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

Nitay Calderon, Eyal Ben-David, Zorik Gekhman, Eran Ofek, Gal Yona

arXiv:2602.14080v2cs.CLcs.AI

TL;DR

The paper addresses whether factual errors reflect missing knowledge or limited access to encoded facts. It introduces a behavioral fact-level profiling framework and WikiProfile, then finds that frontier models encode most benchmark facts while recall remains a major bottleneck; thinking recovers many failures.

  • Problem

    Standard factuality evaluations treat all errors alike, obscuring whether failures arise from missing knowledge or limited access to encoded facts.

  • Method

    The paper profiles facts by encoding and recall, using WikiProfile to test encoding, recall, and recognition across varied question contexts.

  • Results

    Frontier models encode over 95% of benchmark facts, but recall failures concentrate on rare facts and reverse questions; thinking recovers 40–65% of encoded-but-not-directly-known facts.

  • Takeaways & Limitations

    The results identify recall, rather than encoding, as the primary factuality bottleneck and suggest improving access to knowledge models already encode.

  • Takeaways & Limitations

    WikiProfile covers Wikipedia, single-hop facts, and recall along directionality and phrasing, so findings may not generalize to other corpora or query forms.

Abstract

from arXiv · show

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.

1. Introduction

The paper distinguishes missing factual knowledge from failures to access encoded facts by profiling knowledge at the fact level. Using WikiProfile, it finds that frontier models encode most benchmark facts, while recall remains the main bottleneck and thinking can recover inaccessible knowledge.

  • Motivation: Standard accuracy metrics cannot distinguish whether an incorrect answer reflects an unencoded fact or an encoded fact that is inaccessible.These failure types imply different interventions: scaling or broader data for encoding, and methods that improve knowledge utilization for recall.
  • Framework: The framework profiles each fact by encoding and accessibility: unrecalled, directly recalled, or recalled only with inference-time computation.Encoding is behaviorally measured in pre-training-like contexts, while recall is tested across different phrasings and relational orderings.
  • Benchmark: WikiProfile contains 2,150 naturally occurring facts, each paired with 10 questions probing encoding, recall, and multiple-choice recognition.An automated pipeline uses a prompted LLM grounded in web search to generate, refine, and verify questions.
  • Results: 95–98% of facts are encoded by frontier models, yet the same models cannot directly recall 25–33% of facts without thinking.Across 13 LLMs and more than 4 million graded answers, scaling primarily improves encoding rather than recall.
  • Results: Recall gaps are larger for long-tail facts than encoding gaps, and reverse questions are harder to generate despite no multiple-choice recognition disadvantage.These findings suggest that rare and reversed facts are often encoded but inaccessible under changed query conditions.
  • Implications: Thinking recovers 40–65% of encoded-but-not-directly-known facts, especially for long-tail facts and reverse questions.The results point toward post-training and inference-time methods that improve use of existing encoded knowledge.

2. Knowledge Profiling

Knowledge profiling shifts evaluation from questions to facts, separating whether a fact is encoded from whether it can be recalled directly or with thinking. The framework defines behavioral tests and five profiles that distinguish inaccessible stored facts from missing or inferred knowledge.

  • Evaluation: Question grades use the accuracy of gradable correct and incorrect responses, excluding partially correct or unverifiable labels.The autorater assigns four labels, while the aggregate grade uses only CORRECT and INCORRECT responses.
  • Operational Definitions: Encoding is measured by reproducing a fact in a pre-training-like context, while knowledge is tested across semantically equivalent question contexts.Encoding excludes thinking to avoid conflating storage with inference; knowledge is evaluated with and without thinking.
  • Operational Definitions: Knowledge questions vary phrasing and relational direction, using direct and reverse questions to test robust recall rather than surface-form matching.The setup uses two direct and two reverse questions, each with a different phrasing.
  • Knowledge Profiles: Knowledge profiling characterizes each fact by encoding, recall without thinking, and recall only with thinking, yielding five qualitatively distinct profiles.The framework shifts the unit of analysis from individual questions to facts and uses observable behavior rather than model internals.
  • Knowledge Profiles: Encoding failure means a fact is neither encoded nor known, whereas recall failure means it is encoded but inaccessible even with thinking.These profiles imply different intervention targets: pretraining for encoding failures and post-training improvements for recall failures.
  • Knowledge Profiles: Direct recall denotes encoded facts known without thinking, while recall with thinking denotes encoded facts recovered only through additional inference-time computation.Inference without encoding is less reliable because correctness may arise from multi-hop reasoning or educated guessing, and it occurs less frequently.

3. The WikiProfile Benchmark

WikiProfile is a benchmark for fact-level profiling that pairs Wikipedia-derived propositions with encoding, recall, and recognition questions. A prompted LLM grounded in web search automates fact and question construction, followed by filtering and manual validation.

  • Benchmark Design: WikiProfile contains 2,150 facts, each paired with 10 questions spanning encoding, recall, and multiple-choice recognition.The benchmark includes two encoding questions, four direct or reverse knowledge questions, and four multiple-choice verification variants.
  • Pipeline: The benchmark uses Wikipedia facts and a fully automated prompted-LLM pipeline to generate, refine, filter, and verify questions.The pipeline is intended to support profiling across fact extraction, question construction, and answer validation.
  • Pipeline: The pipeline extracts candidate facts, constructs proposition-completion tasks, and generates direct and reverse questions grounded by Google Search.Natural, contextual, and multiple-choice variants are then created from the direct and reverse pairs.
  • Quality Control: Facts are discarded when associated questions fail filtering, and manual validation removes fewer than 2% of facts, producing the final benchmark.Questions are designed to be unambiguous, specific, minimal, and uniquely answerable.

4. Experimental Setup

The experiments evaluate 13 LLMs with and without thinking using repeated sampling, prompted autoraters, and five knowledge profiles. Results are summarized as profile distributions, including a potential-knowledge measure that combines recall-related profiles.

  • Models: 13 LLMs from five model families are evaluated in configurations with and without thinking.The models include Gemini, GPT, and Gemma variants spanning commercial and open-weight systems.
  • Response Generation: Approximately 4.5 million responses are generated by sampling eight responses per example at temperature 1.The evaluation covers 13 models, two thinking settings, 2,150 facts, 10 tasks, and eight responses per task instance.
  • Response Evaluation: Two prompted LLM graders label responses CORRECT, INCORRECT, PARTIALLY, or OTHER, with question grades computed from correct and incorrect responses only.Partially correct and unverifiable responses are excluded because assigning them weights is subjective.
  • Response Evaluation: 98.2% agreement is observed between graders based on Gemini-2.5-Pro and GPT-5, with disagreements primarily involving excluded PARTIALLY or OTHER labels.The reported results are therefore described as insensitive to the underlying grader model.
  • Profile Analysis: The black line in the knowledge-profile plot marks potential knowledge as Direct Recall plus Recall with Thinking plus Inference without Encoding.The figure shows encoding failures decreasing sharply with scale while recall failures persist in frontier models.

5. Results

Across 13 LLMs, recall—not encoding—emerges as the main factuality bottleneck: frontier models encode most facts but fail to access many of them directly. These access failures are systematic, affecting long-tail and reverse questions, while thinking preferentially recovers encoded facts and narrows the gaps.

  • 5.1. The Recall Bottleneck: 95–98% of facts are encoded by frontier LLMs, yet recall failures remain a major share of their errors.Gemini-3-Pro and GPT-5 directly fail to recall 26–34% of encoded facts; recall failures account for more than 70% of GPT-5.2’s errors.
  • 5.1. The Recall Bottleneck: Scaling from 1B to 27B parameters reduces Gemma3 encoding failures from 85% to 23%, but recall failures rise to 40% without thinking and 33% with thinking.The family-level result indicates that greater capacity increases stored knowledge without necessarily improving inference-time access.
  • 5.2. Why Recall Fails: Long-tail facts show only a small encoding gap but often more than a 25% recall gap relative to popular facts.For smaller models, encoding gaps are larger, consistent with scaling primarily improving encoding.
  • 5.2. Why Recall Fails: Reverse questions are harder to generate than direct questions, although multiple-choice verification largely removes this directional disadvantage.For GPT-5, direct recall is 82.9% versus 74% on reverse questions; across nine models, reverse verification is actually no harder than direct verification.
  • 5.3. Thinking as a Recovery Mechanism: Thinking improves recall most where direct recall is weakest, narrowing both popularity and directionality gaps.For Gemini-3-Pro, rare-fact gains are 20.1 points versus 11.3 for popular facts; for GPT-5, reverse-question gains are 19 points versus 12 for direct questions, narrowing gaps from Δ = 21.4 to 12.5 and Δ = 9 to 2.
  • 5.3. Thinking as a Recovery Mechanism: Thinking primarily facilitates recall of encoded knowledge rather than generating correct answers through response diversity or complex inference.It recovers 40–65% of encoded facts in thinking-optimized LLMs but only 5–20% of non-encoded facts, while the benchmark facts are single-hop.

6. Related Work

The paper reframes latent factual knowledge and the reversal curse through a behavioral distinction between encoding and recall. It argues that thinking operates as a recall mechanism, especially when facts are rare or queried in unfamiliar directions.

  • Latent-knowledge studies show that LLMs may encode facts they fail to express during generation.
  • The reversal curse has been attributed to autoregressive objectives, training dynamics, data asymmetries, pretraining changes, and architectural modifications.
  • Verification reveals that models can recognize reverse answers they cannot generate, indicating recall asymmetry rather than absent bidirectional associations.
  • Evidence on thinking and factuality is mixed, including reports of improved accuracy, higher hallucination rates, and inconsistent effects on consistency.
  • The paper unifies these findings by treating thinking as a recall mechanism whose effect is strongest for rare facts and reverse questions.

7. Discussion

The discussion identifies recall, rather than encoding, as the primary factuality bottleneck in frontier LLMs. It connects this diagnosis to query sensitivity, possible interventions, and important limits on generalization and cost.

  • Over 95% of facts are encoded by the strongest evaluated LLMs, but recall failures concentrate on rare facts and reverse questions.
  • Distinguishing encoding from recall failures could extend analysis beyond short-form factuality to long-form generation, multi-step reasoning, and other knowledge-intensive settings.
  • Potential remedies span pretraining, post-training, and inference-time techniques such as thinking to improve access to parametric knowledge.
  • WikiProfile is limited to Wikipedia and single-hop facts queried along directionality and phrasing axes, so findings may not generalize broadly.
  • Fully profiling a frontier model costs approximately $500, although omitting multiple-choice questions or reducing samples can lower the cost.

Impact Statement

The impact statement says the study can clarify when LLMs are likely to fail and when inference-time computation may help. It reports no negative societal consequences specific to the work.

  • The findings could inform deployment decisions by identifying likely failures on rare facts or reverse questions.
  • The findings could also clarify when inference-time computation may be beneficial.
  • The authors foresee no negative societal consequences specific to this work.

A.1. Tasks and Properties

WikiProfile organizes factual evaluation around controlled variations in context, phrasing, direction, and format. Its automated pipeline extracts Wikipedia facts and generates, refines, filters, and verifies multiple question types.

  • WikiProfile varies format, context, verbatim overlap, and relational direction to examine factors affecting factual knowledge.
  • Encoding is measured with proposition completion and contextual questioning over the same source context.
  • The benchmark uses direct, direct-natural, reverse, and reverse-natural closed-book questions, plus multiple-choice variants for verification.
  • Facts are extracted from 10,000 Wikipedia pages using named-entity recognition and selection criteria requiring specific, non-trivial, time-independent candidates.
  • The resulting dataset is downsampled to 5,000 entities after verification and balancing across fact categories and entity types.
  • Questions are generated, refined for specificity, and filtered with search-grounded evaluation to reject ambiguity or multiple possible answers.

B.2. Measuring Availability and Robustness

The correct≥p metric separates whether a model can produce any correct answer from whether it answers correctly consistently. It estimates this distinction across a continuous range of correctness thresholds.

  • correct≥p measures the fraction of questions whose estimated probability of correctness across samples exceeds a threshold p.The threshold is evaluated using a binomial model over sampled responses.
  • The metric aggregates questions when the estimated probability of achieving at least ⌈pn⌉ correct answers exceeds 0.5.
  • At p=0.125, the metric captures availability by asking whether at least 1 of 8 sampled answers is correct.This behavior is analogous to pass@k.
  • At p=0.875, the metric captures robustness by asking whether the model is correct almost all of the time.

B.3. Ruling Out Response Diversity

Thinking improves availability broadly, but its effect on robustness depends on the model family and thinking implementation. For thinking-optimized models, improved robustness rules out response diversity as the sole explanation.

  • Availability and robustness: At p<0.5, thinking improves correct≥p for all evaluated LLMs, consistent with improved availability.Low thresholds correspond to producing at least one correct answer.
  • Availability and robustness: For thinking-optimized LLMs, thinking improves robustness across the full range of p because the +Thinking curve remains above the Base curve.The evaluated families include Gemini-3, Gemini-2.5, GPT-5, and GPT-5.2 variants.
  • Ruling out response diversity: Improved robustness is incompatible with response diversity as the sole explanation because increased output variance cannot produce greater consistency in correctness.
  • Model-family differences: For Gemma3 models, CoT prompting degrades robustness, while GPT-4.1 shows modest robustness gains.Gemma3 curves cross at intermediate p values.

B.4. Evidence for Recall Facilitation

The evidence favors recall facilitation as the primary mechanism by which thinking improves factuality. Thinking disproportionately recovers facts that are encoded but not directly known, while gains on non-encoded facts are smaller.

  • 40–65% of encoded but not directly known facts are recovered by thinking in thinking-optimized LLMs.The corresponding recovery rate for non-encoded facts is less than 20%.
  • Thinking improves robustness, providing evidence against response diversity as the mechanism behind factuality gains.
  • With n=8 samples, correct≥p may underestimate availability gains when correctness probabilities are roughly p≲0.1.Such cases frequently produce zero correct samples, while robustness at high p remains well-estimated.
  • Thinking gains concentrate mostly on encoded facts, consistent with recall facilitation rather than inference over non-encoded facts.The benchmark facts are single-hop, so complex deductive reasoning is unnecessary to derive the correct answer.

B.5. The Role of Thinking-Specific Training

Native thinking and CoT prompting produce different factuality patterns across model families. The results suggest that thinking-specific training may matter, but the experimental design cannot isolate it from other family differences.

  • Comparing thinking implementations: Native thinking consistently improves both availability and robustness, whereas CoT prompting produces mixed effects across model families.
  • Training-specific effects: The observed pattern suggests recall-facilitation benefits may depend on thinking-specific training rather than merely producing additional inference-time tokens.
  • Limitations: The experimental design cannot fully disentangle thinking-specific training from model size, data, and post-training differences between model families.The authors describe the pattern as suggestive but not conclusive.
  • Evaluation controls: None of 104 FDR-corrected phrasing tests was significant, indicating that phrasing did not confound knowledge assessment in this setup.The tests covered 13 LLMs with and without thinking and four question-pair types.

C.4. Reverse Questions

Reverse-question performance is evaluated on encoded facts to isolate recall failures, and these failures remain substantially larger than direct-question failures. Thinking reduces both popularity and directional recall gaps, especially in frontier models.

  • C.4. Reverse Questions: Reverse-question generation remains substantially harder than direct-question generation, even when analysis is restricted to encoded facts.Robustness analyses show this pattern also holds without conditioning on encoding.
  • C.4. Reverse Questions: Errors from reverse questions consistently exceed errors from direct questions across LLMs.For smaller models, failing both directions dominates; with increasing scale, only-reverse failures become dominant, comprising 40–50% plus an additional 15–30%.
  • C.4. Reverse Questions: Thinking mitigates the popularity gap for 8 of 13 LLMs and the directional gap for 9 of 13 LLMs.The mitigation is substantial for frontier LLMs, defined here as stronger proprietary models.

D.1. Handling Partially and Other Grades

The evaluation excludes non-gradable responses from question grades and adopts pair-level fact exclusions to reduce discarded facts while preserving profile distributions. Profile conclusions remain robust across threshold choices, though exact proportions vary.

  • D.1. Handling Partially and Other Grades: Question grades use only CORRECT and INCORRECT responses, excluding PARTIALLY and OTHER because assigning them weights is subjective.When all responses are PARTIALLY or OTHER, the fact is excluded from aggregate statistics.
  • D.1. Handling Partially and Other Grades: Pair-level exclusion reduces discarded facts to 1–4% for nearly all LLMs while producing profile distributions nearly identical to stricter fact-level exclusion.The adopted strategy excludes a fact only when an entire encoding, direct, or reverse task pair is non-gradable.
  • D.1. Handling Partially and Other Grades: Assigning PARTIALLY a weight of 0.51 reduces exclusions below 1% but introduces subjective judgment, so the pair-level strategy is used throughout.Results under the two strategies are very similar.
  • D.1. Handling Partially and Other Grades: Less than 0.5% of facts fall into the excluded unencoded-but-known-without-thinking case, which is omitted without changing results.The paper attributes these rare cases to sampling noise or grader error.
  • D.1. Handling Partially and Other Grades: Exact profile proportions vary with the threshold, but the main conclusions remain robust, including saturated frontier-model encoding and substantial recall failures.Thinking consistently acts as a recovery mechanism across the tested thresholds.

D.3. Grader Evaluation

The paper tests whether grader choice and repeated-response sampling affect its evaluation. Grader agreement is high, and eight responses per question provide stable fact-level estimates across evaluated models.

  • D.3. Grader Evaluation: Grader agreement is 98.2%, with most disagreements involving OTHER or PARTIALLY labels.These labels are excluded from the main analysis, and manual review generally favors Gemini-2.5-Pro’s labels.
  • D.3. Grader Evaluation: The authors conclude that results are not sensitive to the grader’s underlying LLM because graders agree on most responses and disagreements are mainly excluded labels.The primary grader is Gemini-2.5-Pro with thinking, compared against a GPT-5-based grader with thinking.
  • D.3. Grader Evaluation: Eight independent responses per question are used because a single response is noisy and token-level likelihoods are inaccessible for most proprietary LLMs.Repeated sampling estimates fact-level knowledge without requiring model weights or probability outputs.
  • D.3. Grader Evaluation: At n=8, the 90% empirical bootstrap confidence-interval width for the fraction of facts with g(q) > 0.5 falls below 1%.The sensitivity analysis spans encoding and knowledge tasks across eight LLMs.

Box D.1: Analysis of Disagreements Between Graders

Examples of grader disagreements show that labels can differ over vagueness, specificity, permissible paraphrase, and contradiction. Several disagreements favor treating broadly compatible answers as acceptable rather than incorrect.

  • Box D.1: Analysis of Disagreements Between Graders: A more general answer can receive PARTIALLY or OTHER when it lacks the requested specific fact, without necessarily contradicting it.Examples include “Taskmaster” for Antonia Dreykov and a group name instead of Fredrick Allen Hampton.
  • Box D.1: Analysis of Disagreements Between Graders: A vague response can be classified as OTHER rather than INCORRECT when it does not answer the requested entity or name.Examples include answering that people built Beodericsworth or that US 1 transported goods.
  • Box D.1: Analysis of Disagreements Between Graders: Explicit contradiction is treated as INCORRECT, as when a prediction changes the date in the question rather than answering it.The example states that the fossil loan occurred in December 2022 instead of December 2024.
  • Box D.1: Analysis of Disagreements Between Graders: A response may be accepted despite omitting an allowed modifier or using a formal-name variant of the gold answer.“Akshardham” is accepted for “Swaminarayan Akshardham,” and “The World’s Columbian Exposition” matches “1893 Columbian Exposition.”
  • Box D.1: Analysis of Disagreements Between Graders: Nonsense or refusal-like outputs are treated as OTHER or INCORRECT rather than partial answers.The response “Sure” receives OTHER for the reverse album question.

E. Prompts

The prompts operationalize WikiProfile’s data-construction tasks through category classification, named-entity recognition, and selection of factual OBJECT entities for completion tests.

  • Box E.1: Prompt for Classifying Pages into Categories: Pages are assigned exactly one category from a predefined list covering people, history, geography, arts, philosophy and religion, technology, and other topics.The prompt supplies the page title and summary as inputs and requires only the category name as output.
  • Box E.2: Prompt for Performing Named Entity Recognition: Named-entity recognition copies the paragraph’s second part and replaces selected entities with their names and entity types.The prompt illustrates annotations such as PERSON, DATE, GROUP, TITLE, EVENT, and NUMERIC_VALUE.
  • Box E.2: Prompt for Performing Named Entity Recognition: The entity-selection prompt permits up to eight entities and requires choosing specific, non-lengthy named entities rather than overly descriptive phrases.Selected entities are assigned types from a predefined list, and the output preserves the second part while replacing chosen entities with typed placeholders.
  • Box E.3: Prompt for Selecting Object Entities: OBJECT entities are selected for pre-training completion tasks in which the left-context indicates the expected entity kind but recalling the specific value requires factual knowledge.These entities become factual anchors for completion-based and question-answering robustness tests.
  • Box E.3: Prompt for Selecting Object Entities: Suitable OBJECTs require a strong earlier-entity relationship, a unique completion, and factual recall that cannot be obtained by guessing from the left-context alone.The instructions reject predictable completions such as “Chinese cuisine” after an explicit Chinese name or “South Africa” after Johannesburg.
  • Box E.3: Prompt for Selecting Object Entities: The prompts therefore distinguish contextual predictability from knowledge-dependent completion when constructing factual anchors.This distinction is applied across the category, NER, and OBJECT-selection procedures.
  • Box E.3: Prompt for Selecting Object Entities: The Panama disease example rates banana plants and its causal fungus as strong OBJECT choices, while disease, the 1950s, and the opening mention of Panama disease are weaker choices.Gros Michel is considered good but not perfectly constrained because the preceding context does not uniquely identify the variety.
  • Box E.3: Prompt for Selecting Object Entities: The second example illustrates that dates, nationalities, professions, tours, and rankings can be annotated as entities, while the selection rules judge whether their values require factual recall.The prompt separately explains why an entity appearing in the first clause may be ineligible as an OBJECT.
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