Rethinking the Role of Prompting Strategies in LLM Test-Time Scaling: A Perspective of Probability Theory

Nan Xu; Ran He; Tieniu Tan; Yexiang Liu; Zekun Li; Zhi Fang

REVIEW 4 major objections 5 minor 1 cited by

Rethinking the Role of Prompting Strategies in LLM Test-Time Scaling: A Perspective of Probability Theory

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read This paper claims that under majority-voting scaling, simple Chain-of-Thought eventually dominates all eight tested prompting strategies, and provides a closed-form formula to predict the winner.

desk verdict Useful empirical sweep and a plausible predictor, but the CoT-dominance headline is overstated and the probability theory is not tight enough to support it as stated. read the letter →

arxiv 2505.10981 v3 pith:WIUDUIQC submitted 2025-05-16 cs.AI cs.CLcs.LG

Yexiang Liu , Zekun Li , Zhi Fang , Nan Xu , Ran He , Tieniu Tan This is my paper · ORCID

classification cs.AIcs.CLcs.LG

keywords chain-of-thoughtpromptingmajorityvotingtest-timescalingself-consistencystrategiesprobabilitytheorylawLLMreasoning

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper sets out to show that under majority voting, the simplest reasoning prompt—plain chain-of-thought—eventually beats every more elaborate prompting strategy once the number of samples is large, even when those strategies start with higher single-sample accuracy. It argues this is not an accident of the benchmarks: the answer counts follow a multinomial distribution, and the asymptotic winner is determined by whether a question is easy or hard for a strategy and by how flat the wrong-answer distribution is. The paper also claims an O(1) formula that predicts each strategy's scaling curve and selects the best strategy for any sampling budget using only a small sample of answers. If true, this means a large share of test-time scaling gains can be had with simple prompting, and expensive large-N evaluations are unnecessary for strategy selection.

What carries the argument

The load-bearing object is the multinomial model of sampled answers, $X_i \sim \mathrm{Mult}(N, p_{i,1},\dots,p_{i,m})$, with majority voting selecting the most frequent answer. On top of it, Eq. (10) is a closed-form normal approximation: $\Pr(\text{correct}) \approx 1 - \Phi\left(-(p_1 - p_{\max})\big/\sqrt{(p_1(1-p_1) + p_{\max}(1-p_{\max}))/N}\right)$, where $p_1$ is the correct-answer probability and $p_{\max}$ is the largest wrong-answer probability. This formula is the paper's test-time scaling law: it turns any strategy's answer distribution into a predicted scaling curve and a predicted best strategy $P^*_N$. The theorems about easy, moderate, and hard questions supply the qualitative mechanism, while Eq. (10) supplies the quantitative tool.

What would settle it

Record the actual majority-voting accuracy for each prompting strategy at $N$ up to 1000 on a benchmark such as GSM8K, and also compute the exact multinomial majority probability from the empirically estimated answer distributions; if the exact values and the observed values diverge materially from Eq. (10) for large $N$, the normal-max approximation and any strategy ranking based on it are falsified.

Watch

Extended reading notes

Core claim

The central claim is that, for majority voting under a fixed sampling-time or compute budget, the ordering of prompting strategies is not fixed by pass@1 accuracy. For each question, the sampled answers of a strategy are modeled as multinomial draws; a question is 'easy' when the correct answer is the unique most probable answer, 'moderate' when it ties for the most probable, and 'hard' otherwise. Theorems 1–3 state that majority-voting accuracy tends to 1 on easy questions, to $1/|S|$ on moderate ties, and to 0 on hard questions, so the dataset composition of easy versus hard questions governs the scaling limit. Theorem 4 gives conditions under which two strategies cross: one with lower single-sample accuracy but a flatter wrong-answer distribution overtakes another with higher initial accuracy as $N$ grows. Empirically, CoT has the fewest hard questions and the most uniform wrong-answer distribution across six LLMs and six benchmarks, so it dominates at large $N$.

Load-bearing premise

The whole prediction and overtaking argument assumes that each strategy's answer probabilities are fixed across samples and that the largest count among wrong answers is approximately normal with mean and variance set by the second-best answer, an approximation the paper uses without proof.

Editorial extensions

If this is right

At sufficiently large $N$, choosing a prompting strategy reduces to comparing each prompt's answer distribution; the strategy with the best combination of high correct-answer probability and flat wrong-answer distribution wins, so no full large-N run is needed.
The O(1) formula predicts $P^*_N$ using only about 40 samples to estimate each strategy's answer probabilities, and on the tested setup the error falls below 1% once $N \geq 10$, so it can serve as a cheap test-time scaling law.
Because majority voting converges to 0 on hard questions, spending more samples on hard questions is wasteful; accuracy can be improved by scaling only easy or moderate questions.
Because the best strategy differs per question, dynamically choosing the optimal prompt per question—even at $N=1$—can exceed the best fixed strategy's infinite-sample accuracy.
Combining per-question difficulty-aware scaling with per-question strategy selection gives large upper-bound accuracy gains on the reported benchmarks, including GSM8K, MATH-500, GPQA, and AIME.

Reading between the lines

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

The normal-max approximation in Eq. (10) makes the predicted ordering most fragile on questions where $p_1$ and $p_{\max}$ are close, because the crossing point $N_0$ is largest there; a dataset deliberately composed of near-tie questions should delay or reverse CoT's dominance, and testing that composition would isolate whether the approximation or the empirical difficulty split drives the result
The same multinomial argument applies to other aggregation rules beyond majority voting, such as weighted voting or verifier reranking: any selector extracting an answer from multinomial samples is governed by the gap $p_1 - p_{\max}$ and the easy-versus-hard split, so the 'simple prompt wins at scale' finding may extend to other test-time scaling mechanisms.
The dynamic-strategy oracle results suggest a practical calibration route: with a small labeled sample, one could learn a per-question difficulty-and-strategy classifier that approximates the oracle $P^*_N$, turning the theoretical upper bound into an achievable inference-time policy.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

I'll keep this short. The thing to know: the empirical sweep is genuinely useful, but the headline is stronger than the evidence. Section 3 says CoT dominates without exception on all models when largely scaling, yet their own Table 4 shows SBP as best on LLaMA-3-8B-Instruct on GSM8K for every N from 20 to 1000, and the Limitations section concedes only about 80% of results fit. The abstract and intro repeat the strong version. That mismatch should be fixed before this is citable as stated.

What's new and good: the 6 LLMs x 8 prompting strategies x 6 benchmarks comparison under majority voting, with both sampling-time and cost budgets, is a useful reference. The cost-controlled comparison is fairer than most prior work. The two explanatory factors — CoT having a better easy/hard question mix and a flatter wrong-answer distribution — are intuitive and partly quantified via KL divergence and the Theorem 4 condition counts. The O(1) predictor is a nice practical idea: estimate answer probabilities from a small sample, then use a normal approximation to extrapolate to larger N. The oracle-based improvements in Section 6 are clearly labeled upper bounds; no one should mistake them for deployed methods.

Soft spots, in order of importance. First, the universality claim. It is not just a wording issue: the predictor itself selects SBP on LLaMA/GSM8K, so the paper's own tool disagrees with the title claim on that cell. Second, the theory. Theorem 3's "general declining trend" is not a theorem, and the proof relies on limit statements without monotonicity. More seriously, Eq. (6) approximates the maximum of the wrong-answer counts by a normal with mean N p_max and variance N p_max(1-p_max). The max of multinomial counts is not normally distributed that way; the approximation is unproven and could misrank strategies in finite samples. The predictor is validated on one model/dataset pair, so we don't know how often the approximation holds. Third, missing error bars. Five runs are averaged; we need at least ranges or standard deviations, especially because some adjacent strategies are within a point. Fourth, the extended GPQA results show non-monotone aggregate accuracy, which is fine theoretically but further undercuts the simple "CoT eventually dominates" narrative.

Who this is for: anyone working on test-time scaling or budget-aware inference. It deserves a serious referee. I'd send it out, with a request to qualify the central claim, tighten or weaken the theorems, and add uncertainty quantification. As it stands I wouldn't cite the headline; I'd cite the comparison matrix and the predictor once those are fixed.

Referee Report

4 major / 5 minor

Summary. The paper studies the test-time scaling of eight prompting strategies under majority voting, claiming that simple Chain-of-Thought (CoT) eventually outperforms more complex strategies as the number of samples N grows, despite underperforming at small N. The claim is supported by experiments on 6 LLMs, 8 prompting strategies, and 6 benchmarks, with additional results on GPQA and AIME. The authors propose a probabilistic explanation (Theorems 1–4) based on the proportions of easy/moderate/hard questions and the uniformity of incorrect-answer distributions, introduce an O(1) formula (Eq. 10) to predict majority-vote accuracy and select the best strategy P*_N, and present two oracle-based ways to improve scaling performance (adaptive difficulty-based scaling and dynamic strategy selection). The paper's Limitations section explicitly states that the CoT-dominance finding holds for only about 80% of results and does not hold for every LLM/dataset.

Significance. If the central claim were fully established, the paper would be a valuable contribution: it addresses a practical question (which prompting strategy to use when scaling test-time compute), provides a broad empirical matrix under equivalent cost budgets, and offers a cheap predictor for majority-vote scaling. The paper ships code and includes closed and open models. Theorems 1–3, which characterize the limiting behavior of majority voting for easy/moderate/hard questions, are elementary and valid within the multinomial model. The core weakness is that the headline universality claim is contradicted by the paper's own tables, and the proposed predictor and Theorem 4 rely on an unproven normal approximation for the maximum of multinomial counts. These issues are fixable with a more cautious framing and additional finite-N validation, so the contribution is potentially significant but currently overclaimed.

major comments (4)

[Section 3, Table 4, and Limitations] The statement in Section 3 that 'CoT dominates without exception on all models when largely scaling' is directly contradicted by Table 4, which shows that for LLaMA-3-8B-Instruct on GSM8K the true best strategy P*_N is SBP for every N from 20 to 1000. Appendix C further states that 'almost 83% of results satisfy that CoT or DiP performs best,' and the Limitations section concedes that the finding 'does not always hold for every LLM on every dataset.' These statements are inconsistent with the abstract's claim of 'consistently show' and with the title's strong framing. The central claim should be reformulated as an aggregate empirical trend over the tested matrix, with per-dataset tallies and explicit caveats, rather than a universal asymptotic ordering.
[Section 5, Eq. (6)–(10), and Appendix B (Theorem 4)] The O(1) predictor and the proof of Theorem 4 approximate M = max(x2,...,xm) by a normal distribution N(N p_max, N p_max(1-p_max)). This approximation is not justified: the maximum of multinomial counts for fixed m is not asymptotically normal in the relevant tail regime, and the derivation also ignores the dependence between M and x1 when forming Z = x1 - M. No finite-N bound or empirical justification for the approximation is provided beyond a single dataset (LLaMA-3-8B-Instruct on GSM8K). In addition, the proof of Theorem 4 contains an inequality-direction error: it derives Pr(x_i',1 > M'_i) > Pr(x_i,1 > M_i) but then concludes Pr(a1|Pi;N) > Pr(a1|Pi';N), which is the opposite of the theorem's statement; the text should conclude with '<'. Because the predictor is used to select P*_N and the paper claims correctness for arbitrary N, this gap is load-bearing.
[Section 5, 'Experiment' paragraph and Table 4] The experimental validation of the O(1) predictor is limited to one model-dataset pair (LLaMA-3-8B-Instruct on GSM8K) and uses only 40 samples to estimate the per-answer probabilities p_i,j. The paper reports no error bars, confidence intervals, or variance across the five runs, despite averaging over five runs elsewhere. The claim that 'when N≥10, the error is already less than 1%' is based on this single pair, and the stability of the selected P*_N with respect to the noise in the 40-sample estimate is not quantified. To support the practical claim of predicting scaling performance and selecting the best strategy, the validation should be extended to multiple model-dataset pairs, and the sensitivity of P*_N to the probability estimates should be reported (e.g., via bootstrap).
[Section 6 and Abstract] The abstract and introduction state that the authors 'introduce two ways to significantly improve the scaling performance,' but the practical versions of these methods do not deliver the advertised gains: Section 6.1 reports that 'Adaptive' performance is 'almost equal to the usual scaling performance,' and Section 6.2 reports that 'Dynamic' performance is 'almost equal to CoT.' The substantial improvements come only from oracle upper bounds, which the paper acknowledges. This framing overstates the practical contribution and should be revised to clearly distinguish an upper-bound analysis from deployable methods, both in the abstract and in the contributions list.

minor comments (5)

[Table 1] In Table 1, the L2M row for Gemini-1.5-Flash lists Hard as 89.8%, which makes the row sum to more than 100%; it should likely be 8.9% to match the Easy and Moderate entries.
[Figure 37 caption] The caption reads 'GQPA' but the benchmark is GPQA; please correct the typo.
[Appendix B, Theorem 4 proof] Beyond the inequality-direction issue noted above, the proof says 'the distribution of Mi can be approximated by Mi ~ N(N p_i,n, N p_i,1(1-p_i,1))' but uses p_i,q in the variance formula; the notation should be consistent.
[Section 3 and Limitations] The paper gives slightly different percentages for the same claim ('about 80%' in Section 3, '80% of the results' in Limitations, and 'almost 83%' in Appendix C); these numbers should be reconciled with a precise per-model and per-dataset count.
[Section 5, Eq. (10)] The statement that the prediction error 'decreases until 0% as scaling' is not generally guaranteed when p_i,j are estimated from a finite sample; the variance of the estimator should be discussed or the claim qualified.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the scaling predictions and dominance analysis are derived from estimated answer distributions and independent empirical checks, not from the target claims.

full rationale

The paper's derivation chain is self-contained and non-circular. The multinomial majority-vote model (Eq. 4) and the classification of questions into easy/moderate/hard (Definition 1) are formal definitions, not restatements of the conclusion that CoT dominates. Theorems 1-4 are mathematical consequences of the multinomial model; their empirical support comes from measured difficulty proportions, KL divergences, and counts of questions satisfying Theorem 4, which are independent checks rather than fitted restatements of scaling curves. The O(1) predictor in Eq. 10 is derived from a normal approximation to the multinomial counts and uses probabilities estimated from only 40 samples; it is not fitted to the target scaling curves, and the paper validates it against separately measured real scaling performance (Figure 4, Table 4). The oracle-based improvements in Section 6 are explicitly labeled upper bounds, not practical predictions. The only self-citations appear in Related Work and are not load-bearing for any central claim. The normal approximation of the maximum of multinomial counts is mathematically questionable and could affect correctness, but a questionable approximation is not circularity. The Limitations section even disclaims universal CoT dominance, noting exceptions such as Table 4, which further indicates that the empirical claim is not being imposed by construction. No step in the paper reduces its predictions or theoretical conclusions to its own inputs by definition.

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

No free parameters are fitted to the target scaling curves; the 40 samples used to estimate p_i,j are an input measurement. The main load-bearing assumptions are the multinomial fixed-probability model, the normal approximation for the maximum of counts, and the per-round sample equivalence for iterative strategies.

assumptions (4)

domain assumption Answer counts for each prompt strategy follow a multinomial distribution with fixed probabilities p_i,j independent of N and independent across samples.
Used in Section 2.4 Eq. (1) and Section 4 to model majority voting; assumes no correlation or drift in answer distribution.
ad hoc to paper The maximum of the non-correct answer counts M can be approximated by a normal distribution with mean N p_max and variance N p_max(1 - p_max).
Invoked in Section 5 Eq. (6) and Theorem 4 in Appendix B; this is a heuristic, not a theorem for maxima of multinomial counts.
domain assumption For iterative strategies (ToT, S-RF, MAD), one round or reasoning path corresponds to one sample in the equal-sampling-time comparison.
Section 2.4 groups P2 strategies and treats each round as a sample, which ignores their much higher per-round token cost; cost comparisons use a pricing proxy.
domain assumption The answer extractor phi correctly extracts final answers from model outputs.
Assumed throughout; regular expression extraction may fail on some outputs.

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Cite this review

Pith. "Pith review of Rethinking the Role of Prompting Strategies in LLM Test-Time Scaling: A Perspective of Probability Theory." pith.science (2026). https://pith.science/paper/WIUDUIQC

@misc{pith2026250510981,
  author       = {Pith},
  title        = {Pith review of: Rethinking the Role of Prompting Strategies in LLM Test-Time Scaling: A Perspective of Probability Theory},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WIUDUIQC}},
  note         = {Machine review of arXiv:2505.10981}
}

abstract

Recently, scaling test-time compute on Large Language Models (LLM) has garnered wide attention. However, there has been limited investigation of how various reasoning prompting strategies perform as scaling. In this paper, we focus on a standard and realistic scaling setting: majority voting. We systematically conduct experiments on 6 LLMs $\times$ 8 prompting strategies $\times$ 6 benchmarks. Experiment results consistently show that as the sampling time and computational overhead increase, complicated prompting strategies with superior initial performance gradually fall behind simple Chain-of-Thought. We analyze this phenomenon and provide theoretical proofs. Additionally, we propose a probabilistic method to efficiently predict scaling performance and identify the best prompting strategy under large sampling times, eliminating the need for resource-intensive inference processes in practical applications. Furthermore, we introduce two ways derived from our theoretical analysis to significantly improve the scaling performance. We hope that our research can promote to re-examine the role of complicated prompting, unleash the potential of simple prompting strategies, and provide new insights for enhancing test-time scaling performance. Code is available at https://github.com/MraDonkey/rethinking_prompting.

Figures

Figures reproduced from arXiv: 2505.10981 by the authors.

**Figure 2.** Average performances of distinct prompting strategies and the best one [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Illustration of the two reasons why CoT sometimes performs worse with lower N while better with larger N. Left: CoT has more easy questions and fewer hard questions. For example, the probability distribution of L2M is {0.4, 0.5, 0.1, 0.0, 0.0} (hard question), and {0.3, 0.2, 0.2, 0.2, 0.1} (easy question) for CoT. Although L2M has higher pass@1 accuracy, its accuracy reduces until 0% as scaling while CoT increase… view at source ↗

Figures from the paper (39 more)

**Figure 4.** Figure 4: Real and predicted performance using our method of different [PITH_FULL_IMAGE:figures/full_fig_p008_4.png]

**Figure 5.** Figure 5: Results of adaptively scaling for each Pi ∈ P1 based on oracle and predicted question difficulty [PITH_FULL_IMAGE:figures/full_fig_p009_5.png]

**Figure 6.** Figure 6: Results of dynamically choosing the optimal [PITH_FULL_IMAGE:figures/full_fig_p009_6.png]

**Figure 7.** Figure 7: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]

**Figure 8.** Figure 8: Performance of each prompting strategy under given sampling time [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]

**Figure 9.** Figure 9: Performance of each prompting strategy under given cost [PITH_FULL_IMAGE:figures/full_fig_p020_9.png]

**Figure 10.** Figure 10: Performance of each prompting strategy under given sampling time [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

**Figure 11.** Figure 11: Performance of each prompting strategy under given cost [PITH_FULL_IMAGE:figures/full_fig_p021_11.png]

**Figure 12.** Figure 12: Performance of each prompting strategy under given sampling time [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]

**Figure 13.** Figure 13: Performance of each prompting strategy under given cost [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]

**Figure 14.** Figure 14: Performance of each prompting strategy under given sampling time [PITH_FULL_IMAGE:figures/full_fig_p022_14.png]

**Figure 15.** Figure 15: Performance of each prompting strategy under given cost [PITH_FULL_IMAGE:figures/full_fig_p022_15.png]

**Figure 16.** Figure 16: Results of adaptively scaling based on the question difficulty on Llama-3-8B-Instruct on GSM8K. [PITH_FULL_IMAGE:figures/full_fig_p023_16.png]

**Figure 17.** Figure 17: Results of adaptively scaling based on the question difficulty on GLM-4-9B-Chat on GSM8K. [PITH_FULL_IMAGE:figures/full_fig_p023_17.png]

**Figure 18.** Figure 18: Results of adaptively scaling based on the question difficulty on Phi-3.5-mini-Instruct on GSM8K. [PITH_FULL_IMAGE:figures/full_fig_p023_18.png]

**Figure 19.** Figure 19: Results of adaptively scaling based on the question difficulty on Gemini-1.5-Flash on GSM8K. [PITH_FULL_IMAGE:figures/full_fig_p023_19.png]

**Figure 20.** Figure 20: Results of adaptively scaling based on the question difficulty on GPT-4o-mini on GSM8K. [PITH_FULL_IMAGE:figures/full_fig_p023_20.png]

**Figure 25.** Figure 25: Results of dynamically choosing the optimal [PITH_FULL_IMAGE:figures/full_fig_p024_25.png]

**Figure 26.** Figure 26: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p024_26.png]

**Figure 27.** Figure 27: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p024_27.png]

**Figure 28.** Figure 28: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p024_28.png]

**Figure 33.** Figure 33: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p025_33.png]

**Figure 34.** Figure 34: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p025_34.png]

**Figure 35.** Figure 35: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p025_35.png]

**Figure 36.** Figure 36: Results of combining adaptively scaling and [PITH_FULL_IMAGE:figures/full_fig_p025_36.png]

**Figure 37.** Figure 37: Accuracy of each Pi with Qwen2.5-7B-Instruct on GQPA and AIME2024. 0 20 40 60 80 100 Sampling Time 30 32 34 36 38 40 Performance (%) DiP Vanilla Adaptive Oracle 0 20 40 60 80 100 Sampling Time 34 36 38 40 42 44 Performance (%) CoT Vanilla Adaptive Oracle 0 20 40 60 80…

**Figure 38.** Figure 38: Results of adaptively scaling based on the question difficulty on Qwen2.5-7B-Instruct on GPQA. [PITH_FULL_IMAGE:figures/full_fig_p027_38.png]

**Figure 40.** Figure 40: Results of dynamically choosing the optimal [PITH_FULL_IMAGE:figures/full_fig_p027_40.png]

**Figure 39.** Figure 39: Scaling performance of AnP on the easy/hard [PITH_FULL_IMAGE:figures/full_fig_p027_39.png]

**Figure 42.** Figure 42: Prompt of DiP. User: Question: <question> Answer: Let’s think step by step. Assistant: <answer> Chain-of-Thought prompt [PITH_FULL_IMAGE:figures/full_fig_p028_42.png]

**Figure 43.** Figure 43: Prompt of CoT. User: Question: Elsa has 5 apples. Anna has 2 more apples than Elsa. How many apples do they have together? Answer: Let's break down this problem: 1. How many apples does Anna have? 2. How many apples do they have together? 1. Anna has 2 more apples tha…

**Figure 44.** Figure 44: Prompt of L2M on GSM8K [PITH_FULL_IMAGE:figures/full_fig_p028_44.png]

**Figure 45.** Figure 45: Prompt of L2M on GSM-Hard. User: In order to solve the question more conveniently and efficiently, break down the question into progressive sub-questions. Answer the sub-questions and get the final result according to sub-questions and their answers. Question: <questi…

**Figure 46.** Figure 46: Prompt of L2M on MATH and MMLU [PITH_FULL_IMAGE:figures/full_fig_p029_46.png]

**Figure 47.** Figure 47: Prompt of ToT. User: <question> Assistant: <previous answer> User: Review your previous answer and find problems with your answer. Assistant: <feedback> User: Based on the problems of your previous answer, improve your answer. Assistant: <revised answer> Self-Refine P…

**Figure 48.** Figure 48: Prompt of S-RF [PITH_FULL_IMAGE:figures/full_fig_p030_48.png]

**Figure 49.** Figure 49: Prompt of SBP [PITH_FULL_IMAGE:figures/full_fig_p031_49.png]

**Figure 50.** Figure 50: Prompt of AnP [PITH_FULL_IMAGE:figures/full_fig_p032_50.png]

**Figure 51.** Figure 51: Prompt of MAD [PITH_FULL_IMAGE:figures/full_fig_p033_51.png]

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Visual Access Boundaries in Vision-Language Model Reasoning
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CoT in VLMs extends language-side computation over early image-derived states rather than prolonging direct image-token access, with gains limited by perceptual readout reliability.

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2023

Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

online" 'onlinestring :=

ENTRY address archivePrefix author booktitle chapter edition editor eid eprint eprinttype howpublished institution journal key month note number organization pages publisher school series title type volume year doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block STRING...

[2] [2]

write newline

" write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

[3] [3]

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work page 2023

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arXiv 2023

[5] [5]

Maciej Besta, Nils Blach, Ales Kubicek, Robert Gerstenberger, Michal Podstawski, Lukas Gianinazzi, Joanna Gajda, Tomasz Lehmann, Hubert Niewiadomski, Piotr Nyczyk, et al. 2024 a . Graph of thoughts: Solving elaborate problems with large language models. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38, pages 17682--17690

work page 2024

[6] [6]

u rgen M \

Maciej Besta, Florim Memedi, Zhenyu Zhang, Robert Gerstenberger, Nils Blach, Piotr Nyczyk, Marcin Copik, Grzegorz Kwa \'s niewski, J \"u rgen M \"u ller, Lukas Gianinazzi, et al. 2024 b . Topologies of reasoning: Demystifying chains, trees, and graphs of thoughts. arXiv preprint arXiv:2401.14295

arXiv 2024

[7] [7]

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arXiv 2024

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2024