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Long-form factuality in large language models

Jerry Wei, Chengrun Yang, Xinying Song, Yifeng Lu, Nathan Hu, Jie Huang, Dustin Tran, Daiyi Peng, Ruibo Liu, Da Huang, Cosmo Du, Quoc V. Le

arXiv:2403.18802v4cs.CLcs.AIcs.LG

TL;DR

Evaluating open-ended, long-form factual answers is difficult because preset references may not cover all their facts. This paper introduces LongFact and SAFE, an LLM-and-search evaluator, and finds larger models generally more factual while SAFE outperforms human annotators on sampled disagreements.

  • Problem

    Long-form factuality evaluation lacks reliable methods because preset answers or knowledge sources are difficult to make comprehensive and nonredundant for all facts in open-ended responses.

    Source: §3 · p. 3

  • Method

    LongFact supplies 2,280 prompts across 38 topics, while SAFE decomposes responses into individual facts and checks relevant facts against Google Search results.

    Source: §2 · p. 3, §9 · p. 9

  • Results

    Larger models generally achieved better long-form factuality; on 100 sampled disagreements, SAFE annotations were correct 76% of the time.

    Source: §4 · p. 5, §6 · p. 7

  • Takeaways & Limitations

    SAFE offers an automated alternative to crowdsourced human annotation at more than 20× lower cost.

    Source: §9 · p. 9

    SAFE relies on Google Search, which may miss facts or lack depth in expert domains such as law and medicine.

    Source: §8 · p. 9

Abstract

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Large language models (LLMs) often generate content that contains factual errors when responding to fact-seeking prompts on open-ended topics. To benchmark a model's long-form factuality in open domains, we first use GPT-4 to generate LongFact, a prompt set comprising thousands of questions spanning 38 topics. We then propose that LLM agents can be used as automated evaluators for long-form factuality through a method which we call Search-Augmented Factuality Evaluator (SAFE). SAFE utilizes an LLM to break down a long-form response into a set of individual facts and to evaluate the accuracy of each fact using a multi-step reasoning process comprising sending search queries to Google Search and determining whether a fact is supported by the search results. Furthermore, we propose extending F1 score as an aggregated metric for long-form factuality. To do so, we balance the percentage of supported facts in a response (precision) with the percentage of provided facts relative to a hyperparameter representing a user's preferred response length (recall). Empirically, we demonstrate that LLM agents can outperform crowdsourced human annotators - on a set of ~16k individual facts, SAFE agrees with crowdsourced human annotators 72% of the time, and on a random subset of 100 disagreement cases, SAFE wins 76% of the time. At the same time, SAFE is more than 20 times cheaper than human annotators. We also benchmark thirteen language models on LongFact across four model families (Gemini, GPT, Claude, and PaLM-2), finding that larger language models generally achieve better long-form factuality. LongFact, SAFE, and all experimental code are available at https://github.com/google-deepmind/long-form-factuality.

1 Introduction

LLMs still make factual errors on in-depth factuality questions, limiting reliability in settings where accurate responses are expected. The paper introduces LongFact, SAFE, and F1@K, then uses them to benchmark language models.

Introduction

  • 72% of SAFE annotations agreed with human annotations from Min et al. (2023), and SAFE won 76% of 100 randomly sampled disagreement cases.SAFE was also reported to be 20× cheaper than human annotators.Source: §1 · p. 2
  • LongFact contains 2,280 fact-seeking prompts across 38 manually selected topics for benchmarking long-form factuality.The authors describe it as the first prompt set for evaluating long-form factuality across a wide variety of domains.Source: §1 · p. 2
  • SAFE decomposes a long-form response into individual facts, sends fact-checking queries to Google Search, and reasons about whether search results support each fact.The method uses an LLM agent to perform this evaluation automatically.Source: §1 · p. 2, Figure 1 · p. 2
  • F1@K measures factual precision as the ratio of supported facts and recall as the ratio of provided supported facts over a desired number K.K represents the human-preferred “ideal” number of facts in a response.Source: §1 · p. 2
  • Across thirteen models in the Gemini, GPT, Claude, and PaLM-2 families, larger language models generally achieved better long-form factuality on LongFact.Responses were evaluated using SAFE and performance was quantified using F1@K.Source: §1 · p. 2

2 LongFact: Using LLMs to generate a multi-topic benchmark for long-form factuality

LongFact is a GPT-4-generated benchmark for evaluating factuality in multi-paragraph responses across a broad range of topics. It contains separate concept and object tasks, with 1,140 prompts per task across 38 topics.

LongFact: Using LLMs to generate a multi-topic benchmark for long-form factuality

  • Unlike short-answer benchmarks such as TruthfulQA, HaluEval (Li et al., 2023), FreshQA (Vu et al., 2023), HalluQA (Cheng et al., 2023b), and FELM (Chen et al., 2023), LongFact tests long-form responses; unlike FActScore (Min et al., 2023), it covers broad topics.The paper motivates LongFact by noting the lack of a comprehensive prompt set for factuality in responses several paragraphs long.Source: §2 · pp. 2–3, Figure 2 · p. 3
  • LongFact contains 1,140 prompts each for concepts and objects, generated by GPT-4 from 30 prompts per topic across 38 manually selected topics.Its questions target a specific concept or object and require multiple detailed factoids in a long-form answer.Source: §2 · p. 3, Figure 2 · p. 3

3 SAFE: LLM agents as factuality autoraters

SAFE evaluates long-form factuality by decomposing responses into individual facts and using an LLM agent to iteratively search Google and reason about whether results support each relevant fact. This avoids relying on preset reference answers that may not cover the facts in an open-ended response.

3 SAFE: LLM agents as factuality autoraters

  • Reference-based metrics and prompted LLMs suit short answers but are suboptimal for long-form responses, whose facts are difficult to cover comprehensively and without redundancy in preset references.The cited approaches include BLEURT, ROUGE (Ganesan, 2018), and prompting language models (Min et al., 2023; Vu et al., 2023).Source: §3 · p. 3
  • SAFE evaluates at individual-fact granularity, following Min et al. (2023), and uses Google Search for dynamic references tailored to each fact, balancing accuracy, accessibility, and timeliness (Augenstein et al., 2023).Fact-level evaluation enables focused assessment when one sentence contains multiple facts.Source: §3 · p. 3
  • SAFE uses an LLM to extract individual facts, assess their relevance, and iteratively query Google Search and reason over results to determine support.Figure 3 illustrates the multi-step search and reasoning process.Source: §3 · pp. 3–4, Figure 3 · p. 4
  • The evaluator splits each response sentence into facts, resolves vague references, filters irrelevant facts, then rates the remaining facts as supported or not supported.In the reported setting, it uses five search steps and keeps three results per query; outputs include counts of supported, irrelevant, and not-supported facts.Source: §3 · p. 4

4 LLM agents can be better factuality annotators than humans

SAFE agreed with human annotations on 72.0% of individual facts and was more often correct than human raters on sampled disagreements, while costing more than 20× less per response. The evaluation used 16,011 facts from 496 prompt–response pairs.

4 LLM agents can be better factuality annotators than humans

  • SAFE annotations agreed with human annotations on 72.0% of 16,011 individual facts.The facts came from 496 prompt–response pairs with human labels of supported, irrelevant, or not supported.Source: Figure 4 · p. 5, §4 · p. 5
  • On 100 disagreement cases, SAFE was correct 76% of the time versus humans’ 19%, a 4-to-1 win ratio.The manually re-annotated labels, made with access to Google Search, served as ground truth.Source: §4 · p. 5, Figure 5 · p. 5
  • SAFE cost $0.19 per model response versus $4 per response for crowdsourced human annotations, making it more than 20× cheaper.For the 496 prompt–response pairs, SAFE’s total cost was $96.31.Source: §4 · p. 5, Figure 5 · p. 5

5 F1@K: Extending F1 with recall from human-preferred length

F1@K extends long-form factuality beyond precision by combining the share of supported facts with recall measured against a user-preferred target length. The metric uses K to cap recall and enables standardized comparisons between models and response-generation methods.

5 F1@K: Extending F1 with recall from human-preferred length

  • 13 models across Gemini, GPT, Claude, and PaLM-2 are compared on 250 LongFact-Objects prompts at K = 64 and K = 178; rankings remain relatively stable at sufficiently large K.Figure 6 reports F1@K results, with raw metrics referenced in Table 2.Source: Figure 6 · p. 6
  • Precision is the number of supported facts S(y) divided by all facts, supported and unsupported: Prec(y) = S(y)/(S(y)+N(y)).SAFE supplies the supported-fact count S(y) and unsupported-fact count N(y) for each response.Source: §5 · pp. 5–6
  • Recall is defined against K supported facts because no definite set of facts can be specified for every long-form response; supported facts beyond K do not increase recall.K is a hyperparameter representing the number of supported facts a user cares about; its selection is discussed in Appendix D.3.Source: §5 · p. 6
  • F1@K combines factual precision and recall, ranges from 0 to 1, and awards a full score only to responses with no unsupported facts and at least K supported facts.Higher scores indicate more-factual responses; the authors propose the metric for standardized comparisons between language models and response-generation methods.Source: §5 · p. 6

6 Larger LLMs are more factual

Across 13 models from four families evaluated on 250 LongFact-Objects prompts, larger models generally achieve better long-form factuality. The results also show family-specific exceptions and newer models matching or surpassing GPT-4.

6 Larger LLMs are more factual

  • The benchmark tested 13 models on the same random 250-prompt subset of LongFact-Objects, decoded responses up to 1,024 tokens at temperature zero, and aggregated SAFE metrics with F1@K for K = 64 and 178.K = 64 was the median number of relevant facts among responses for the tested prompts; K = 178 was the maximum.Source: §6 · p. 7
  • Larger models generally achieve better long-form factuality: GPT-4-Turbo > GPT-4 > GPT-3.5-Turbo, Gemini-Ultra > Gemini-Pro, and PaLM-2-L-IT-RLHF > PaLM-2-L-IT.GPT-4-Turbo, Gemini-Ultra, and PaLM-2-L-IT-RLHF are the three most-factual models at both selected K values.Source: §6 · p. 7
  • Gemini models, Claude-3-Opus, and Claude-3-Sonnet can match or surpass GPT-4, which the paper identifies as an older model.The GPT-4 model evaluated was gpt-4-0613.Source: §6 · p. 7
  • Claude-3-Sonnet achieves factuality similar to Claude-3-Opus despite being smaller, while Claude-3-Haiku appears less factual than older Claude models.The authors suggest Haiku’s apparent result may reflect prioritizing precision over recall, and say Sonnet’s similarity is unexplained without further model details.Source: §6 · p. 7

7 Related work

The section situates LongFact as a broad-coverage benchmark for long-form factuality and SAFE as an automatic evaluator for that setting. It also presents F1@K as a way to measure response precision and recall without preset ground-truth answers.

Benchmarking factuality

  • LongFact targets broad long-form factuality coverage, unlike benchmarks of isolated factoids or the limited set of long-form topics covered by prior work such as Min et al. (2023).Source: §7 · p. 7

Evaluating factuality in model responses

  • SAFE adapts component-by-component evaluation with external tools to long-form factuality and is automatic, requires neither fine-tuning nor preset references, and is reported more reliable and cheaper than crowdsourced annotations.The related work also identifies search-augmented language models as a line of prior work for fact verification (Gao et al., 2023; Wang et al., 2023; Zhang & Gao, 2023).Source: §7 · p. 8

Quantifying long-form factuality

8 Limitations

LongFact and SAFE depend on the capabilities of their underlying LLMs, while SAFE’s Google Search grounding and F1@K metric have additional limitations. The paper describes ways to bound or mitigate these weaknesses and identifies possible future work.

Limitations

  • SAFE’s LLM can make errors in fact decomposition, relevance reasoning, search-query selection, and judging support; the authors use GPT-3.5-Turbo and suggest fine-tuning as future work.LongFact prompt generation also depends on instruction following, so the authors use GPT-4 to maximize prompt quality.Source: §8 · p. 9
  • Google Search may miss facts or lack depth in expert domains, so SAFE labels claims as supported or not supported by its results rather than globally factual or non-factual.The authors describe Google Search as a widely accessible, comprehensive source for open-domain tasks; SAFE can also search restricted sources using site queries or another API.Source: §8 · p. 9
  • F1@K assumes responses contain no repeated facts, allowing a metric-gaming risk; the authors suggest deduplication in SAFE or measuring repetition with fluency or usefulness metrics.They leave deduplication for future work because handling duplicates would add complexity.Source: §8 · p. 9

9 Conclusion … A.2 Why does SAFE use “supported”, “irrelevant”, and “not supported” as labels?

The conclusion presents LongFact and SAFE’s approach to evaluating long-form factuality, reports SAFE’s comparison with human annotators and model-benchmark trend, and identifies limitations and future research directions. The appendices explain reproducibility choices and why SAFE evaluates whether facts are supported by Google Search rather than globally accurate.

9 Conclusion

  • LongFact comprises 2,280 GPT-4-generated prompts across 38 topics, while SAFE decomposes responses into facts, checks relevance and searches Google for factual support, then aggregates precision and recall as F1@K.K serves as a proxy for users’ preferred response length.Source: §9 · p. 9
  • 72% of SAFE annotations agreed with crowdsourced human annotations; SAFE won 76% of 100 randomly sampled disagreement cases and cost more than 20× less.The benchmark also found that larger language models generally had better long-form factuality.Source: §9 · p. 9
  • Larger language models generally had better long-form factuality in a benchmark of thirteen models from Gemini, GPT, Claude, and PaLM-2 families.The benchmark evaluated these models on LongFact.Source: §9 · p. 9
  • Future work could improve long-form factuality through better pretraining or finetuning and external tools, improve SAFE’s reliance on search-enabled agents, and develop reliable measures of hallucination relative to models’ internal knowledge.The paper distinguishes factuality against world knowledge from hallucination relative to a model’s internal knowledge.Source: §9 · p. 10
  • The authors argue that reliable datasets, evaluation methods, and aggregated metrics can improve understanding of long-form model capabilities and encourage further measurement and improvement research.Source: §9 · p. 10

A.1 Can I reproduce your results?

  • The authors open-sourced code for generating LongFact, implementing SAFE, and experimentation, and provided prompt templates and exemplars for both LongFact generation and SAFE.They used temperature zero to reduce response variation, model snapshots when possible, and publicly accessible Gemini, GPT, and Claude models; two PaLM-2 models were internal and inaccessible.Source: §A.1 · p. 16

A.2 Why does SAFE use “supported”, “irrelevant”, and “not supported” as labels?

  • Google Search cannot surface infinitely many accurate facts about unrecorded people, so search results cannot establish global accuracy for every fact.The paper notes that Google Search nevertheless offers a strong proxy for factual accuracy (Augenstein et al., 2023).Source: §A.2 · p. 16
  • Following Min et al. (2023) and Wadden et al. (2022), the paper defines factuality as whether a fact is supported by world knowledge—here, Google Search results—rather than globally accurate; such support is its best-available proxy for factual accuracy.Source: §A.2 · p. 16

A.3 What are the common causes of failure for SAFE? … B LongFact details

The appendices explain the strengths and limitations of SAFE and human factuality ratings, motivate F1@K and test prompt and dataset choices. They also discuss applying length-adjusted recall beyond factuality and clarify the scope of SAFE’s comparison with humans.

A.3 What are the common causes of failure for SAFE?

  • On SAFE’s 24 incorrectly rated facts among 100 disagreement cases, reasoning errors were the largest cause, missing search information the second-largest, and revision errors the smallest.The authors suggest stronger reasoning models could mitigate reasoning and revision errors; search failures may be reduced with better queries or more search results.Source: §A.3 · pp. 16–17, Figure 7 · p. 16

A.4 What are the common causes of failure for human annotators?

  • More than one-third of presumed human annotation errors involved confusing “irrelevant” with “not supported,” while other errors included missing evidence on the reference page or misreading the response.Google Search can surface supporting information unavailable on the supplied Wikipedia page, and fact-focused search results may make relevant evidence easier to find.Source: §A.4 · p. 17, Figure 8 · p. 17

A.5 Why is the “irrelevant” label not counted?; A.9 How can recall with human-preferred length be applied in other domains?

  • F1@K excludes “irrelevant” facts because they neither improve nor reduce factuality, and the authors argue that K-based recall can also suit other long-form tasks.For tasks such as creative writing, K can represent the number of statements after which users do not value additional content; irrelevant facts may instead reflect instruction-following, as discussed by Min et al. (2023).Source: §A.5 · p. 17, §A.9 · p. 20

A.6 Why is it important to measure factual recall?

  • F1@64 correlates more strongly with Chatbot Arena ELO than precision alone: r = 0.754 (p = 0.031) versus r = 0.502 (p = 0.205).The precision-only correlation was not statistically significant, whereas the correlation including recall was statistically significant.Source: §A.6 · p. 18, Figure 9 · p. 18

A.7 How does the prompt postamble affect model responses?

  • Adding a postamble requesting specific details slightly lowers factual precision at K = 1 but increases factuality at higher K by eliciting more supported facts.The tested postamble asked models to provide as many specific details and examples as possible.Source: §A.7 · p. 18, Figure 10 · p. 19

A.8 Why was LongFact-Concepts excluded from benchmarking?

  • GPT-4-Turbo, Claude-3-Opus, and PaLM-2-L-IT-RLHF achieved better long-form factuality on LongFact-Concepts than LongFact-Objects for all tested K, supporting use of the harder Objects set for benchmarking.The comparison used 250 randomly selected Concepts prompts without the postamble; Concepts asks about general topics rather than specific entities.Source: §A.8 · p. 19, Figure 11 · p. 19

A.10 How does SAFE perform with respect to other humans?; A.11 Is there canary text included in LongFact?

  • SAFE’s reported advantage is over crowdsourced human raters, not necessarily expert humans, because expert-level individual-fact annotations for open-ended factual prompts were unavailable for rigorous evaluation.LongFact files include a canary string intended to discourage benchmark prompts from entering future language-model training corpora.Source: §A.10 · p. 20, §A.11 · p. 20

B.1 Data-generation process … C.6 Response-level rating performance

The appendices detail how LongFact was generated and how SAFE processes and evaluates responses. They report response-level correlations with human ratings, alongside evidence about fact splitting, query diversity, and rating errors.

B.1 Data-generation process

  • LongFact prompts were generated with GPT-4 using ten evolving in-context examples, then deduplicated and sampled to yield 1,140 prompts each for Concepts and Objects at about $260.The process began with 60 prompts per topic per task; duplicates were questions answerable with approximately the same response, and 30 prompts per topic were randomly kept after deduplication.Source: §B.1 · p. 21, Table 3 · p. 21, Table 4 · p. 22

B.2 List of topics

  • LongFact covers 38 manually selected topics, including MMLU topics and popular-culture areas; Tables 7–10 show example prompts across those topics.The topics are classified as STEM, social sciences, humanities, or other.Source: §B.2 · p. 23, §B.3 · p. 23, Table 7 · p. 24

C.1 Implementation

  • SAFE splits responses into facts, revises them to be self-contained, checks contextual relevance, and uses Google Search evidence to label relevant facts supported or not supported.For each relevant fact, it may issue five queries and retrieve three results per query; it skips rating irrelevant facts and reports supported, irrelevant, and not-supported fact counts per response.Source: §C.1 · pp. 28–29

C.3 Examples of failed ratings

  • The appendix illustrates correct SAFE annotations across its label categories and errors caused by reasoning failures, missed search evidence, and revisions that remove needed context.The authors also note that the implementation does not explicitly disallow duplicate queries, and that vague references such as pronouns or unknown entities can challenge self-contained revisions.Source: §C.2 · p. 29, §C.3 · pp. 29, 30, 31, 37

C.4 Performance of splitting a response into individual facts

  • On 496 prompt–response pairs, SAFE’s fact counts correlated with human annotations at Pearson r = 0.798 (p = 1.2 × 10−110) and Spearman r = 0.846 (p = 2.7 × 10−137).The authors also manually examined random sentence-splitting examples and report seeing no errors, while describing the step’s quality as reasonably high.Source: §C.4 · p. 40, Table 22 · p. 40

C.5 Diversity of fact-checking queries

  • SAFE’s fixed five-query requirement can produce duplicates: objective claims may need fewer queries, while subjective judgments may require diverse evidence; allowing early stopping could reduce cost.The authors suggest better instruction-following and prompts emphasizing diversity as possible ways to reduce duplication.Source: §C.5 · pp. 40–41

C.6 Response-level rating performance

  • SAFE’s response-level supported-fact counts had the highest correlation with human ratings; not-supported counts correlated less, while irrelevant-fact counts had low correlation.The comparison used a fixed set of human-selected facts from prompt–response pairs in Min et al. (2023); the supplied passage gives no correlation values.Source: §C.6 · p. 41, Table 23 · p. 41

C.7 Search scope ablation

The search-scope ablation found that unrestricted web search more often provided the right information than Wikipedia-only search, while also exposing cases where irrelevant results misled SAFE.

C.7 Search scope ablation

  • The ablation compared unrestricted Google Search with Wikipedia-only queries on 146 differently rated claims among 657 claims from 20 randomly sampled FActScore biography questions.The Wikipedia-only condition added “site:https://en.wikipedia.org” to queries.Source: §C.7 · p. 41
  • Unrestricted search helped when Wikipedia lacked the needed information, while Wikipedia-only search helped when irrelevant open-web results led SAFE to rate a claim “Not Supported.”The latter case suggests that improving interaction between LLMs and search engines could help identify correct information when it exists.Source: §C.7 · p. 42
  • Three times more often, Case 1 occurred than Case 2, suggesting open-web search more often supplies the right information; the authors expect this advantage to be greater where Wikipedia coverage is thinner.Source: §C.7 · p. 42

C.8 Hyperparameter ablation · C.9 Choice of LLMs — comparison with Mixtral 8×7B · C.10 Generalization to more professional domains

Across these evaluations, SAFE’s default search settings performed best in human-annotation correlation, while its professional-domain errors mainly involved extracting or revising atomic facts. GPT-3.5-Turbo outperformed Mixtral 8×7B in the reported comparison.

C.8 Hyperparameter ablation

  • Five search queries per fact generally produced the highest correlation with human annotations for supported and not-supported facts; more queries did not improve it.The study held results per query at three, and concluded that additional queries were not worth their added computational cost.Source: §C.8 · p. 42, Figure 12 · p. 43
  • Three search results per query produced the highest correlation with human annotations for supported and not-supported facts; fewer or more results degraded performance.Too few results may omit needed information, while too many may obscure important evidence or add noisy, lower-quality results; the selected default also avoids extensive search and model API calls.Source: §C.8 · p. 42, Figure 13 · p. 43

C.9 Choice of LLMs — comparison with Mixtral 8×7B

  • Among 196 differently rated facts, Mixtral 8×7B won one-third of comparisons, while GPT-3.5-Turbo won two-thirds.The comparison used SAFE with Serper on 20 randomly selected FActScore biography questions, comprising 658 atomic facts; both settings sometimes failed to find the right search result.Source: §C.9 · p. 42
  • Mixtral 8×7B’s main weakness was revising atomic facts without preserving their exact subject, suggesting weaker instruction following than GPT-3.5-Turbo.For example, it changed “Justified aired in 2015” to a claim that the television series Jonathan Tucker appeared in aired in 2015; the paper suggests post-training or prompt tuning could help.Source: §C.9 · pp. 42–43

C.10 Generalization to more professional domains

  • 79.7% of law facts and 94.9% of medicine facts received the same SAFE and researcher rating; over 90% of incorrect ratings involved fact extraction or revision.The study manually checked SAFE ratings on six additional law and medicine questions; the errors more often concerned breaking sentences into atomic facts or making facts self-contained than judging search support.Source: §C.10 · pp. 43–44
  • For nuanced professional-domain claims, SAFE’s errors more often arose in generating self-contained atomic facts than in using search results to assess support.The paper therefore suggests stronger-reasoning LLMs to improve fact generation, not necessarily search-tool interaction.Source: §C.10 · p. 44
  • SAFE correctly used search evidence to support the FGF21 metabolic-stress claim and reject a claim of 50,000 annual diversity visas against evidence of approximately 55,000.These are reported success cases for judging whether self-contained atomic facts are supported by search results.Source: §C.10 · p. 44

D Metric details … E.4 RLHF improves long-form factuality

The appendices clarify F1@K’s assumptions and response-length trade-offs, then analyze how scaling, metric choices, and RLHF affect long-form factuality. They also document recurring causes of human annotation errors.

D.1 Assumption of F1@K: facts are non-repeated

  • F1@K assumes each response contains distinct facts; the benchmarked models did not repeat information to extend responses, while repetition is better assessed by usefulness or fluency.Repeating one supported fact can remain factually accurate while giving the user little information.Source: §D.1 · p. 45

D.2 Case analysis

  • F1@K rates a supported answer above an unsupported one, rewards more supported facts up to K through recall, and rates responses containing only unsupported facts equally.Source: §D.2 · p. 45

D.3 Selecting K

  • K models how many supported facts a user wants: the appendix reports K = 64 (median) and K = 178 (maximum), and shows that K = 1 ranks by precision while sufficiently large K ranks by supported-fact count.To set K so only a response filled with supported facts can score 1, the authors propose estimating the maximum fact count as T × W × F, using output-token limit T, average words per token W, and facts per word F.Source: §D.3 · p. 46

D.4 Factual precision–recall curves

  • Longer GPT-4-Turbo responses increase factual recall but lower precision, revealing a precision–recall trade-off as response length varies.The experiment instructed the model to respond in 1, 2, 4, 8, or 16 sentences; this length-control method requires strong instruction-following capability.Source: Figure 14 · p. 47, §D.4 · p. 47

E.1 Examples of incorrect human annotations

  • The appendix groups incorrectly rated human facts into five presumed causes: label confusion, missing information, failure to read carefully, or missed technicalities and reasoning errors.It provides an example for each category.Source: §E.1 · p. 49, Table 25 · p. 49, Table 26 · p. 50

E.2 Scaling large language models improves long-form factuality

  • Under the assumed scale ordering, larger Gemini, GPT, and PaLM-2 models always score better, while Claude-3-Sonnet and Claude-3-Opus outperform earlier Claude generations.Claude-3-Haiku shows a large precision increase over Claude-2.1 despite no large F1@64 or F1@178 improvement; this may reflect training to reduce unsupported facts.Source: Figure 16 · p. 54, §E.2 · p. 54, Figure 15 · p. 54

E.3 Model performance at other K values

  • At sufficiently large K, model rankings are relatively constant, but rankings change significantly at K = 1, which measures precision alone.The appendix reports results at K = 48, 84, and 1 in addition to the previously reported K = 64 and 178.Source: §E.3 · p. 54, Figure 17 · p. 55

E.4 RLHF improves long-form factuality

  • 72.9 versus 13.2 supported facts per response: PaLM-2-L-IT-RLHF beats PaLM-2-L-IT on F1@K at every K, with a larger advantage at higher K.The difference also appears at K = 1, indicating higher factual precision, and grows at larger K, indicating relatively higher recall for RLHF responses.Source: Figure 18 · p. 55, §E.4 · pp. 55–56

E.5 Full model-benchmarking results · E.6 Full benchmarking prompt set

This section documents the full benchmarking setup and prompt coverage: SAFE-based evaluation of thirteen models on 250 randomly sampled LongFact-Objects prompts, alongside the sampled base prompts organized by topic. The prompts span diverse fields and ask about people, events, concepts, and institutions.

E.5 Full model-benchmarking results

  • The full benchmark evaluates thirteen language models on the same 250 random LongFact-Objects examples, averages SAFE raw and aggregated metrics across responses, and reports them in Table 30.Aggregated metrics are precision, recall, and F1@K; the table caption gives the scope but no score values in the supplied passage.Source: §E.5 · p. 56, Table 30 · p. 56

E.6 Full benchmarking prompt set

  • The prompt appendix lists the 250 sampled base prompts sorted by topic and notes that benchmarking appended a postamble not shown in those prompts.The passage refers readers to Appendix B.2 for LongFact’s topic list and Appendix A.7 for the postamble description.Source: §E.6 · p. 56

E.6.1 20th Century Events; E.6.17 History

  • Examples span event and history questions, including prompts about Apollo 13 and the 79 AD eruption of Mount Vesuvius.Other listed prompts address the Berlin Wall construction, Oklahoma City bombing, and Bloody Sunday.Source: §E.6.1 · p. 56, §E.6.17 · p. 60

E.6.2 Accounting; E.6.3 Architecture; E.6.4 Astronomy; E.6.5 Biology

  • The sampled prompts also cover accounting, architecture, astronomy, and biology, with examples asking about FASB, Versailles, the James Webb Space Telescope, and the Bird of Paradise flower..Source: §E.6.2 · p. 57, §E.6.3 · p. 57, §E.6.4 · p. 57

E.6.8 Chemistry; E.6.10 Computer Science; E.6.11 Computer Security; E.6.12 Economics

E.6.18 Immigration Law; E.6.19 International Law; E.6.20 Jurisprudence

  • Legal prompts cover immigration law, international law, and jurisprudence, asking about statutes, treaties, institutions, and legal figures.Examples include the I-765 application, the UN Charter, and lawyer Barry Scheck.Source: §E.6.18 · p. 60, §E.6.19 · p. 60, §E.6.20 · p. 60

E.6.21 Machine Learning; E.6.22 Management; E.6.23 Marketing

  • Business and technology prompts address machine learning, management, and marketing through questions about organizations, leaders, and campaigns.Examples include NLTK, Bob Iger’s leadership at Disney, and Amazon Prime Day.Source: §E.6.21 · p. 61, §E.6.22 · p. 61, §E.6.23 · p. 61

E.6.24 Mathematics; E.6.25 Medicine; E.6.26 Moral Disputes

E.6.27 Movies; E.6.28 Music; E.6.29 Philosophy

E.6.30 Physics; E.6.31 Prehistory; E.6.32 Psychology

E.6.32 Psychology

  • Psychology prompts ask about the Asch conformity experiments, the marshmallow experiment, Aaron T. Beck, and the Thematic Apperception Test.They ask how group pressure affects judgment, what the marshmallow experiment focused on, Beck’s work in cognitive therapy, and how the TAT is used.Source: §E.6.32 · p. 64

E.6.33 Public Relations

  • Public-relations prompts cover FIFA’s response to its 2015 corruption scandal, Crystal Pepsi’s launch, Boeing’s 737 MAX safety concerns, Samsung’s Note 7 crisis, Bell Pottinger, and FleishmanHillard.The questions ask what actions or roles were involved, or what is known about the firms.Source: §E.6.33 · p. 64

E.6.34 Sociology

  • Sociology prompts ask who Peter L. Berger, Anthony Giddens, Norbert Elias, Max Weber, Thorstein Veblen, and Vilfredo Pareto are.Source: §E.6.34 · p. 64

E.6.35 Sports

  • Sports prompts ask about the Stanley Cup, the Masters’ Green Jacket, the Ryder Cup, Serena Williams, and the America’s Cup.Source: §E.6.35 · p. 64

E.6.36 US Foreign Policy; E.6.37 Virology; E.6.38 World Religions

  • Other prompts ask about U.S. foreign policy figures and topics, virologists and outbreaks, and landmarks or figures in world religions.Examples include John Bolton, the 2002–2003 SARS outbreak, Guru Nanak, the Kaaba, and St. Peter’s Basilica.Source: §E.6.36 · p. 64, §E.6.37 · p. 65, §E.6.38 · p. 65

2. Limitations

The authors direct readers to Section 8 and Appendix A for limitations. They report detailed reproducibility materials and released code, but say compute use is difficult to estimate because many experiments query proprietary models.

Limitations

  • The authors say limitations are discussed in Section 8 and frequently asked questions in Appendix A.Source: §2 · p. 66

Experimental details

  • The authors report no theoretical results and say they did not train models, instead evaluating existing models and specifying the data split in Appendix E.6.Source: §2 · pp. 67–68

Reproducibility

  • They report that experiments and implementations are detailed in Appendices B, C.1, and E, with reproducibility steps in Appendix A.1 and experimental code released.Source: §2 · pp. 67–68

Limitations

  • Compute use is difficult to calculate because most experiments query proprietary models that are not publicly available.Source: §2 · p. 69

Societal impact and release

  • They report no anticipated significant societal impacts, release no models, and say their generated dataset was manually reviewed and includes a canary string to deter pretraining use.Source: §2 · pp. 69–70

Human subjects

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