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REVIEW 4 major objections 5 minor 1 cited by

First Finish Search: Efficient Test-Time Scaling in Large Language Models

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Reasoning-model answers that finish first are the most likely to be correct, so a decode that launches n parallel samples and returns whichever trace finishes first can match or beat majority voting and budget forcing while using up to…

desk verdict A simple, API-friendly test-time scaling trick with a solid empirical core and a shaky theoretical wrapper; worth review once Table 4 is fixed or dropped. read the letter →

arxiv 2505.18149 v1 pith:4VCF7PAZ submitted 2025-05-23 cs.CL

Aradhye Agarwal , Ayan Sengupta , Tanmoy Chakraborty This is my paper
classification cs.CL
keywords test-timescalingfirstfinishsearchreasoninglanguagemodelsmajorityvotingbudgetforcingtrace-lengthdistributionparalleldecodingtokenefficiency
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

First Finish Search (FFS) is a training-free test-time scaling rule: launch $n$ independent decodes of a reasoning model on the same prompt and return whichever trace finishes first. On AIME24, AIME25-I, AIME25-II, and GPQA Diamond, the paper reports that this 'shortest trace wins' rule matches or exceeds majority voting, beam search, and budget forcing across four reasoning models while consuming up to 45% fewer tokens, and that DeepSeek-R1 with FFS reaches 82.23% average AIME accuracy, roughly 15 points above the model's standalone score and close to o4-mini's 83.7%. The claim matters because test-time scaling usually buys accuracy with long or many decoding paths; FFS claims comparable or better accuracy at lower latency and lower cost, using only standard sampling APIs. The argument is carried by a Bayes-derived expression for the probability that a trace of a given length is correct, plus an extreme-value bound showing the expected minimum trace length falls as $O(\sqrt{\log n})$ as the number of samples grows.

What carries the argument

The carrying mechanism is the first-finish selection rule: run $n$ stochastic decodes at beam width 1 in parallel, and as soon as any trace emits the end-of-sequence token, stop the whole batch and return that trace. Its theoretical support is two identities. Result 1 writes $\Pr(\text{correct} \mid |T|=x)$ as a closed-form Bayes expression in the two length distributions' normal parameters; it is what converts the empirical observation 'correct traces are short' into the normative rule 'return the shortest trace.' Result 2, borrowed from extreme value theory, states that the expected minimum of $n$ i.i.d. normal random variables is asymptotically $\mu - \sigma\sqrt{2\log n}$, which is why the paper can claim FFS becomes cheaper, not more expensive, as more samples are launched. The empirical load is the separation of the correct and incorrect trace-length distributions (Figures 1 and 5): FFS succeeds exactly where those distributions' means are well separated, which the paper confirms for two reasoning models and finds absent for a non-reasoning one.

What would settle it

Count how often short traces are correct after removing every trace that hit the maximum token limit without producing an answer, or raise the limit so no trace truncates; if the short-trace advantage largely disappears, the effect FFS exploits is a truncation artifact rather than a property of reasoning. As a second check, run FFS and majority voting on a reasoning model while logging the correctness of the shortest, median, and longest traces separately: the paper's claim predicts the shortest traces win at a materially higher rate than the longest, not merely that truncated traces lose.

Watch

Extended reading notes

Core claim

The paper's central claim is that, for models that reason explicitly, correct answers come from shorter traces, and that a selection rule exploiting this — First Finish Search — is a strong, cheap test-time scaling strategy. Formally, it models correct and incorrect trace lengths as drawn from two normal distributions with means $\mu_1, \mu_2$ and standard deviations $\sigma_1, \sigma_2$, and derives (Result 1) that the probability a random trace of length $x$ is correct is a closed-form formula in those parameters and the overall accuracy $\alpha$; when incorrect traces are on average longer ($\mu_2 > \mu_1$), the formula makes short traces the most reliable. FFS operationalizes this by running $n$ stochastic decodes with beam width 1 and returning the first trace to emit the end-of-sequence token, a rule equivalent to maximizing the negative length reward $R(T) = -|T|$. A second result from extreme value theory (Result 2) gives the expected minimum of $n$ i.i.d. normal lengths as $\mu - \sigma\sqrt{2\log n}$, supporting the paper's claim that FFS's sequential cost shrinks as $n$ grows while majority voting's cost, tied to the longest trace, grows. Empirically, FFS matches or exceeds majority voting and budget forcing on four reasoning models across four benchmarks, cuts total tokens by up to 45% and sequential tokens roughly in half, and gains more from model capacity than any competing method; on a non-reasoning model (DeepSeek-V3) the effect reverses, delimiting the claim to reasoning-oriented models.

Load-bearing premise

The paper's core premise — that shorter traces are likelier to be correct, and hence that the first trace to finish is the best answer — is measured on distributions in which traces that hit the token limit are automatically marked wrong, so the premise may be an artifact of truncation rather than a property of reasoning quality.

Editorial extensions

If this is right

  • FFS needs nothing beyond ordinary parallel sampling — no logit edits, no extra tokens, no verifier — so the same accuracy and token savings should transfer to closed, API-metered deployments where other strategies are impractical.
  • Because FFS's sequential cost is the expected minimum of $n$ trace lengths, more parallel samples shorten the wait for an answer (falling like $O(\sqrt{\log n})$), whereas majority voting must wait for the longest trace, so FFS's latency advantage grows with $n$.
  • The accuracy gap FFS opens over the baselines grows with model capability (the paper's Distill-Qwen-32B to DeepSeek-R1 comparison), suggesting the rule becomes more valuable, not less, as reasoning models improve.
  • On non-reasoning models the rule backfires: majority voting beats FFS on every dataset for DeepSeek-V3, so the rule's advantage is specific to models with explicit chain-of-thought.

Reading between the lines

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

  • A natural extension the paper does not test is to stop at the first $k$ finishers and apply a cheap verifier among them, which would keep most of the token savings while hedging against short-but-wrong traces.
  • If the short-trace bias is real, trace length itself could serve as a zero-shot confidence proxy for reasoning models, offering a selection signal in settings where no verifier or reward model is available.
  • The cost analysis predicts a concrete scaling law: accuracy as a function of sample count $n$ should track the falling expected minimum length, $\mu - \sigma\sqrt{2\log n}$, which a focused benchmark sweep could test directly.
  • Because traces that hit the maximum token limit are always scored wrong, the briefness–correctness correlation, and with it FFS's apparent advantage, may be inflated by truncation; re-testing with generous or absent token limits is the minimal experiment that would separate the two effects.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes First Finish Search (FFS), a training-free test-time scaling strategy that decodes n independent traces in parallel and returns the first trace that emits the end-of-sequence token. The authors motivate FFS by the empirical observation that, for reasoning models, trace length and correctness are negatively correlated (Figure 1, Figure 5). They formulate a normal-mixture Bayes expression (Eq. 1) for P(correct | length=x), use extreme-value theory to argue that the expected sequential cost of FFS decreases with n (Result 2), and evaluate FFS against simple decoding, beam search, majority voting, budget forcing, and a last-finish baseline on AIME24, AIME25-I, AIME25-II, and GPQA Diamond with four reasoning models plus DeepSeek-V3. The headline empirical claim is that FFS matches or exceeds majority voting and budget forcing while consuming up to 45% fewer tokens, reaching 82.23% average AIME accuracy with DeepSeek-R1.

Significance. If the empirical result holds, FFS is a conceptually simple, training-free, API-friendly baseline that offers latency and token savings over parallel and sequential test-time scaling methods. The paper deserves credit for comparing four reasoning models across four benchmarks, for reporting token budgets, and for shipping a code link (Section 1, footnote 3). However, the theoretical support is not currently convincing, and the empirical comparisons lack error bars; the central 'shorter traces are more likely correct' correlation is partially confounded by truncation. With a corrected analysis and more careful statistics, the paper could make a useful contribution.

major comments (4)
  1. [Table 4, Eq. (1)] Equation (1) gives P(correct | |T|=x) for a single randomly drawn trace, but FFS selects the trace with the minimum length among n i.i.d. draws. The quantity the paper claims to report in Table 4—'the probability that FFS returns a correct answer'—is an order-statistic probability, P(label of argmin_i |T_i| = correct), which depends on the joint distribution of length and correctness and is not obtained by plugging fitted means and variances into Eq. (1) at any single x. The paper never states which x is used (e.g., E[min_i |T_i|], mu_1, or zero). The reported values (0.92, 0.97, 0.66) are also far above the observed FFS accuracies in Tables 2-3 (e.g., R1-Distill-Qwen averages roughly 62% on the three AIME sets), so Table 4 does not measure what it claims. This section should be replaced by a direct computation of the FFS success probability or by an empirical check using the same decoding traces.
  2. [Section 6, Figure 5, Table 4; Section 3] The motivating length-correctness correlation is confounded by truncation at the max-length limit. Traces that hit 32K tokens produce no final answer, are marked incorrect, and are included in the 'incorrect' length distributions in Figure 5 and Table 4. This mechanically adds a mass of long, incorrect traces and can create or exaggerate the finding that correct traces are shorter. The paper should either exclude truncated traces, mark them as a separate category, or show that the correlation survives after truncation is accounted for. In addition, Section 3 itself states that the normal assumption underlying Eq. (1) is violated for long traces, yet Table 4 fits normal distributions to the full length range; the fitted parameters are therefore questionable for the large-x regime and for any plug-in use of Eq. (1).
  3. [Tables 2-3, Section 4] The accuracy comparisons are reported as single point estimates without error bars, multiple seeds, or significance tests. The AIME subsets are small (the paper reports 60 problems total across the three AIME sets), so differences such as R1-Distill-Qwen AIME25-II (FFS 46.7% vs. MV 60.0%) and QwQ-32B AIME25-II (FFS 78.0% vs. MV 81.9%) are within binomial sampling noise. The abstract's claim that FFS reaches 82.23% average AIME accuracy with DeepSeek-R1 rests on a single run per setting. I request confidence intervals or per-item bootstrap intervals, and ideally multiple temperature or seed runs, before the 'matches or exceeds' claim is treated as established. The token-savings results are less affected by this concern because the differences are large.
  4. [Section 5, Table 1, Result 2] The paper's cost accounting is ambiguous and one statement is not correct as written. Section 5 says FFS's cost 'scales linearly with the number of parallel samples and never exceeds a single-trace budget'; for total tokens, FFS generates n x min_i |T_i| tokens, which grows with n and exceeds the shortest single trace. What is true is that the sequential (latency) cost is min_i |T_i|, which decreases like O(sqrt(log n)) under the normality assumption (Result 2). Table 1's 'T-parallelizable' criterion ('total GPU/CPU cost drop when decoding is parallelized') is not a property of FFS either: adding workers does not reduce total computation, it reduces wall-clock latency. These claims should be stated in terms of sequential vs. total compute, and the table should be revised.
minor comments (5)
  1. [Appendix 8.1 and footnote 1] The derivation of 'relative lift' L uses 'Pr(S|¬C)/Pr(S|C) is vanishingly small' without a bound; please replace this with an explicit inequality or state it as intuition. The footnote 'Note that Figure 1 actually implies the reverse' is confusing because the paper's own claim is that correct traces are more likely to be short; reword to avoid the apparent contradiction.
  2. [Section 3, Appendix 8.3] Equation (4) mixes notation, writing E[max{Y1, Y2, ..., Zk}], and the step from the max formula to the min formula is abbreviated; please correct the notation and expand the derivation.
  3. [Figure 3, Figure 5] The figures would be more informative if the fitted normal curves and the 32K truncation boundary were shown; also fix the typo 'Shapiro-Wilk T est' in Figure 3's caption.
  4. [Table 7] The hyperparameter 'Answer-reserve for BF' is not explained in the text; clarify how budget forcing is configured and whether the reserved tokens are included in the reported token counts.
  5. [References] Reference [25] is attributed to 'Q. Team' with a blog-post title; a standard citation to the Qwen technical report or an explicit author list would be cleaner.

Circularity Check

1 steps flagged · score 6.0 of 10

Table 4's 'predicted FFS success rates' are fitted conditional probabilities from the trace-length data, not predictions of the first-finish order statistic; the benchmark results themselves are independent.

  1. fitted input called prediction [Section 6, Table 4 and surrounding text; Eq. (1) in Section 3]
    "Using Equation (1) with a neutral prior (α=0.5), we estimate the probability that FFS returns a correct answer, for each model (distributions of text lengths shown in Figure 5). Table 4 reports this probability (Pr) together with normal parameters for the trace-length distributions of correct and incorrect generations."

    Equation (1) is Pr(correct | |T|=x) for a single trace, a function solely of the fitted normal parameters (µ1, σ1, µ2, σ2) and prior α. FFS returns the shortest of n traces, so its success probability is the order-statistic quantity Pr(label of argmin_i |T_i| = correct), which is not Equation (1) evaluated at any single x. The paper never states which x (E[min |T_i|], µ1, 0, or another value) is plugged in, and the reported 0.92/0.97 values far exceed the observed FFS accuracies (e.g., R1-Distill averages about 62% on the AIME sets in Table 2). The 'predicted FFS success rates' are therefore fitted conditional probabilities from the same trace-length data, renamed as predictions of FFS's behavior; they reduce by construction rather than by an independent derivation.

full rationale

The central empirical claims in Tables 2-3 are self-contained benchmark evaluations with stated hyperparameters, and the accuracy/token comparisons do not depend on the theoretical section. The motivating trace-length observation is also directly empirical. The circularity is confined to Section 6's Table 4, where Equation (1) is built from normal parameters fitted to the same trace-length distributions and then labeled a 'predicted FFS success rate'; because the reported Pr is a function of those fitted inputs and does not even represent the FFS argmin event, this step reduces by construction. The truncated-trace and heavy-tail concerns are real but belong to correctness risk rather than circularity. Because the paper's headline FFS efficiency results remain externally benchmarked and independent, the score is 6 (partial circularity) rather than 8 or 10.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The central empirical claim requires no fitted parameters, but the theoretical analysis in Section 6 and Table 4 depends on fitted normal parameters and a chosen prior α. The method itself introduces no new physical or architectural entities.

free parameters (3)
  • µ1, σ1 (correct trace length mean and std) = 7.2, 4.8 for R1-Distill-Qwen; 10.7, 5.7 for QwQ-32B (Table 4)
    Fitted to correct trace lengths from AIME data and used in Equation (1) to claim short traces are more likely correct.
  • µ2, σ2 (incorrect trace length mean and std) = 15.4, 6.0 for R1-Distill-Qwen; 21.3, 6.7 for QwQ-32B (Table 4)
    Fitted to incorrect trace lengths and used to compute predicted FFS success rates.
  • α (proportion of correct samples) = 0.5
    Set as a 'neutral prior' in Section 6, not estimated from data. This choice directly affects the predicted FFS success probabilities in Table 4.
assumptions (5)
  • domain assumption Trace lengths are normally distributed for reasoning models.
    Used throughout Equations (1)-(3) and Table 4. Figure 3 shows mixed Shapiro-Wilk p-values, and the paper admits heavy tails for long traces in Section 6.
  • standard math Bayes' theorem applies to the binary correct/incorrect event.
    Used to derive Result 1 in Appendix 8.2; this is mathematically valid.
  • domain assumption Extreme value theory formulas for the mean of min/max of i.i.d. normals apply to trace lengths.
    Used to derive Result 2 and the claim that FFS sequential cost decreases with sample count. The assumption requires normality and i.i.d. sampling, which is only approximately satisfied.
  • domain assumption The 'solution portion' of a trace is typically small, so full trace length ranks by reasoning length.
    Invoked in Section 3 to justify using full trace length instead of reasoning length.
  • ad hoc to paper An 'oracle model' never transitions from a correct reasoning state to an incorrect one.
    Invoked in Section 6 to explain why FFS benefits from larger model capacity. This is an idealized assumption, not empirically validated.

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Cite this review

Pith. "Pith review of First Finish Search: Efficient Test-Time Scaling in Large Language Models." pith.science (2026). https://pith.science/paper/4VCF7PAZ

@misc{pith2026250518149,
  author       = {Pith},
  title        = {Pith review of: First Finish Search: Efficient Test-Time Scaling in Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4VCF7PAZ}},
  note         = {Machine review of arXiv:2505.18149}
}
abstract

Test-time scaling (TTS), which involves dynamic allocation of compute during inference, offers a promising way to improve reasoning in large language models. While existing TTS methods work well, they often rely on long decoding paths or require a large number of samples to be generated, increasing the token usage and inference latency. We observe the surprising fact that for reasoning tasks, shorter traces are much more likely to be correct than longer ones. Motivated by this, we introduce First Finish Search (FFS), a training-free parallel decoding strategy that launches $n$ independent samples and returns as soon as any one completes. We evaluate FFS alongside simple decoding, beam search, majority voting, and budget forcing on four reasoning models (DeepSeek-R1, R1-Distill-Qwen-32B, QwQ-32B and Phi-4-Reasoning-Plus) and across four datasets (AIME24, AIME25-I, AIME25-II and GPQA Diamond). With DeepSeek-R1, FFS achieves $82.23\%$ accuracy on the AIME datasets, a $15\%$ improvement over DeepSeek-R1's standalone accuracy, nearly matching OpenAI's o4-mini performance. Our theoretical analysis explains why stopping at the shortest trace is likely to yield a correct answer and identifies the conditions under which early stopping may be suboptimal. The elegance and simplicity of FFS demonstrate that straightforward TTS strategies can perform remarkably well, revealing the untapped potential of simple approaches at inference time.

Figures

Figures reproduced from arXiv: 2505.18149 by the authors.

Figure 1
Figure 1. Distribution of trace lengths for correct [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Sampling-based TTS strategies. (a) BS: expands [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Lengths of generated reasoning traces on AIME24. (a) Per-example violin plots of trace [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 5
Figure 5. Figure 5: Distribution of generated text lengths for different reasoning and non-reasoning models [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 4
Figure 4. Figure 4: Accuracy versus total token budget for three test-time scaling methods averaged over R1-Distill-Qwen and QwQ-32B on AIME24 and AIME25-I. FFS attains higher accuracy at lower budgets; MV improves more slowly and consumes more tokens; BF plateaus near the 32K token limit…

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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

  1. Towards Concise and Adaptive Thinking in Large Reasoning Models: A Survey

    cs.AI 2025-07 conditional novelty 3.0 of 10

    A comprehensive review that categorizes methods for shortening and adaptively triggering chain-of-thought reasoning in large language models.

Reference graph

Works this paper leans on

38 extracted references · 8 canonical work pages · cited by 1 Pith paper

  1. [1]

    Abdin, S

    M. Abdin, S. Agarwal, A. Awadallah, V . Balachandran, H. Behl, L. Chen, G. de Rosa, S. Gu- nasekar, M. Javaheripi, N. Joshi, et al. Phi-4-reasoning technical report.arXiv preprint arXiv:2504.21318, 2025

    arXiv 2025

  2. [2]

    Aggarwal and S

    P. Aggarwal and S. Welleck. L1: Controlling how long a reasoning model thinks with reinforce- ment learning.arXiv preprint arXiv:2503.04697, 2025

    arXiv 2025

  3. [3]

    Bandyopadhyay, S

    D. Bandyopadhyay, S. Bhattacharjee, and A. Ekbal. Thinking machines: A survey of llm based reasoning strategies.arXiv preprint arXiv:2503.10814, 2025

    arXiv 2025

  4. [4]

    Brown, J

    B. Brown, J. Juravsky, R. Ehrlich, R. Clark, Q. V . Le, C. Ré, and A. Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling.arXiv preprint arXiv:2407.21787, 2024

    arXiv 2024

  5. [5]

    Y . Chow, G. Tennenholtz, I. Gur, V . Zhuang, B. Dai, S. Thiagarajan, C. Boutilier, R. Agarwal, A. Kumar, and A. Faust. Inference-aware fine-tuning for best-of-n sampling in large language models.arXiv preprint arXiv:2412.15287, 2024

    arXiv 2024

  6. [6]

    Galambos

    J. Galambos. The asymptotic theory of extreme order statistics.The Theory and Applications of Reliability with Emphasis on Bayesian and Nonparametric Methods, pages 151–164, 1977. 9

    work page 1977

  7. [7]

    Gandhi, D

    K. Gandhi, D. Lee, G. Grand, M. Liu, W. Cheng, A. Sharma, and N. D. Goodman. Stream of search (sos): Learning to search in language.arXiv preprint arXiv:2404.03683, 2024

    arXiv 2024

  8. [8]

    D. Guo, D. Yang, H. Zhang, J. Song, R. Zhang, R. Xu, Q. Zhu, S. Ma, P. Wang, X. Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning.arXiv preprint arXiv:2501.12948, 2025

    arXiv 2025

Show all 38 references
  1. [9]

    Z. Hou, X. Lv, R. Lu, J. Zhang, Y . Li, Z. Yao, J. Li, J. Tang, and Y . Dong. Advancing language model reasoning through reinforcement learning and inference scaling, 2025.URL https://arxiv. org/abs/2501, 11651

    2025

  2. [10]

    Huang, Z

    Z. Huang, Z. Wang, S. Xia, and P. Liu. Olympicarena medal ranks: Who is the most intelligent ai so far?arXiv preprint arXiv:2406.16772, 2024

    2024 arXiv

  3. [11]

    K.-H. Lee, I. Fischer, Y .-H. Wu, D. Marwood, S. Baluja, D. Schuurmans, and X. Chen. Evolving deeper llm thinking.arXiv preprint arXiv:2501.09891, 2025

    2025 arXiv

  4. [12]

    N. Levi. A simple model of inference scaling laws.arXiv preprint arXiv:2410.16377, 2024

    2024 arXiv

  5. [13]

    D. Li, S. Cao, C. Cao, X. Li, S. Tan, K. Keutzer, J. Xing, J. E. Gonzalez, and I. Stoica. S*: Test time scaling for code generation.arXiv preprint arXiv:2502.14382, 2025

    2025 arXiv

  6. [14]

    Y . Li, M. Lyu, and L. Wang. Learning to reason from feedback at test-time.arXiv preprint arXiv:2502.15771, 2025

    2025 arXiv

  7. [15]

    Z.-Z. Li, D. Zhang, M.-L. Zhang, J. Zhang, Z. Liu, Y . Yao, H. Xu, J. Zheng, P.-J. Wang, X. Chen, et al. From system 1 to system 2: A survey of reasoning large language models.arXiv preprint arXiv:2502.17419, 2025

    2025 arXiv

  8. [16]

    A. Liu, B. Feng, B. Xue, B. Wang, B. Wu, C. Lu, C. Zhao, C. Deng, C. Zhang, C. Ruan, et al. Deepseek-v3 technical report.arXiv preprint arXiv:2412.19437, 2024

    2024 arXiv

  9. [17]

    J. Liu, A. Cohen, R. Pasunuru, Y . Choi, H. Hajishirzi, and A. Celikyilmaz. Don’t throw away your value model! generating more preferable text with value-guided monte-carlo tree search decoding.arXiv preprint arXiv:2309.15028, 2023

    2023 arXiv

  10. [18]

    Aime problems and solutions

    MAA Committee. Aime problems and solutions. https://artofproblemsolving.com/ wiki/index.php/AIME_Problems_and_Solutions, 2025. Accessed: 2025-05-06

    2025

  11. [19]

    Muennighoff, Z

    N. Muennighoff, Z. Yang, W. Shi, X. L. Li, L. Fei-Fei, H. Hajishirzi, L. Zettlemoyer, P. Liang, E. Candès, and T. Hashimoto. s1: Simple test-time scaling.arXiv preprint arXiv:2501.19393, 2025

    2025 arXiv

  12. [20]

    Learning to reason with llms

    OpenAI. Learning to reason with llms. https://openai.com/research/ learning-to-reason-with-llms, 2024. Accessed: 2025-05-06

    2024

  13. [21]

    J. Pan, S. Deng, and S. Huang. Coat: Chain-of-associated-thoughts framework for enhancing large language models reasoning.arXiv preprint arXiv:2502.02390, 2025

    2025

  14. [22]

    H. Peng, Y . Qi, X. Wang, Z. Yao, B. Xu, L. Hou, and J. Li. Agentic reward modeling: Integrating human preferences with verifiable correctness signals for reliable reward systems.arXiv preprint arXiv:2502.19328, 2025

    2025 arXiv

  15. [23]

    D. Rein, B. L. Hou, A. C. Stickland, J. Petty, R. Y . Pang, J. Dirani, J. Michael, and S. R. Bowman. Gpqa: A graduate-level google-proof q&a benchmark. InFirst Conference on Language Modeling, 2024

    2024

  16. [24]

    Snell, J

    C. Snell, J. Lee, K. Xu, and A. Kumar. Scaling llm test-time compute optimally can be more effective than scaling model parameters.arXiv preprint arXiv:2408.03314, 2024

    2024 arXiv

  17. [25]

    Q. Team. Qwq-32b: Embracing the power of reinforcement learning, March 2025. URL https://qwenlm.github.io/blog/qwq-32b/. 10

    2025

  18. [26]

    A. K. Vijayakumar, M. Cogswell, R. R. Selvaraju, Q. Sun, S. Lee, D. Crandall, and D. Batra. Diverse beam search: Decoding diverse solutions from neural sequence models.arXiv preprint arXiv:1610.02424, 2016

    2016 arXiv

  19. [27]

    Y . Wang, P. Ji, C. Yang, K. Li, M. Hu, J. Li, and G. Sartoretti. Mcts-judge: Test-time scaling in llm-as-a-judge for code correctness evaluation.arXiv preprint arXiv:2502.12468, 2025

    2025 arXiv

  20. [28]

    Y . Wang, Q. Liu, J. Xu, T. Liang, X. Chen, Z. He, L. Song, D. Yu, J. Li, Z. Zhang, et al. Thoughts are all over the place: On the underthinking of o1-like llms.arXiv preprint arXiv:2501.18585, 2025

    2025 arXiv

  21. [29]

    Welleck, A

    S. Welleck, A. Bertsch, M. Finlayson, H. Schoelkopf, A. Xie, G. Neubig, I. Kulikov, and Z. Harchaoui. From decoding to meta-generation: Inference-time algorithms for large language models.arXiv preprint arXiv:2406.16838, 2024

    2024 arXiv

  22. [30]

    Y . Wu, Z. Sun, S. Li, S. Welleck, and Y . Yang. An empirical analysis of compute-optimal inference for problem-solving with language models. 2024

    2024

  23. [31]

    Y . Xie, A. Goyal, W. Zheng, M.-Y . Kan, T. P. Lillicrap, K. Kawaguchi, and M. Shieh. Monte carlo tree search boosts reasoning via iterative preference learning.arXiv preprint arXiv:2405.00451, 2024

    2024 arXiv

  24. [32]

    A. Yang, B. Yang, B. Zhang, B. Hui, B. Zheng, B. Yu, C. Li, D. Liu, F. Huang, H. Wei, H. Lin, J. Yang, J. Tu, J. Zhang, J. Yang, J. Yang, J. Zhou, J. Lin, K. Dang, K. Lu, K. Bao, K. Yang, L. Yu, M. Li, M. Xue, P. Zhang, Q. Zhu, R. Men, R. Lin, T. Li, T. Tang, T. Xia, X. Ren, X...

    2024 arXiv

  25. [33]

    A. Yang, A. Li, B. Yang, B. Zhang, B. Hui, B. Zheng, B. Yu, C. Gao, C. Huang, C. Lv, C. Zheng, D. Liu, F. Zhou, F. Huang, F. Hu, H. Ge, H. Wei, H. Lin, J. Tang, J. Yang, J. Tu, J. Zhang, J. Yang, J. Yang, J. Zhou, J. Zhou, J. Lin, K. Dang, K. Bao, K. Yang, L. Yu, L. Deng, M. L...

    2025 arXiv

  26. [34]

    Yang, X.-Y

    X.-W. Yang, X.-Y . Zhu, W.-D. Wei, D.-C. Zhang, J.-J. Shao, Z. Zhou, L.-Z. Guo, and Y .-F. Li. Step back to leap forward: Self-backtracking for boosting reasoning of language models.arXiv preprint arXiv:2502.04404, 2025

    2025 arXiv

  27. [35]

    Zhang, F

    Q. Zhang, F. Lyu, Z. Sun, L. Wang, W. Zhang, Z. Guo, Y . Wang, I. King, X. Liu, and C. Ma. What, how, where, and how well? a survey on test-time scaling in large language models.arXiv preprint arXiv:2503.24235, 2025

    2025 arXiv

  28. [36]

    relative lift

    S. Zhang, Z. Chen, Y . Shen, M. Ding, J. B. Tenenbaum, and C. Gan. Planning with large language models for code generation.arXiv preprint arXiv:2303.05510, 2023. 11 8 Theoretical Results and Proofs 8.1 Short traces are more likely to be correct Let C be the event that a random...

    2023 arXiv

  29. [37]

    So, 22 = 4 does not divide n4 + 1for any n

    n= 3 : 81 + 1 = 82, which is 2∗41 , not divisible by 4. So, 22 = 4 does not divide n4 + 1for any n. Because n odd: n4 ≡1 mod 4 , so 1 + 1 = 2 mod 4. So 2 isn’t going to work. So, for primes p≡1 mod 8 , we can have solutions to n4 ≡ −1 modp, and if the derivative 4n3 is not 0 m...

  30. [208]

    Find the least positive integermsuch thatm 4 + 1is divisible byp 2

    2082 = 43264. 43264 mod 289. 289∗149 = 289∗(150−1) = 289∗150−289 = 43350−289 = 43061. 43264−43061 = 203. So 534 + 1≡203 + 1 = 204 mod 289̸= 0. So, not divisible. Similarly, m= 70 . 70 mod 289 is 70. 702 = 4900. 4900 mod 289: 289∗16 = 4624 , 4900−4624 = 276 . 2762 = 76176. 7617...

    2023

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.