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Most LLM factual errors are not missing knowledge but failures to recall facts the model already encodes, and thinking recovers many of them.

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T0 review

2026-08-02 23:20 UTC pith:VNBMUBUP

load-bearing objection Solid, well-controlled empirical paper with a new benchmark; the headline claim is real but inflated by an ∃/∀ definitional asymmetry, and the paper should re-run under symmetric quantifiers before the strongest claims hold. the 3 major comments →

arxiv 2602.14080 v2 pith:VNBMUBUP submitted 2026-02-15 cs.CL cs.AI

Empty Shelves or Lost Keys? Recall Is the Bottleneck for Parametric Factuality

Nitay Calderon , Eyal Ben-David , Zorik Gekhman , Eran Ofek , Gal Yona This is my paper
classification cs.CL cs.AI
keywords parametric factualityknowledge profilingrecall vs encodingLLM evaluationreversal curselong-tail knowledgechain-of-thoughtWikiProfile
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that most factual errors made by large language models are not cases where the knowledge is missing from the model, but cases where the model cannot access facts it does store. The authors define a fact as encoded if the model can reproduce it in a context that mimics how pre-training documents present it, and as known if the model can answer minimal questions about it from memory. Applying this split to 13 models with a new benchmark called WikiProfile, they report that frontier models encode 95–98% of tested facts yet fail to directly recall 26–34% of them, and that thinking (chain-of-thought or reasoning mode) recovers a large fraction. The conclusion is that further scaling of pre-training will buy less than methods that improve recall, such as post-training and inference-time computation. If right, this reframes long-tail errors and the reversal curse as access problems rather than missing knowledge.

Core claim

The central claim is that recall, not encoding, is the bottleneck for parametric factuality. The paper introduces five knowledge profiles—encoding failure, recall failure, direct recall, recall with thinking, and inference without encoding—and measures them behaviorally. Using WikiProfile, 2,150 Wikipedia-derived facts each paired with ten questions, the authors generate over four million graded responses from 13 LLMs. They find that as model scale increases, encoding failures drop sharply (e.g., from 85% for a 1B model to 23% for a 27B model in one family), while recall failures persist and even grow as a share of errors; frontier models like GPT-5 and Gemini-3-Pro encode 95–98% of facts bu

What carries the argument

The key mechanism is a behavioral encoding-vs-knowledge split. A fact counts as encoded if the model passes at least one of two heavily primed tasks—proposition completion or contextual questioning using the source left-context—with grade above 0.5 (existential criterion). It counts as known only if it passes all four minimal-context questions—direct and reverse, each in two phrasings—with grade above 0.5 (universal criterion). The asymmetry between existential encoding and universal knowledge is what separates stored-but-inaccessible facts from missing ones, and it drives all five knowledge profiles.

Load-bearing premise

The load-bearing premise is that success on the two heavily primed encoding tasks (completion and contextual questioning with the exact source left-context) is a valid measure of whether a fact is stored in the model's parameters, and that failure on any one of the unprimed minimal questions truly means the fact is not accessible without extra computation.

What would settle it

Measure encoding with the same unprimed questions used for knowledge, or with multiple-choice recognition. If the recall-failure bucket largely disappears under that alternative probe—for example, if 'encoded but not known' facts are recognized at chance in multiple-choice while primed completion succeeds—then the bottleneck is the probe's format, not recall.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

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If this is right

  • Frontier LLMs will gain less from scale than from recall-oriented interventions; the paper shows encoding is near saturation while 11–34% of facts remain inaccessible without thinking.
  • Long-tail factuality errors should be treated as recall failures rather than knowledge gaps, shifting the goal of long-tail work from data coverage to retrieval.
  • The reversal curse is a recall asymmetry: models verify reverse answers in multiple-choice at near-parity, so bidirectional associations are stored; only generation in the reverse direction fails.
  • Thinking (CoT or reasoning mode) is a recovery mechanism for encoded facts: it recovers 40–65% of encoded-but-not-directly-known facts and narrows popularity and directionality gaps.
  • Benchmarking factuality should report knowledge profiles, not just accuracy, because the same error rate hides different bottlenecks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the recall bottleneck is real, then retrieval-augmented generation is not the only fix: improving parametric recall (e.g., better retrieval cues, self-generated QA training) could raise factuality without external memory.
  • The existential/universal definition asymmetry implies the reported recall-failure share partly depends on how lenient the encoding test is; using recognition (MCQA) as the encoding probe would likely shrink the gap, since the paper itself shows recognition is near-parity for reverse questions.
  • A direct test: train or fine-tune a model on facts with varied question phrasings and directions, and measure whether the recall-failure share shrinks; the framework predicts it will, without any change in stored content.
  • Tip-of-the-tongue analogies suggest a 'reminiscence' effect: repeated varied retrieval attempts may convert recall-with-thinking facts into direct-recall facts; the paper's framework gives a way to measure such practice effects.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper proposes a behavioral framework for separating two sources of LLM factuality errors: facts that are not parametrically encoded ('empty shelves') and facts that are encoded but not accessible at inference time ('lost keys'). Encoding is operationalized as passing at least one of two heavily primed tasks (left-context proposition completion or contextual questioning), while knowledge is operationalized as passing all four minimal-context direct/reverse questions. This yields five knowledge profiles. The authors introduce WikiProfile, a 2,150-fact benchmark with ten tasks per fact, constructed through an automated LLM pipeline grounded in web search, and evaluate 13 LLMs with and without thinking (≈4.5M graded responses). They report that frontier models encode 95–98% of facts yet directly recall only 66–74%, that the encoding gap between popular and long-tail facts is small while the recall gap is large, that reverse questions are hard to generate but easy to verify in multiple-choice format, and that thinking recovers 40–65% of encoded-but-unrecalled facts. Extensive robustness checks include grader agreement, threshold sensitivity, bootstrap response-count stability, and alternative PARTIALLY/OTHER handling strategies.

Significance. If the central claim holds, this is a valuable reframing: long-tail errors and the reversal curse would be access failures rather than missing knowledge, and the practical implication that post-training and inference-time methods matter more than further scaling would be important for the field. The paper's strengths include the scale of the evaluation, the new WikiProfile benchmark, and a commendable set of internal controls (98.2% cross-grader agreement, five-threshold sensitivity, bootstrap CIs, and three label-handling strategies). However, the headline conclusion rests on a quantifier asymmetry in the operational definitions that may partly manufacture the 'recall bottleneck' it reports. Because that concern is load-bearing, the paper needs a symmetric reanalysis before the central claim can be accepted.

major comments (3)
  1. [§2.1 (definitions of encodes and knows)] The two central definitions are not symmetric. Encodes is defined existentially: a fact is encoded if ∃q∈E_f, g(q)>τ, where E_f contains two maximally primed tasks. Knows is defined universally: a fact is known only if ∀q∈Q_f, g(q)>τ, where Q_f contains four minimal-context questions. The paper states that this contrast is intentional, but the consequence is that any fact reproducible under one heavily primed context yet failing any one of four unprimed phrasings is automatically a 'recall failure.' The reported 26–34% recall-failure share is therefore partly a theorem of the ∃/∀ asymmetry, not purely an empirical discovery. The paper's own §5.2 result—reverse MCQA is at parity with direct while reverse generation lags—shows that much of the gap is format/direction-specific. I request a reanalysis under symmetric definitions (e.g., encoding requires both E tasks, or knowledge is satisfie
  2. [§5.2, Fig. 6] The claim that 'the reversal curse is a recall phenomenon rather than a lack of bidirectional association' relies on the MCQA parity result. But multiple-choice verification supplies the correct answer among distractors, so success can reflect partial association, plausibility ranking, or distractor weakness rather than a fully encoded bidirectional fact. The observed pattern—reverse verification is easier than direct verification for 9 of 13 models—suggests that reverse MCQA may be systematically easier (e.g., the object entity in the question makes the subject easier to identify, or distractors are weaker for reverse questions). Please report distractor-difficulty calibration or an alternative forced-choice control, or soften the conclusion to 'verification is more robust than generation for reverse questions.'
  3. [§5.3, Fig. 8] The inference that 'thinking primarily helps models access knowledge they have already encoded' is weaker than the data license. Recovery is conditioned on the asymmetric ∃-definition of encoding, and the paper's own 'Inference without Encoding' profile (§2.2, Fig. 4) shows that non-encoded facts can become known with thinking. Because the facts are single-hop, thinking could still recruit other parametric associations or produce a valid answer through a different surface form; the paper does not rule out these alternatives. I suggest either adding a control that isolates recall facilitation (e.g., facts for which there is no plausible inferential path from other encoded facts) or explicitly presenting recall facilitation as one of several plausible mechanisms rather than the concluded mechanism.
minor comments (6)
  1. [Abstract/§5.1] The Abstract says 'fail to directly recall 26–34% of facts,' while §5.1 says '25–33%' and the Introduction says '25–33%.' Please harmonize the numbers.
  2. [§1/§4] The Abstract and Introduction report '4 million responses,' while §4 reports '≈4.5 million responses.' Please use one consistent figure.
  3. [§2.2/Table 2] The 'Inference without Encoding' profile is excluded for facts that are not encoded but known without thinking, with the justification that these are <0.5% and likely noise. This is reasonable, but the 0.5% threshold is itself a design choice; a brief sensitivity note would help.
  4. [§3] The paper states 'We will announce the release of WikiProfile and add a link.' For a benchmark paper, the dataset and prompts should be available or at least provided as supplementary material for review.
  5. [§5.4] The human-cognition parallels (tip-of-the-tongue, feeling-of-knowing) are clearly marked as suggestive, but the section could be shortened or moved to the Discussion to keep the Results focused.
  6. [Appendix C.4] The bootstrap analysis says the 90% CI width 'falls below 1%' and then interprets this as '±0.5%.' This is correct, but the phrasing could be confusing; consider saying 'width below 1 percentage point.'

Circularity Check

1 steps flagged

The ∃-encoding vs ∀-knowledge definitions in §2.1 make the reported recall-failure bucket partly a theorem of the quantifier asymmetry, though the magnitudes and auxiliary evidence are not purely circular.

specific steps
  1. self definitional [§2.1, Operationalizing Encoding and Knowledge]
    "We say an LLM encodes the fact f if: ∃q∈E_f , g(q)>τ ... We say an LLM knows a fact f if: ∀q∈Q_f , g(q)>τ. The contrast with encoding is intentional: encoding uses existential quantification (∃) because reproducing a fact in any priming context suffices as evidence of storage, whereas knowledge uses universal quantification (∀) because robust recall should not depend on phrasing or query direction."

    Encoding is defined as passing ONE of two heavily primed tasks (left-context completion or contextual question), while knowledge is defined as passing ALL four minimal-context generation questions. Under these definitions, the 'recall failure' category (encoded ∧ not known) is logically equivalent to (∃ success on a primed task) ∧ (∃ failure on an unprimed question). Any model that fails even one unprimed question while passing one primed task is automatically assigned to the recall-failure bucket, independent of whether the fact is 'stored but inaccessible' versus merely sensitive to question format or direction. The central finding in §5.1 — near-saturated encoding (95–98%) but 26–34% not directly recalled — therefore inherits the ∃/∀ asymmetry by construction. The qualitative conclusion

full rationale

The paper is not fitting parameters and then calling them predictions; no hidden self-citation chain is load-bearing; and the reversal-curse analysis includes an independent MCQA verification result that goes beyond the bare definitions. That independent evidence (models recognize reverse answers they cannot generate) supports the 'format/direction sensitivity' reading and keeps this from being a purely forced result. However, the headline claim 'recall is the bottleneck' is substantially determined by the operational definitions in §2.1: given the ∃ encoding criterion and ∀ knowledge criterion, a recall-failure bucket is guaranteed for any imperfect model, and the reported shares are not compared against a symmetric redefinition (e.g., ∀ encoding or ∃ knowledge). The robustness appendix varies the threshold τ but never varies the quantifier structure, so the constructional contribution is not quantified. Accordingly, the appropriate finding is partial circularity: the central profile categories are self-definitional in part, but the empirical magnitudes, threshold robustness, and verification experiments retain independent content. Score 4 rather than 6 because no fitted parameter is renamed as a prediction and because the paper's own MCQA results partially corroborate a genuine recall/format dissociation.

Axiom & Free-Parameter Ledger

3 free parameters · 5 axioms · 1 invented entities

The ledger reflects that the paper is an empirical measurement rather than a derivation. The dominant load-bearing choices are the behavioral definition of encoding (ad hoc), the Wikipedia/pre-training correspondence, the LLM grader and its PARTIALLY/OTHER exclusion rule, and the page-view popularity proxy. The five knowledge profiles are invented behavioral categories with no falsifiable handle outside the paper's own probes. Free parameters are the grade threshold τ = 0.5, the popularity-tier cutoffs, and the response count n = 8; all three are robustness-checked, which limits their distortion.

free parameters (3)
  • Grade threshold τ = 0.5
    Binary encoding/knowledge labels use g(q) > τ with τ = 0.5 (§2.1). Robustness is shown in Fig. 17 for τ ∈ {0.01, 0.5, 0.99}, but the headline percentages are threshold-relative.
  • Popularity tier cutoffs = bottom 20% / top 20% of page views
    The popularity-gap analyses (§5.2, Fig. 5) split facts at the 20th/80th percentiles of Wikipedia page views; the Δ values depend on this motivated but arbitrary choice.
  • Response count n = 8
    Chosen so the 90% bootstrap CI width drops below 1% (Appendix C.4, Fig. 18). Justified, but hand-picked.
axioms (5)
  • ad hoc to paper Behavioral encoding-via-memorization: passing one of two heavily primed tasks (proposition completion with the source left-context; contextual question) with grade > 0.5 suffices to establish that the fact is parametrically 'encoded'.
    §2.1 defines encoding behaviorally because model weights are inaccessible; it is the paper's central operational choice and the fragility point of the whole framework.
  • domain assumption Wikipedia pages and source-text positions used for completion are representative of pre-training encounters.
    §3 motivates WikiProfile by Wikipedia being a trusted, likely pre-training source; the completion task mimics the pre-training objective.
  • domain assumption The prompted LLM grader (Gemini-2.5-Pro with thinking) produces correct labels for the 4.5M responses.
    §4 and Appendix C.3; cross-grader agreement with GPT-5 is 98.2%, with disagreements mostly in excluded OTHER/PARTIALLY labels.
  • domain assumption Page views proxy pre-training frequency of facts.
    §5.2; the authors call it 'a reasonable but imperfect proxy' and expect stronger trends with a more direct measure.
  • domain assumption Excluding PARTIALLY/OTHER responses does not bias question grades.
    §4 and Appendix C.1; such labels are rare (<5%) and three handling strategies give near-identical profile distributions.
invented entities (1)
  • Five knowledge profiles no independent evidence
    purpose: Classify each fact as Encoding Failure, Recall Failure, Direct Recall, Recall with Thinking, or Inference without Encoding; the paper's headline rates are shares of these buckets.
    The profiles are pure behavioral definitions (Fig. 1, §2.2); the paper offers no falsifiable handle outside its own probes that a 'Recall Failure' corresponds to a stored-but-inaccessible memory state. The only independent-looking signal — thinking recovers encoded-but-not-direct facts — is measured on the same probes used to define the buckets.

reviewed 2026-08-02 · how reviews work

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Cite this review

Pith. "Pith review of Empty Shelves or Lost Keys? Recall Is the Bottleneck for Parametric Factuality." pith.science (2026). https://pith.science/paper/VNBMUBUP

@misc{pith2026260214080,
  author       = {Pith},
  title        = {Pith review of: Empty Shelves or Lost Keys? Recall Is the Bottleneck for Parametric Factuality},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VNBMUBUP}},
  note         = {Machine review of arXiv:2602.14080}
}
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read the original abstract

Standard factuality evaluations of LLMs treat all errors alike, obscuring whether failures arise from missing knowledge (empty shelves) or from limited access to encoded facts (lost keys). We propose a behavioral framework that profiles factual knowledge at the level of facts rather than questions, characterizing each fact by whether it is encoded, and then by how accessible it is: cannot be recalled, can be directly recalled, or can only be recalled with inference-time computation (thinking). To support such profiling, we introduce WikiProfile, a new benchmark constructed via an automated pipeline with a prompted LLM grounded in web search. Across 4 million responses from 13 LLMs, we find that encoding is nearly saturated in frontier models on our benchmark, with GPT-5 and Gemini-3 encoding 95--98% of facts. However, recall remains a major bottleneck: many errors previously attributed to missing knowledge instead stem from failures to access it. These failures are systematic and disproportionately affect long-tail facts and reverse questions. Finally, we show that thinking improves recall and can recover a substantial fraction of failures, indicating that future gains may rely less on scaling and more on methods that improve how models utilize what they already encode.

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Forward citations

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    One of the questions asks for dynamic information ( like statistics or current roles ) without specifying a timeframe , making the answer subject to decay . ---- ### ** NOT SUITABLE Examples ** ** Direct Question :** What language's complete form was published in the book Toki Pona : The Language of Good ? ** Answer ( Object ) :** Toki Pona ** Reverse Que...

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    Minor rephrasing of the context or question may be needed to improve the flow and remove redundancy . ---- ### ** Required Output Format ** You must return * only * a string with the contextual question . ---- ### ** Examples ** 1. 50 Empty Shelves or Lost Keys? Recall Is the Bottleneck for Parametric Factuality * ** Context :** Erika Nordby ( born Februa...

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    URL https: //doi.org/10.48550/arXiv.2509.07968

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    doi: 10.18653/V1/2024.EMNLP-MAIN.232

    Association for Computational Linguistics, 2024. doi: 10.18653/V1/2024.EMNLP-MAIN.232. URLhttps: //doi.org/10.18653/v1/2024.emnlp-main.232. Q. Guo, R. Wang, J. Guo, X. Tan, J. Bian, and Y. Yang. Mitigating reversal curse in large language models via semantic-aware permutation training. In L. Ku, A. Martins, and V. Srikumar, editors,Findings of the Associa...

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This paper was first reviewed by deepseek-v4-flash on August 2, 2026.