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REVIEW 4 major objections 6 minor 21 references

How Knowledge Popularity Influences and Enhances LLM Knowledge Boundary Perception

T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Popularity of a fact predicts how well an LLM knows it.

desk verdict Correlation findings are worthwhile; the headline 5.24% calibration gain is undercut by a missing same-classifier control. read the letter →

arxiv 2505.17537 v1 pith:BBJV4RCY submitted 2025-05-23 cs.CL

Shiyu Ni , Keping Bi , Jiafeng Guo , Xueqi Cheng This is my paper
classification cs.CL
keywords knowledgeboundaryperceptionconfidencecalibrationpopularityentity-centricQArelationhallucinationlargelanguagemodelsanswercorrectnessprediction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that a large language model's ability to know, and to know that it knows, is systematically tied to how popular the knowledge is in the world. On entity-centric factual questions, it measures popularity as the number of Wikipedia language editions linking to an entity and as the co-occurrence frequency of the question and answer entities in Wikipedia documents. It reports that models answer more popular questions more accurately and with higher confidence, that their confidence aligns better with reality on popular knowledge, and that relation popularity is the strongest predictor. It then turns this correlation into a practical calibration signal: adding popularity to generation-probability confidence improves prediction of whether an answer is correct by an average of 5.24%, and asking the model to rate its own familiarity is a workable substitute for external corpora.

What carries the argument

The central machinery is a three-part popularity measure built from external corpora: entity popularity of the question entity, entity popularity of the answer entity, each counted as Wikidata sitelinks, and relation popularity, counted as co-occurrences of the two entities in a Wikipedia dump. The paper links these to the model's behavior through Spearman correlations with binary accuracy, generation-probability confidence, and the alignment score $1 - |\text{acc} - c|$. The calibration stage then turns popularity into a correctness predictor: a threshold on a single popularity score, or a three-layer MLP over combined features, trained to classify whether the generated answer contains the ground truth; the same features can be replaced by the model's self-reported familiarity on a 1-to-10 scale.

What would settle it

Compute, for a sample of the entities and entity pairs in the three datasets, the actual frequencies and co-occurrence counts in the pretraining corpora of Llama-3-8B and Qwen2-7B, and compare their ranking with the Wikidata-sitelink and Wikipedia-dump proxies. If the rank orders diverge substantially, or if the popularity–accuracy correlation disappears after controlling for true training exposure, the paper's central explanation and its 5.24% calibration gain would not generalize.

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Extended reading notes

Core claim

On entity-centric factual questions drawn from Wikidata (movie directors, song performers, birthplace cities), the paper claims that knowledge popularity—the number of Wikipedia language editions in which an entity appears and the number of Wikipedia documents in which the question and answer entities co-occur—systematically tracks how well an LLM knows a fact. Llama3-8B-Instruct, Qwen2-7B-Instruct, and ChatGPT all answer more popular knowledge more accurately, express higher generation-probability confidence, and show confidence that agrees more closely with actual accuracy; relation popularity shows the strongest correlation in most cases. The paper also claims that when models hallucinate, they tend to over-generalize, generating more popular answer entities that co-occur less with the question entity than the ground-truth answers do. Because these popularity signals predict correctness, the paper augments probabilistic confidence with them and reports an average 5.24% improvement in answer-correctness prediction across all models and datasets, with model self-estimated familiarity as a viable external-corpus-free substitute.

Load-bearing premise

The load-bearing premise is that Wikidata sitelink counts and Wikipedia document co-occurrence counts faithfully reflect how often each fact actually appeared in the training data of Llama3, Qwen2, and ChatGPT; if these proxies diverge from true training exposure, the reported correlations and the 5.24% calibration gain would not generalize.

Editorial extensions

If this is right

  • Adding question, generated-answer, and relation popularity to probabilistic confidence raises answer-correctness prediction accuracy by an average of 5.24% across all models and datasets, and the combination of all three beats any single signal.
  • Relation popularity between the question entity and the generated answer is the strongest single calibration signal, outperforming all baselines in six of nine model–dataset settings.
  • Because question popularity correlates more strongly with confidence than with accuracy, LLMs can be overconfident purely from question familiarity, and popularity-aware calibration corrects part of that overconfidence.
  • Model-estimated familiarity on a 10-point scale substitutes for corpus-based popularity without external corpora, and zero-shot self-estimation performs as well as few-shot prompting.
  • When hallucinating, models over-generalize by selecting more popular answers that co-occur less with the question entity, which explains why generated-answer relation popularity discriminates correct from incorrect outputs better than answer popularity alone.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If the proxy-popularity assumption holds, the same three-feature calibration recipe should transfer to other entity-centric QA domains and to newer open-weight models; the expected transfer is measurable as the PC versus PC+ALL gap on held-out data.
  • The correlations suggest a retrieval policy the paper does not explicitly propose: trigger adaptive retrieval when the question entity is unpopular or when the generated answer co-occurs rarely with the question entity, rather than only when confidence is low.
  • Self-estimated familiarity may tap the same latent signal as verbalized confidence, so combining the two self-reports could narrow the remaining gap between corpus-based and model-generated calibration.
  • For non-entity knowledge, popularity could be represented by n-gram document frequency or relation-schema frequency; whether the 5.24% gain survives such representations is a direct, untested extension.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. This paper studies how knowledge popularity, measured via Wikidata sitelink counts and Wikipedia co-occurrence, relates to LLM QA performance, confidence, and confidence-accuracy alignment on three entity-centric QA datasets (Movies, Songs, Basketball) using Llama3-8B-Instruct, Qwen2-7B-Instruct, and ChatGPT. It reports positive correlations between popularity and accuracy/confidence/alignment, with relation popularity (co-occurrence of question and answer entities) generally strongest, and proposes using PopQ, PopGe, and RPopGe to improve answer-correctness prediction, claiming an average 5.24% improvement over probabilistic confidence. It also tests prompting the models themselves to estimate popularity, finding this a viable but weaker alternative to corpus-based popularity.

Significance. If the claims withstand the controls I describe below, this is a useful empirical contribution: external corpus popularity is an independent, cheap signal for predicting when an LLM answer can be trusted, with potential applications to selective prediction and adaptive retrieval. The paper's strengths include using popularity features derived from Wikidata/Wikipedia that are external to the tested models, covering three datasets and three model families, providing code, and explicitly probing a self-estimated popularity variant, which it correctly ranks below the corpus-based variant. The correlational story is plausible, but it currently lacks inferential support and the headline calibration gain is not yet attributable to popularity features because of a classifier-family confound.

major comments (4)
  1. [Section 6.4, Eqs. (3)-(4), Table 5] The headline 5.24% improvement compares a threshold-based PC baseline (Eq. 3) with an MLP-based PC+ALL model (Eq. 4). This changes the classifier family, capacity, and feature scaling simultaneously, and no MLP trained on PC alone (d=1) is reported. The gain could therefore reflect the MLP's nonlinear decision boundary rather than the popularity features. Please add an MLP-only PC control, and use the same classifier for all feature sets, or otherwise show that the improvement is not a classifier-family artifact.
  2. [Appendix A and Tables 2 and 4] The document-count threshold of 6,000 is hand-chosen, and the filtering removes about 60% of the Songs dataset (2,157 to 852 samples) and 25% of the Movies dataset (10,964 to 8,184 samples). Since all correlations and calibration results are computed on the filtered data, the paper should provide a sensitivity analysis over this threshold and justify it independently of the observed results; otherwise the main correlations may depend on the specific filtering choice.
  3. [Tables 2, 4, and 7] Spearman correlations are reported without confidence intervals or significance tests, and several cells are near zero or negative: for example, PopGe versus accuracy for ChatGPT on Basketball is -0.164 (Table 4), and PopQ versus accuracy for Qwen2 on Basketball is 0.014 (Table 2). These cells contradict the blanket claim that all three popularity measures positively correlate with performance, confidence, and perception. Please report significance levels or confidence intervals, and separate the general trend from dataset- and model-specific exceptions.
  4. [Appendix D and Table 5] For the Basketball dataset, the MLP experiments for Llama3 and Qwen2 use a rebalanced subset consisting of all correctly answered samples plus an equal number of randomly sampled incorrect ones (seed 0). It is unclear whether the PC threshold baseline is evaluated on the same rebalanced test set or on the original highly imbalanced test set. If baselines and proposed method are evaluated on different test distributions, the reported gains for Basketball and the 5.24% average are not directly comparable. Please clarify the evaluation protocol and, if necessary, report results on both the balanced and the original distributions.
minor comments (6)
  1. [Abstract] The phrase "Cause knowledge popularity shows strong correlation" should be "Because knowledge popularity shows a strong correlation".
  2. [Section 6.4, Eq. (3)] The word "formualted" in the sentence introducing Eq. (3) should be "formulated".
  3. [Figures 9 and 10 captions] The captions refer to the "Moveis" dataset; this should be "Movies".
  4. [Section 5.2, Figure 4 legend] The legend labels "Acc=1 & GT Ans" and "Acc=0 & GT Ans" are confusing; please spell out the correct/incorrect distinction and the ground-truth/generated answer distinction.
  5. [Section 4.1 and Table 1] The dataset name appears as "Song" in Table 1 but as "Songs" elsewhere; please standardize the name.
  6. [Section 6.1] The sentence "familiarity with a given the entity or the relation" contains a grammatical error; it should be "a given entity or relation".

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: popularity features are external (Wikidata/Wikipedia) and calibration is fit/evaluated on a proper train/test split; the 5.24% attribution is confounded by a threshold-vs-MLP comparison, but no equation reduces a prediction to its input.

full rationale

Walking the paper's derivation chain, no step reduces a predicted quantity to an input by construction. Popularity features are defined externally and independently of the model and the correctness labels: entity popularity is the Wikidata sitelink count and relation popularity is the Wikipedia document co-occurrence count (Section 4.1); self-estimated popularity is a prompted familiarity score (Section 6.1). None of these is defined in terms of confidence (Eq. 1), accuracy, alignment, or the binary correctness label, so the correlations in Tables 2/4 and the calibration gains in Table 5 are empirical findings rather than tautologies. The calibration pipeline (Section 6.4) fits a threshold (Eq. 3) or an MLP (Eq. 4) on a random half of each dataset and reports accuracy on the held-out half, so the 5.24% gain is a genuine out-of-sample result, not a fitted parameter renamed as a prediction. The paper's self-citations (Ni et al. 2024a, 2024b, 2025) support the choice of probabilistic confidence and the RAG motivation, but they are not the load-bearing premise: the popularity-performance correlations hold in the paper's own experiments, and the calibration baselines include external methods (Verb, Consis, PC from Kumar et al. 2024). These are at most minor, non-load-bearing self-citations, which is why the score sits at 2 rather than 0. Two concerns are genuine but are not circularity: (1) the headline 5.24% compares a threshold-based PC baseline with an MLP-based PC+ALL model and never reports an MLP trained on PC alone, so part of the gain may reflect classifier capacity or the Basketball rebalancing (Appendix D) rather than the popularity features; (2) Section 4.1's sentence 'This reflects relation popularity in the model's training data, as it shows a strong correlation with QA performance' uses the paper's own Table 2 correlation to validate the training-frequency interpretation of the proxy, a rhetorical validation loop rather than a definitional reduction, since the proxy is defined independently. The stated limitation that actual training data 'would likely yield greater improvements' confirms the proxy assumption is acknowledged, not suppressed.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The central claims rest on external popularity proxies (sitelinks and Wikipedia co-occurrence) and on the validity of token probability as confidence. No new entities are introduced. The free parameters are mostly in the calibration pipeline and data filtering, not in the main correlation analysis.

free parameters (4)
  • Document count threshold (6000) = 6000
    Hand-chosen cutoff in Appendix A to exclude ambiguous high-frequency entities like 'Queen'; applied only to Movies and Songs.
  • Basketball class-balancing seed = 0
    In Appendix D, all correct samples plus an equal random sample of incorrect ones (seed=0) are used, altering the test distribution for Llama3 and Qwen2.
  • Single-feature threshold lambda = chosen to maximize training accuracy
    Section 6.4: threshold for binary classification of correctness from a single feature, selected on the training split.
  • MLP weights = learned (3-layer, 64-32-2)
    Section 6.4 and D: trained with Adam on each dataset split; checkpoint selected by training accuracy.
assumptions (4)
  • domain assumption Wikidata sitelink count is a valid proxy for entity frequency in LLM training data
    Section 4.1: 'using the number of sitelinks on a page as a proxy for entity popularity', citing Yuksekgonul et al. (2023) for strong correlation with training frequency.
  • domain assumption Wikipedia document co-occurrence reflects relation popularity in training data
    Section 4.1: relation popularity is estimated by counting Wikipedia documents where both entities appear; treated as a proxy for training co-occurrence.
  • domain assumption Average generation probability of answer tokens is a valid confidence measure
    Section 3, Eq. (1): confidence defined as mean token probability under greedy decoding; the paper relies on this for all perception and calibration results.
  • domain assumption Entity-centric Wikidata QA data is representative of factual knowledge
    Section 4.1: three datasets from Yuksekgonul et al. (2023) are used to draw general conclusions about knowledge popularity effects.

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Pith. "Pith review of How Knowledge Popularity Influences and Enhances LLM Knowledge Boundary Perception." pith.science (2026). https://pith.science/paper/BBJV4RCY

@misc{pith2026250517537,
  author       = {Pith},
  title        = {Pith review of: How Knowledge Popularity Influences and Enhances LLM Knowledge Boundary Perception},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BBJV4RCY}},
  note         = {Machine review of arXiv:2505.17537}
}
read the original abstract

Large language models (LLMs) often fail to recognize their knowledge boundaries, producing confident yet incorrect answers. In this paper, we investigate how knowledge popularity affects LLMs' ability to perceive their knowledge boundaries. Focusing on entity-centric factual question answering (QA), we quantify knowledge popularity from three perspectives: the popularity of entities in the question, the popularity of entities in the answer, and relation popularity, defined as their co-occurrence frequency. Experiments on three representative datasets containing knowledge with varying popularity show that LLMs exhibit better QA performance, higher confidence, and more accurate perception on more popular knowledge, with relation popularity having the strongest correlation. Cause knowledge popularity shows strong correlation with LLMs' QA performance, we propose to leverage these signals for confidence calibration. This improves the accuracy of answer correctness prediction by an average of 5.24% across all models and datasets. Furthermore, we explore prompting LLMs to estimate popularity without external corpora, which yields a viable alternative.

Figures

Figures reproduced from arXiv: 2505.17537 by the authors.

Figure 1
Figure 1. Question examples for each dataset. 2023; Zhang et al., 2024a). Consistency-based Confidence. If the model is confident in its answer, it should maintain consis￾tency across multiple generations. Recent studies have used self-consistency across generations as a proxy for LLM confidence (Manakul et al., 2023; Kuhn et al., 2023). Zhang et al. (2023) extended this by evaluating the consistency of answers across multipl… view at source ↗
Figure 2
Figure 2. The QA performance, confidence, and alignment of ChatGPT under different question popularity. [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Comparison of the correlation between Chat [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (23 more)
Figure 4
Figure 4. Figure 4: PopGT, PopGe in incorrectly answered samples and PopGT (also PopGe) in correctly answered samples. 50 60 70 80 90 Movies Songs Basketball Ratio (%) Llama3 Qwen2 ChatGPT [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: Proportion of incorrectly answered samples [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 6
Figure 6. Figure 6: QA performance and NMI calculated based on ChatGPT. R-Pop means relation popularity, where P(R|Q) and P(R|A) denote the co-occurrence propor￾tion of question and answer entities relative to their individual occurrences in documents. B Analysis on Relationship Strength …
Figure 7
Figure 7. Figure 7: The prediction accuracy obtained by perform [PITH_FULL_IMAGE:figures/full_fig_p012_7.png]
Figure 9
Figure 9. Figure 9: The case where Llama3-8B generates incor [PITH_FULL_IMAGE:figures/full_fig_p013_9.png]
Figure 10
Figure 10. Figure 10: The case where Llama3-8B generates correct [PITH_FULL_IMAGE:figures/full_fig_p013_10.png]
Figure 11
Figure 11. Figure 11: The case where Llama3-8B generates correct [PITH_FULL_IMAGE:figures/full_fig_p013_11.png]
Figure 12
Figure 12. Figure 12: The QA performance, confidence, and alignment of Llama3 under different question popularity. [PITH_FULL_IMAGE:figures/full_fig_p014_12.png]
Figure 13
Figure 13. Figure 13: The QA performance, confidence, and alignment of Qwen2 under different question popularity. [PITH_FULL_IMAGE:figures/full_fig_p014_13.png]
Figure 14
Figure 14. Figure 14: The QA performance, confidence, and alignment of Llama3 under different answer popularity. [PITH_FULL_IMAGE:figures/full_fig_p014_14.png]
Figure 15
Figure 15. Figure 15: The QA performance, confidence, and alignment of Qwen2 under different answer popularity. [PITH_FULL_IMAGE:figures/full_fig_p015_15.png]
Figure 16
Figure 16. Figure 16: The QA performance, confidence, and alignment of ChatGPT under different answer popularity. [PITH_FULL_IMAGE:figures/full_fig_p015_16.png]
Figure 17
Figure 17. Figure 17: The QA performance, confidence, and alignment of Llama3 under different relation popularity. [PITH_FULL_IMAGE:figures/full_fig_p015_17.png]
Figure 18
Figure 18. Figure 18: The QA performance, confidence, and alignment of Qwen2 under different relation popularity. [PITH_FULL_IMAGE:figures/full_fig_p015_18.png]
Figure 19
Figure 19. Figure 19: The QA performance, confidence, and alignment of ChatGPT under different relation popularity. [PITH_FULL_IMAGE:figures/full_fig_p015_19.png]
Figure 20
Figure 20. Figure 20: A question-answering example for Llama3. [PITH_FULL_IMAGE:figures/full_fig_p016_20.png]
Figure 21
Figure 21. Figure 21: An example for verbalized confidence. Question: Rate how familiar you are with the movie 'The Intouchables'. The familiarity is rated on a scale from 1 to 10, where 10 means you are highly familiar with it, and 1 means you have little to no knowledge about it. Your an…
Figure 22
Figure 22. Figure 22: An example of obtaining question popularity on the movies dataset using LLaMA3 in a zero-shot setting. [PITH_FULL_IMAGE:figures/full_fig_p016_22.png]
Figure 23
Figure 23. Figure 23: An example of obtaining generated answer popularity on the movies dataset using LLaMA3 in a zero-shot [PITH_FULL_IMAGE:figures/full_fig_p016_23.png]
Figure 24
Figure 24. Figure 24: An example of obtaining relation popularity on the movies dataset using LLaMA3 in a zero-shot setting. [PITH_FULL_IMAGE:figures/full_fig_p016_24.png]
Figure 25
Figure 25. Figure 25: An example of obtaining question popularity on the movies dataset using ChatGPT in a 3-shot setting. [PITH_FULL_IMAGE:figures/full_fig_p017_25.png]
Figure 26
Figure 26. Figure 26: An example of obtaining answer popularity on the movies dataset using ChatGPT in a 3-shot setting. [PITH_FULL_IMAGE:figures/full_fig_p017_26.png]
Figure 27
Figure 27. Figure 27: An example of obtaining relation popularity on the movies dataset using ChatGPT in a 3-shot setting. [PITH_FULL_IMAGE:figures/full_fig_p018_27.png]

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