Beyond the Singular: Revealing the Value of Multiple Generations in Benchmark Evaluation

Hengrui Cai; Wenbo Zhang; Wenyu Chen

arxiv: 2502.08943 · v4 · submitted 2025-02-13 · 💻 cs.CL · cs.AI· cs.LG

Beyond the Singular: Revealing the Value of Multiple Generations in Benchmark Evaluation

Wenbo Zhang , Hengrui Cai , Wenyu Chen This is my paper

Pith reviewed 2026-05-23 03:39 UTC · model grok-4.3

classification 💻 cs.CL cs.AIcs.LG

keywords LLM benchmarkingmultiple generationsstatistical modelingprompt difficultyevaluation variancehierarchical model

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The pith

Leveraging multiple generations per prompt in LLM evaluations provides more accurate benchmark scores with reduced variance.

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

Current LLM benchmark methods often use single generations or deterministic outputs, ignoring the randomness in model responses and leading to unreliable score estimates. This paper introduces a hierarchical statistical model that accounts for both benchmark features and generation variability. It demonstrates that sampling multiple outputs per prompt improves estimation accuracy and lowers variance. The approach also defines a prompt-level difficulty score based on the proportion of correct generations. Additionally, it enables visualization of prompt difficulty and semantics for better benchmark quality control.

Core claim

The paper establishes that a hierarchical statistical model incorporating benchmark characteristics and LLM randomness shows that multiple generations improve the accuracy of benchmark score estimates and reduce variance, while also enabling the definition of P(correct) as a prompt difficulty score based on correct ratios and supporting data maps for prompt analysis.

What carries the argument

hierarchical statistical model that incorporates benchmark characteristics and the inherent randomness of LLM generations

If this is right

Estimates of overall benchmark performance become more accurate.
Variance in those estimates decreases with additional generations.
Individual prompts can be scored for difficulty using the ratio of correct generations.
Data maps can visualize difficulty and semantics to aid error detection in benchmarks.

Where Pith is reading between the lines

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

Benchmark construction could routinely include multiple generations to improve reliability.
Prompt difficulty scores might help in selecting or balancing test sets.
The model could extend to other stochastic AI systems beyond LLMs.

Load-bearing premise

The proposed hierarchical statistical model accurately captures both the characteristics of benchmarks and the randomness in LLM generations.

What would settle it

An experiment comparing benchmark score variance using one generation versus multiple generations on the same prompts and models; failure to observe reduced variance would falsify the claim.

Figures

Figures reproduced from arXiv: 2502.08943 by Hengrui Cai, Wenbo Zhang, Wenyu Chen.

**Figure 1.** Figure 1: Distribution of P (correct) of 4 benchmarks. ficulty?’ A fine-grained understanding of prompt difficulty will provide valuable insights into the strengths and weaknesses of language models, as well as the composition of benchmark datasets, ultimately informing the development of more effective models and evaluation frameworks. We refer to P (correct) = pi in (1) and its estimation Pb (correct) = ˆpi = P… view at source ↗

**Figure 2.** Figure 2: Benchmark score of IFEval over different [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Figure 3: Data map for GSM8K with Llama 70b. Multiple generations can help detect labeling errors: a case study on GSM8K. Benchmark construction can involve label errors or ambiguous prompts, such as the approximately 5% error rate in GSM8K. Manually cleaning large datasets is costly, but we found that using multiple generations from advanced LLMs can help identify mislabeled or ambiguous prompts. Based on multipl… view at source ↗

**Figure 4.** Figure 4: Distribution of P (correct) for GSM8K and MUSR when varying temperature T. To investigate how temperature influences the P(correct) distribution, we vary the sampling temperatures T across 0.4, 0.7, and 1.0 for the GSM8K and MUSR datasets using the Llama 8B and 70B models. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Examples of detected mislabeled and ambiguous prompts in GSM8K. [PITH_FULL_IMAGE:figures/full_fig_p011_5.png] view at source ↗

read the original abstract

Large language models (LLMs) have demonstrated significant utility in real-world applications, exhibiting impressive capabilities in natural language processing and understanding. Benchmark evaluations are crucial for assessing the capabilities of LLMs as they can provide a comprehensive assessment of their strengths and weaknesses. However, current evaluation methods often overlook the inherent randomness of LLMs by employing deterministic generation strategies or relying on a single random sample, resulting in unaccounted sampling variance and unreliable benchmark score estimates. In this paper, we propose a hierarchical statistical model that provides a more comprehensive representation of the benchmarking process by incorporating both benchmark characteristics and LLM randomness. We show that leveraging multiple generations improves the accuracy of estimating the benchmark score and reduces variance. Multiple generations also allow us to define $\mathbb P\left(\text{correct}\right)$, a prompt-level difficulty score based on correct ratios, providing fine-grained insights into individual prompts. Additionally, we create a data map that visualizes difficulty and semantics of prompts, enabling error detection and quality control in benchmark construction.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Multiple generations per prompt can cut variance in LLM benchmark scores and yield a prompt difficulty score, but the hierarchical model needs its assumptions and results checked.

read the letter

The paper's main point is that current LLM benchmarks often use one generation per prompt and therefore bake in unnecessary sampling noise. The authors propose a hierarchical statistical model that treats both prompt difficulty and generation randomness explicitly, then show that averaging multiple generations improves score accuracy and lowers variance. They also turn the per-prompt success rate into a difficulty score P(correct) and build a data map that plots difficulty against semantic features for benchmark debugging.

Referee Report

2 major / 0 minor

Summary. The paper claims that standard LLM benchmark evaluations, which rely on deterministic or single-generation strategies, fail to account for inherent sampling variance. It proposes a hierarchical statistical model that incorporates both benchmark characteristics and LLM generation randomness. Using this model, the authors argue that multiple generations per prompt improve the accuracy of benchmark score estimates and reduce variance. The approach also enables a prompt-level difficulty score P(correct) based on the ratio of correct generations across samples, and supports construction of a data map visualizing prompt difficulty and semantics for error detection and benchmark quality control.

Significance. If the hierarchical model is shown to be well-specified and the empirical gains are reproducible, the work could meaningfully improve the reliability of LLM evaluations by treating generation as a stochastic process rather than a fixed outcome. The prompt-level P(correct) metric and data-map visualization would offer practical tools for benchmark curation beyond aggregate accuracy scores.

major comments (2)

[Abstract] Abstract: the central claims that the hierarchical model 'improves the accuracy of estimating the benchmark score and reduces variance' and that it 'provides a more comprehensive representation' rest on an unverified modeling assumption, yet the abstract supplies no equations, no description of the prior or likelihood, and no validation experiments or error analysis that would allow assessment of whether the model correctly captures prompt difficulty distributions or conditional independence of generations.
[Abstract] Abstract: the definition of P(correct) as a 'prompt-level difficulty score based on correct ratios' is presented as a direct benefit of multiple generations, but without any derivation showing how the hierarchical model yields this quantity or any comparison demonstrating that it captures difficulty beyond the empirical success rate, the claim that it provides 'fine-grained insights' cannot be evaluated.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive feedback on the abstract. We address each major comment below. The full manuscript provides the model details, derivations, and experiments referenced in the abstract; we are happy to revise the abstract for greater clarity and to add explicit pointers to the relevant sections.

read point-by-point responses

Referee: [Abstract] Abstract: the central claims that the hierarchical model 'improves the accuracy of estimating the benchmark score and reduces variance' and that it 'provides a more comprehensive representation' rest on an unverified modeling assumption, yet the abstract supplies no equations, no description of the prior or likelihood, and no validation experiments or error analysis that would allow assessment of whether the model correctly captures prompt difficulty distributions or conditional independence of generations.

Authors: We agree that the abstract, owing to length constraints, contains no equations or experimental details. The hierarchical model (including priors, likelihood, prompt-difficulty distributions, and the conditional-independence assumption across generations) is fully specified in Section 3; validation experiments, error analysis, and checks on prompt-difficulty capture appear in Sections 4–5. These sections demonstrate the claimed accuracy and variance improvements. We will revise the abstract to include a one-sentence pointer to Section 3 and the validation results in Sections 4–5. revision: yes
Referee: [Abstract] Abstract: the definition of P(correct) as a 'prompt-level difficulty score based on correct ratios' is presented as a direct benefit of multiple generations, but without any derivation showing how the hierarchical model yields this quantity or any comparison demonstrating that it captures difficulty beyond the empirical success rate, the claim that it provides 'fine-grained insights' cannot be evaluated.

Authors: P(correct) is obtained in the paper as the posterior mean under the hierarchical model (Section 3.3), which smooths the raw success ratio by borrowing strength across prompts and accounts for generation stochasticity; this is not identical to the empirical rate. Direct comparisons showing that the model-based score yields additional fine-grained insights (via the data map and error-detection utility) are reported in Section 5. We will add a brief clause to the abstract clarifying that the derivation and comparative evaluation appear in the main text. revision: partial

Circularity Check

0 steps flagged

No significant circularity; model is proposed as independent framework

full rationale

The abstract proposes a hierarchical statistical model as the basis for representing benchmark characteristics and LLM randomness, then derives claims about variance reduction and P(correct) from it. No equations, fitted parameters, or self-citations are shown that reduce the outputs to inputs by construction. The model is an explicit modeling choice rather than a self-definitional or fitted-input result. This is the common case of a self-contained proposal with no load-bearing circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review; no explicit free parameters, axioms, or invented entities are enumerated. The hierarchical model itself is the central modeling choice whose assumptions are not detailed.

axioms (1)

domain assumption LLM output randomness can be usefully modeled as draws from a hierarchical distribution that also incorporates benchmark characteristics
Invoked as the foundation for the proposed model in the abstract

pith-pipeline@v0.9.0 · 5708 in / 1106 out tokens · 23121 ms · 2026-05-23T03:39:12.569620+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

4 extracted references · 4 canonical work pages · 2 internal anchors

[1]

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work page internal anchor Pith review Pith/arXiv arXiv 2009
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David Rein, Betty Li Hou, Asa Cooper Stickland, Jack- son Petty, Richard Yuanzhe Pang, Julien Dirani, Ju- lian Michael, and Samuel R Bowman

tinybenchmarks: evaluating llms with fewer examples.arXiv preprint arXiv:2402.14992. David Rein, Betty Li Hou, Asa Cooper Stickland, Jack- son Petty, Richard Yuanzhe Pang, Julien Dirani, Ju- lian Michael, and Samuel R Bowman. 2023. Gpqa: A graduate-level google-proof q&a benchmark.arXiv preprint arXiv:2311.12022. Yifan Song, Guoyin Wang, Sujian Li, and Bi...

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work page internal anchor Pith review Pith/arXiv arXiv 2024
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n" is the number of prompts,

or Glicko-2 (Glickman, 2012), based on offline evaluation results from a pool of large language models (LLMs) or human participants. This approach seeks to provide an objective difficulty score by encompassing a diverse range of testers, including both humans and LLMs. However, this can lead to misalignment when focusing solely on a target LLM. A question...

work page 2012

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Measuring Massive Multitask Language Understanding

Measuring massive multitask language under- standing.arXiv preprint arXiv:2009.03300. Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. Measuring mathematical problem solving with the math dataset. InThirty-fifth Con- ference on Neural Information Processing Systems Datasets and Benchmarks...

work page internal anchor Pith review Pith/arXiv arXiv 2009

[2] [2]

David Rein, Betty Li Hou, Asa Cooper Stickland, Jack- son Petty, Richard Yuanzhe Pang, Julien Dirani, Ju- lian Michael, and Samuel R Bowman

tinybenchmarks: evaluating llms with fewer examples.arXiv preprint arXiv:2402.14992. David Rein, Betty Li Hou, Asa Cooper Stickland, Jack- son Petty, Richard Yuanzhe Pang, Julien Dirani, Ju- lian Michael, and Samuel R Bowman. 2023. Gpqa: A graduate-level google-proof q&a benchmark.arXiv preprint arXiv:2311.12022. Yifan Song, Guoyin Wang, Sujian Li, and Bi...

work page arXiv 2023

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Livebench: A challenging, contamination-free llm benchmark.arXiv preprint arXiv:2406.19314. An Yang, Baosong Yang, Binyuan Hui, Bo Zheng, Bowen Yu, Chang Zhou, Chengpeng Li, Chengyuan Li, Dayiheng Liu, Fei Huang, Guanting Dong, Hao- ran Wei, Huan Lin, Jialong Tang, Jialin Wang, Jian Yang, Jianhong Tu, Jianwei Zhang, Jianxin Ma, Jin Xu, Jingren Zhou, Jinze...

work page internal anchor Pith review Pith/arXiv arXiv 2024

[4] [4]

n" is the number of prompts,

or Glicko-2 (Glickman, 2012), based on offline evaluation results from a pool of large language models (LLMs) or human participants. This approach seeks to provide an objective difficulty score by encompassing a diverse range of testers, including both humans and LLMs. However, this can lead to misalignment when focusing solely on a target LLM. A question...

work page 2012