No explicit evaluation mode was extracted from available metadata.
  • No benchmark/dataset or metric anchors were extracted.
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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

Background context only.

Main weakness

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

Trust level

Low

Eval-Fit Score

0/100 • Low

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

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

HFEPX Fit

Adjacent candidate

Extraction confidence: Low

If you are doing eval pipeline work, start here:

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What This Page Found In The Paper

Each field below shows whether the signal looked explicit, partial, or missing in the available metadata. Use this to judge what is safe to trust directly and what still needs full-paper validation.

Human Feedback Types

missing

None explicit

Confidence: Low Not found

No explicit feedback protocol extracted.

Evidence snippet: Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Evaluation Modes

missing

None explicit

Confidence: Low Not found

Validate eval design from full paper text.

Evidence snippet: Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Quality Controls

missing

Not reported

Confidence: Low Not found

No explicit QC controls found.

Evidence snippet: Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Benchmarks / Datasets

missing

Not extracted

Confidence: Low Not found

No benchmark anchors detected.

Evidence snippet: Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Reported Metrics

missing

Not extracted

Confidence: Low Not found

No metric anchors detected.

Evidence snippet: Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Rater Population

missing

Unknown

Confidence: Low Not found

Rater source not explicitly reported.

Evidence snippet: Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Human Data Lens

  • Uses human feedback: No
  • Feedback types: None
  • Rater population: Unknown
  • Unit of annotation: Unknown
  • Expertise required: General
  • Signal basis: Structured extraction plus abstract evidence.

Evaluation Lens

  • Evaluation modes:
  • Agentic eval: None
  • Quality controls: Not reported
  • Signal confidence: 0.15
  • Known cautions: low_signal, possible_false_positive

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

  • Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.
  • We formalize the memorization of such facts as a membership testing problem, unifying the discrete error metrics of Bloom filters with the continuous log-loss of LLMs.
  • By analyzing this problem in the regime where facts are sparse in the universe of plausible claims, we establish a rate-distortion theorem: the optimal memory efficiency is characterized by the minimum KL divergence between score distributions on facts and non-facts.

Researcher Actions

  • Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
  • Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
  • Use related-paper links to find stronger protocol-specific references.

Caveats

  • Generated from abstract + metadata only; no PDF parsing.
  • Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Research Summary

Contribution Summary

  • Large language models often hallucinate with high confidence on "random facts" that lack inferable patterns.
  • We formalize the memorization of such facts as a membership testing problem, unifying the discrete error metrics of Bloom filters with the continuous log-loss of LLMs.
  • By analyzing this problem in the regime where facts are sparse in the universe of plausible claims, we establish a rate-distortion theorem: the optimal memory efficiency is characterized by the minimum KL divergence between score…

Why It Matters For Eval

  • Abstract shows limited direct human-feedback or evaluation-protocol detail; use as adjacent methodological context.

Researcher Checklist

  • Gap: Human feedback protocol is explicit

    No explicit human feedback protocol detected.

  • Gap: Evaluation mode is explicit

    No clear evaluation mode extracted.

  • Gap: Quality control reporting appears

    No calibration/adjudication/IAA control explicitly detected.

  • Gap: Benchmark or dataset anchors are present

    No benchmark/dataset anchor extracted from abstract.

  • Gap: Metric reporting is present

    No metric terms extracted.

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