Pith. sign in

REVIEW 5 major objections 7 minor 3 cited by

VeriThinker: Learning to Verify Makes Reasoning Model Efficient

T0 review · 5 major / 7 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read VeriThinker claims that fine-tuning a reasoning model on a binary verification task, rather than on distilled short chains, suppresses overthinking and shortens chain-of-thought reasoning while preserving or slightly improving accuracy.

desk verdict The compression effect is real and the SVFT objective is new, but the paper's own reversed-label control contradicts the claimed verification mechanism; still worth refereeing. read the letter →

arxiv 2505.17941 v1 pith:AUAKEHVY submitted 2025-05-23 cs.LG

Zigeng Chen , Xinyin Ma , Gongfan Fang , Ruonan Yu , Xinchao Wang This is my paper
classification cs.LG
keywords chain-of-thoughtcompressionoverthinkingverificationfine-tuninglargereasoningmodelsself-reflectionmathematicalspeculativesupervised
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

VeriThinker claims that the overthinking of large reasoning models can be suppressed without constructing synthetic short reasoning chains. The recipe is to fine-tune the model on an auxiliary verification task: given a question and a full chain-of-thought solution, the model must classify the solution as correct or incorrect. After this training, the model emits fewer unnecessary self-reflection steps, so its chains get shorter while accuracy stays level or rises. On three DeepSeek-R1-Distill models, VeriThinker reduces MATH500 reasoning tokens from about 3790 to 2125 and AIME25 tokens from about 14321 to 10287, with slight accuracy gains on most benchmarks. If the transfer mechanism is correct, chain-of-thought compression becomes cheaper and avoids the accuracy degradation usually seen when models are trained to imitate short chains.

What carries the argument

The central object is Supervised Verification Fine-Tuning (SVFT), a training scheme that turns each instance into a question-solution pair, labels the pair correct or incorrect by comparing the solution's final answer with the ground truth, and fine-tunes the reasoning model through a low-rank adapter so that the model produces a fixed binary verification response; only the response tokens contribute to the loss. SVFT is meant to convert the model into a sharper binary classifier of solution correctness, and the paper's hypothesis is that this same classification ability governs whether the model triggers a self-reflection step such as 'Wait' during generation. A second component, Solution-wise Speculative Reasoning (SSR), reuses the trained verifier at inference time: a short-CoT draft model proposes an entire solution, the SVFT model accepts or rejects it, and only rejected problems activate the model's long chain-of-thought reasoning.

What would settle it

A concrete test: take a set of generated chains, insert a single arithmetic error at a known position, and measure the probability of emitting a reflection word like 'Wait' immediately after that position. If SVFT improves step-level verification, the SVFT model should show a localized spike at the error; if the spike is absent or appears only at the very end, compression is better explained by generic style shortening than by better self-reflection decisions.

Watch

Extended reading notes

Core claim

The central claim is that overthinking is a verification failure: the model often cannot tell that the steps it has just written are correct, so it re-checks them. VeriThinker therefore trains the model on a whole-solution binary verification task, using two fixed responses ('Yes, every step is absolutely correct' versus 'No, there may be mistakes'), with the training loss applied only to the verification response tokens. The paper argues that this whole-solution training transfers to the model's step-level decision of whether to launch a self-reflection, even though the labels are derived only from final-answer correctness. The empirical signature is adaptive behavior: on correct reasoning prefixes the probability of emitting a pivot word like 'Wait' drops sharply, while on prefixes with an injected arithmetic mistake it does not drop and even rises slightly. This is why, in the reported measurements, token counts fall by roughly a quarter to a third without an accuracy penalty, and on AIME benchmarks accuracy improves by a small margin.

Load-bearing premise

The method rests on a transfer assumption: training a model to label whole solutions as correct or incorrect also sharpens the moment-by-moment decision of whether to double-check the steps it has just written, even though that moment-by-moment decision is never directly trained.

Editorial extensions

If this is right

  • Chain-of-thought compression no longer requires generating expensive synthetic concise target chains, which prior long-to-short methods depend on.
  • The same verification training lets the model act as a solution-level verifier, so a cheap short-CoT draft model can handle easy problems while the reasoning model engages only on hard ones, raising throughput several-fold in the reported runs.
  • Token reductions of roughly 24 to 34 percent are achievable while keeping accuracy stable or slightly higher across three model families and three benchmark sets.
  • Because the loss is restricted to the short verification response, the method is cheap to train and, at the reported scales, does not cause the accuracy collapse that the paper observes for supervised fine-tuning on synthetic short chains.
  • Ablations with reversed and simplified labels indicate that the contrast between two fixed response classes, rather than the semantic words 'correct' and 'incorrect', carries the compression effect.

Reading between the lines

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

  • An implication the paper leaves implicit: if the active ingredient is a stable binary contrast rather than semantic accuracy, then any consistent two-class labeling of solutions might compress chains; this could be tested by training on random-but-consistent labels at the full dataset scale and measuring whether token reduction survives.
  • The claimed transfer from whole-solution verification to step-level reflection is the link that would benefit from direct evidence: one could localize the change by measuring when, relative to an injected error, the model's reflection probability rises.
  • The speculative-reasoning pipeline suggests a natural deployment handle the paper does not tune: a confidence threshold on the verifier could trade acceptance rate against accuracy, letting operators choose how often the long reasoning chain is activated.
  • If verification training transfers beyond mathematics, the same scheme could compress reasoning in code generation or tool-use domains, where solution correctness is objectively checkable, though the paper only demonstrates mathematical benchmarks.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 7 minor

Summary. The paper proposes VeriThinker, a method for compressing the chain-of-thought (CoT) outputs of large reasoning models (LRMs). Instead of fine-tuning on synthetic short-CoT targets, it fine-tunes the model solely on a binary verification task: given a question and a CoT solution, the model learns to output a fixed affirmative or negative response according to whether the solution's final answer is correct (Eq. 2). The authors name this Supervised Verification Fine-Tuning (SVFT). They report that SVFT reduces reasoning token counts by roughly 25--35% across three DeepSeek-R1-Distill models on MATH500, AIME2024, and AIME2025, while maintaining or slightly improving accuracy. They also propose Solution-wise Speculative Reasoning (SSR), which uses the SVFT-trained model as a verifier that either accepts a short-CoT draft solution or activates full long-CoT reasoning. The paper includes control experiments in Section 3.3 that vary the verification response labels (reversed, simplified, neutral, random), plus a 50-problem study of the probability of generating the pivot word 'Wait'.

Significance. If the empirical result holds, the paper makes a useful practical contribution: it offers a training objective that compresses CoT without requiring synthetic concise-CoT data, and the token reductions are consistent and large across model architectures. The SSR extension is also an interesting way to trade throughput against accuracy. The paper ships code, and the verification dataset construction is described in enough detail to be reproduced. However, the central mechanistic claim — that accurate verification makes the model more discerning about when to self-reflect — is not supported by the paper's own controls. The authors themselves retreat in Section 3.3 to a contrastive-learning interpretation, but even that interpretation is not coherent with the reversed-label result. The accuracy gains on 30-problem AIME sets lack variance estimates, and several SSR configurations show accuracy drops rather than maintenance. These issues undermine the stronger claims but do not automatically invalidate the core compression finding.

major comments (5)
  1. [§3.2 & §3.3, Dataset (2)] The claimed mechanism — that SVFT improves p(acc|h), the accuracy of step-level correctness judgments, and thereby suppresses redundant self-reflection — is contradicted by the reversed-label experiment. With Dataset (2), the model is trained to respond affirmatively to incorrect solutions and negatively to correct ones; it cannot be accurately verifying solution correctness in any meaningful sense, yet it still compresses CoT as much as the correct-label version. The interpretation in §3.3 that 'SVFT empowers the LRM to differentiate between correct and incorrect solutions' is of little help here, because a reversed-label model differentiates along the same two classes but with an incorrect mapping. The active ingredient appears to be the existence of a consistent binary contrast, not the accuracy of the verification judgment. This undermines the causal story in the abstract and in §3.2. The authors should either provide a mechanism consistent with all five datasets (including Dataset (2)) or explicitly re-frame the central claim as an empirical correlation without the step-level accuracy account.
  2. [§3.3, Figure 4(c)] The only direct evidence for the step-level transfer mechanism — that SVFT reduces 'Wait' probability on correct sub-solutions and maintains/increases it on incorrect ones — is based on 50 hand-selected problems, a single pivot token as a proxy for self-reflection, and 'manually introduced mistakes' without a precise protocol. No error bars or significance tests are reported. This is too weak to support the strong causal conclusion drawn in the text. If the mechanism claim is retained, this experiment needs a larger sample, standard errors, and a clearly defined mistake-injection procedure.
  3. [Table 1] The accuracy differences on AIME are small relative to the dataset size: an AIME set has 30 problems, so a 2.1--4.0% absolute change is 0.6--1.2 problems. The paper states that results are 'averages computed over 2 to 16 independent runs' but gives no standard deviations or significance tests. Consequently, the claim that VeriThinker 'maintains or even slightly improves accuracy' is not statistically supported. The token reductions are large and consistent, so they are likely real, but the accuracy assertions need variance reporting or at least per-run breakouts.
  4. [Table 3] The claim in §4.2 that SSR 'maintains or even enhances reasoning accuracy' is not supported by the reported numbers. For R1-Distill-Qwen-7B on MATH500, accuracy drops from 94.0% (baseline) to 91.8% with the Qwen-2.5-Math-1.5B draft, and for R1-Distill-Qwen-14B it drops from 95.2% to 93.0%. Only the GSM8K rows and some 7B-draft rows show improvements. The abstract's statement that VeriThinker 'zero-shot generalizes to speculative reasoning' also needs qualification given these accuracy costs.
  5. [§4.1, Baselines] The SFT baseline used in Table 1 is not adequately described. The text mentions 'SFT [57], a supervised fine-tuning method that uses synthesized concise CoT chains as targets' but gives no details on how the synthetic chains were generated, what data was used, or the training hyperparameters. Without this information, it is unclear whether the comparison is fair (e.g., whether the SFT baseline used the same LoRA configuration and compute budget as VeriThinker). A full description should be provided in the main text or appendix.
minor comments (7)
  1. [Abstract & Table 1] The abstract says 'reducing reasoning tokens on MATH500 from 3790 to 2125', but Table 1 lists the original value as 3791; please reconcile the numbers.
  2. [Figure 2(c)] Figure 2(c) is referenced in §3.2 before the empirical analysis in §3.3 that explains it; consider moving the figure or its description to §3.3.
  3. [Table 3] The caption says 'Underlined numbers indicate the token counts during the draft phase for short-CoT LLMs,' but no numbers in the table are underlined in the provided text; update the table or caption.
  4. [Appendix B] The dataset construction section says 'we collected approximately 300K mathematical problems' yet the final fine-tuning set is '350K instances' and later 'approximately 340k question-CoT pairs' in §4.1; clarify the exact counts and the relationship between problems and instances.
  5. [Appendix B] The correctness labeling step uses the Hugging Face math_verify function to compare final answers, but the function is not described. Please specify the matching rules (e.g., how equivalent algebraic expressions are handled) or provide a reference.
  6. [Appendix B] The reference for PRM12K, [32], is 'Let's Verify Step by Step' (Lightman et al.), but PRM12K is a specific dataset release; the citation should point to the dataset itself or a more specific source.
  7. [§1] The terms 'LRM' and 'LLM' are used interchangeably in places (e.g., §3.2, Appendix C); define them once and use them consistently.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: VeriThinker's compression results are measured on held-out reasoning benchmarks, and no benchmark number is fit from the verification training labels.

full rationale

The paper's central claim is that fine-tuning an LRM on an auxiliary whole-solution binary verification task compresses generated CoT while preserving accuracy. The derivation chain is not circular: verification training labels are produced from ground-truth final answers of short-CoT solutions (Appendix B), and the reported compression and accuracy numbers are measured on MATH500, AIME2024, and AIME2025 generation tasks that are separate from the fitted training objective. No parameter is fit to those benchmark token counts or accuracies, so the headline reductions are empirical outcomes rather than restatements of the training data. The only same-group citations (CoT-Valve [41] and Thinkless [10]) are used as baselines or related work, not as evidence for the central mechanism, so they are not load-bearing circularity. The paper's own control experiments (Datasets 2 and 4 in Section 3.3, where reversed or semantically neutral verification responses still compress CoT) do weaken the causal attribution to 'accurate verification,' and Appendix B's final-answer-only labeling leaves the step-level transfer assumption under-supported; however, an unsupported mechanistic assumption is a correctness or evidence concern, not a circular reduction. No equation or result is defined in terms of the target result, and the speculative-reasoning numbers are a composition of draft-model outputs and verifier decisions rather than a renamed input. The manuscript even flags its own limitation (Appendix C: smaller models do not compress well), which is inconsistent with a result forced by construction. Accordingly, the circularity burden is not met; score 0.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The paper introduces a new training objective (SVFT) but no new physical or mathematical entities. Its load-bearing assumptions are about how verification training transfers to generation behavior; these are plausible but empirically underdetermined.

free parameters (1)
  • LoRA rank and alpha per model = 7B: 256/512; 14B: 128/128; Llama-8B: 128/128
    Hand-selected in Appendix A; used for all VeriThinker results. The method's effectiveness may depend on these, though they are not fitted to evaluation targets.
assumptions (4)
  • domain assumption Self-reflection decisions are a binary classification over hidden states of previous steps, and improving that classification reduces overthinking.
    Stated in Section 3.2 without formal proof; the entire method rests on this mapping.
  • domain assumption Whole-solution verification labels (final answer matches ground truth) transfer to step-level self-reflection decisions.
    Training labels in Appendix B compare only final answers; the claimed benefit is at the level of individual 'Wait' self-checks, with no step-level supervision.
  • ad hoc to paper Consistent arbitrary binary labels (reversed or neutral) create the same compression effect as correctness labels.
    The paper interprets Dataset (2)-(4) results as contrastive learning in Section 3.3, but this is an untested post hoc explanation rather than a measured mechanism.
  • domain assumption Short-CoT model solutions are representative of solution distributions for verification.
    The verification dataset is generated by Qwen-2.5 models without reasoning models (Appendix B); the transfer to reasoning-model-generated solutions is assumed.

how reviews work

0 comments
Cite this review

Pith. "Pith review of VeriThinker: Learning to Verify Makes Reasoning Model Efficient." pith.science (2026). https://pith.science/paper/AUAKEHVY

@misc{pith2026250517941,
  author       = {Pith},
  title        = {Pith review of: VeriThinker: Learning to Verify Makes Reasoning Model Efficient},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/AUAKEHVY}},
  note         = {Machine review of arXiv:2505.17941}
}
read the original abstract

Large Reasoning Models (LRMs) excel at complex tasks using Chain-of-Thought (CoT) reasoning. However, their tendency to overthinking leads to unnecessarily lengthy reasoning chains, dramatically increasing inference costs. To mitigate this issue, we introduce VeriThinker, a novel approach for CoT compression. Unlike conventional methods that fine-tune LRMs directly on the original reasoning task using synthetic concise CoT data, we innovatively fine-tune the model solely through an auxiliary verification task. By training LRMs to accurately verify the correctness of CoT solutions, the LRMs inherently become more discerning about the necessity of subsequent self-reflection steps, thereby effectively suppressing overthinking. Extensive experiments validate that VeriThinker substantially reduces reasoning chain lengths while maintaining or even slightly improving accuracy. When applied to DeepSeek-R1-Distill-Qwen-7B, our approach reduces reasoning tokens on MATH500 from 3790 to 2125 while improving accuracy by 0.8% (94.0% to 94.8%), and on AIME25, tokens decrease from 14321 to 10287 with a 2.1% accuracy gain (38.7% to 40.8%). Additionally, our experiments demonstrate that VeriThinker can also be zero-shot generalized to speculative reasoning. Code is available at https://github.com/czg1225/VeriThinker

Figures

Figures reproduced from arXiv: 2505.17941 by the authors.

Figure 1
Figure 1. The key distinction between VeriThinker and traditional SFT or RL-based long-to-short [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. (a)-(b): Token counts and accuracy in reasoning tasks across different training datasets. (c) [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Speculative reasoning results on three reasoning models. When using Qwen-2.5-Math [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: Training data format comparison. Correctness Labeling. In the third step, we label the correctness of each generated CoT solution. Rather than evaluating each reasoning step, we simplify labeling by verifying only the final answers against known ground-truth solutions.…
Figure 5
Figure 5. Figure 5: Case study 1 on CoT Compression. D Social Impacts In this paper, we propose VeriThinker, a simple yet effective method for compressing reasoning chains while preserving high accuracy. As large reasoning models become increasingly prevalent, their lengthy reasoning chai…
Figure 6
Figure 6. Figure 6: Case study 2 on CoT Compression. 17 [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: Case study 3 on CoT Compression. 18 [PITH_FULL_IMAGE:figures/full_fig_p018_7.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 3 Pith papers

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

  1. Performative Thinking? The Brittle Correlation Between CoT Length and Problem Complexity

    cs.AI 2025-09 conditional novelty 6.0 of 10

    A transformer trained to imitate A* produces traces whose length reflects similarity to training data, not true problem complexity, so long chain-of-thought should not be read as more 'thinking'.

  2. MixReasoning: Switching Modes to Think

    cs.AI 2025-10 conditional novelty 5.0 of 10

    A reasoning model can cut token usage by roughly a third to a half without losing accuracy if it switches to brief output on low-uncertainty steps and expands only at high-uncertainty forks.

  3. 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

75 extracted references · 4 canonical work pages · cited by 3 Pith papers

  1. [57]

    Finetuned language models are zero-shot learners

    Jason Wei, Maarten Bosma, Vincent Y Zhao, Kelvin Guu, Adams Wei Yu, Brian Lester, Nan Du, Andrew M Dai, and Quoc V Le. Finetuned language models are zero-shot learners. arXiv preprint arXiv:2109.01652, 2021

    arXiv 2021

  2. [1]

    L1: Controlling how long a reasoning model thinks with reinforcement learning

    Pranjal Aggarwal and Sean Welleck. L1: Controlling how long a reasoning model thinks with reinforcement learning. arXiv preprint arXiv:2503.04697, 2025

    arXiv 2025

  3. [2]

    Training language models to reason efficiently

    Daman Arora and Andrea Zanette. Training language models to reason efficiently. arXiv preprint arXiv:2502.04463, 2025

    arXiv 2025

  4. [3]

    Medusa: Simple llm inference acceleration framework with multiple decoding heads

    Tianle Cai, Yuhong Li, Zhengyang Geng, Hongwu Peng, Jason D Lee, Deming Chen, and Tri Dao. Medusa: Simple llm inference acceleration framework with multiple decoding heads. arXiv preprint arXiv:2401.10774, 2024

    arXiv 2024

  5. [4]

    Unveiling the key factors for distilling chain-of-thought reasoning.arXiv preprint arXiv:2502.18001, 2025

    Xinghao Chen, Zhijing Sun, Wenjin Guo, Miaoran Zhang, Yanjun Chen, Yirong Sun, Hui Su, Yijie Pan, Dietrich Klakow, Wenjie Li, et al. Unveiling the key factors for distilling chain-of-thought reasoning.arXiv preprint arXiv:2502.18001, 2025

    arXiv 2025

  6. [5]

    Do not think that much for 2+ 3=? on the overthinking of o1-like llms

    Xingyu Chen, Jiahao Xu, Tian Liang, Zhiwei He, Jianhui Pang, Dian Yu, Linfeng Song, Qiuzhi Liu, Mengfei Zhou, Zhuosheng Zhang, et al. Do not think that much for 2+ 3=? on the overthinking of o1-like llms. arXiv preprint arXiv:2412.21187, 2024

    arXiv 2024

  7. [6]

    Training verifiers to solve math word problems

    Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168, 2021

    arXiv

  8. [7]

    One-minute video generation with test-time training

    Karan Dalal, Daniel Koceja, Gashon Hussein, Jiarui Xu, Yue Zhao, Youjin Song, Shihao Han, Ka Chun Cheung, Jan Kautz, Carlos Guestrin, et al. One-minute video generation with test-time training. arXiv preprint arXiv:2504.05298, 2025

    arXiv 2025

Show all 75 references
  1. [8]

    From explicit cot to implicit cot: Learning to internalize cot step by step

    Yuntian Deng, Yejin Choi, and Stuart Shieber. From explicit cot to implicit cot: Learning to internalize cot step by step. arXiv preprint arXiv:2405.14838, 2024

    2024 arXiv

  2. [9]

    Implicit chain of thought reasoning via knowledge distillation

    Yuntian Deng, Kiran Prasad, Roland Fernandez, Paul Smolensky, Vishrav Chaudhary, and Stuart Shieber. Implicit chain of thought reasoning via knowledge distillation. arXiv preprint arXiv:2311.01460, 2023

    2023 arXiv

  3. [10]

    Thinkless: Llm learns when to think

    Gongfan Fang, Xinyin Ma, and Xinchao Wang. Thinkless: Llm learns when to think. arXiv preprint arXiv:2505.13379, 2025

    2025 arXiv

  4. [11]

    Scaling up test-time compute with latent reasoning: A recurrent depth approach

    Jonas Geiping, Sean McLeish, Neel Jain, John Kirchenbauer, Siddharth Singh, Brian R Bartoldson, Bhavya Kailkhura, Abhinav Bhatele, and Tom Goldstein. Scaling up test-time compute with latent reasoning: A recurrent depth approach. arXiv preprint arXiv:2502.05171, 2025

    2025 arXiv

  5. [12]

    rstar-math: Small llms can master math reasoning with self-evolved deep thinking

    Xinyu Guan, Li Lyna Zhang, Yifei Liu, Ning Shang, Youran Sun, Yi Zhu, Fan Yang, and Mao Yang. rstar-math: Small llms can master math reasoning with self-evolved deep thinking. arXiv preprint arXiv:2501.04519, 2025

    2025 arXiv

  6. [13]

    Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning

    Daya Guo, Dejian Yang, Haowei Zhang, Junxiao Song, Ruoyu Zhang, Runxin Xu, Qihao Zhu, Shirong Ma, Peiyi Wang, Xiao Bi, et al. Deepseek-r1: Incentivizing reasoning capability in llms via reinforcement learning. arXiv preprint arXiv:2501.12948, 2025

    2025 arXiv

  7. [14]

    Token-budget- aware llm reasoning

    Tingxu Han, Zhenting Wang, Chunrong Fang, Shiyu Zhao, Shiqing Ma, and Zhenyu Chen. Token-budget- aware llm reasoning. arXiv preprint arXiv:2412.18547, 2024

    2024 arXiv

  8. [15]

    Training large language models to reason in a continuous latent space

    Shibo Hao, Sainbayar Sukhbaatar, DiJia Su, Xian Li, Zhiting Hu, Jason Weston, and Yuandong Tian. Training large language models to reason in a continuous latent space. arXiv preprint arXiv:2412.06769, 2024. 10

    2024 arXiv

  9. [16]

    Measuring mathematical problem solving with the math dataset

    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. arXiv preprint arXiv:2103.03874, 2021

    2021 arXiv

  10. [17]

    Thinkprune: Pruning long chain-of-thought of llms via reinforcement learning

    Bairu Hou, Yang Zhang, Jiabao Ji, Yujian Liu, Kaizhi Qian, Jacob Andreas, and Shiyu Chang. Thinkprune: Pruning long chain-of-thought of llms via reinforcement learning. arXiv preprint arXiv:2504.01296, 2025

    2025 arXiv

  11. [18]

    Lora: Low-rank adaptation of large language models

    Edward J Hu, Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, Weizhu Chen, et al. Lora: Low-rank adaptation of large language models. ICLR, 1(2):3, 2022

    2022

  12. [19]

    Vision-r1: Incentivizing reasoning capability in multimodal large language models

    Wenxuan Huang, Bohan Jia, Zijie Zhai, Shaosheng Cao, Zheyu Ye, Fei Zhao, Zhe Xu, Yao Hu, and Shaohui Lin. Vision-r1: Incentivizing reasoning capability in multimodal large language models. arXiv preprint arXiv:2503.06749, 2025

    2025 arXiv

  13. [20]

    Openai o1 system card

    Aaron Jaech, Adam Kalai, Adam Lerer, Adam Richardson, Ahmed El-Kishky, Aiden Low, Alec Hel- yar, Aleksander Madry, Alex Beutel, Alex Carney, et al. Openai o1 system card. arXiv preprint arXiv:2412.16720, 2024

    2024 arXiv

  14. [21]

    T2i-r1: Reinforcing image generation with collaborative semantic-level and token-level cot

    Dongzhi Jiang, Ziyu Guo, Renrui Zhang, Zhuofan Zong, Hao Li, Le Zhuo, Shilin Yan, Pheng-Ann Heng, and Hongsheng Li. T2i-r1: Reinforcing image generation with collaborative semantic-level and token-level cot. arXiv preprint arXiv:2505.00703, 2025

    2025 arXiv

  15. [22]

    Bandit based monte-carlo planning

    Levente Kocsis and Csaba Szepesvári. Bandit based monte-carlo planning. In European conference on machine learning, pages 282–293. Springer, 2006

    2006

  16. [23]

    Efficient memory management for large language model serving with pagedattention

    Woosuk Kwon, Zhuohan Li, Siyuan Zhuang, Ying Sheng, Lianmin Zheng, Cody Hao Yu, Joseph Gonzalez, Hao Zhang, and Ion Stoica. Efficient memory management for large language model serving with pagedattention. In Proceedings of the 29th Symposium on Operating Systems Principles, p...

    2023

  17. [24]

    How well do llms compress their own chain-of-thought? a token complexity approach

    Ayeong Lee, Ethan Che, and Tianyi Peng. How well do llms compress their own chain-of-thought? a token complexity approach. arXiv preprint arXiv:2503.01141, 2025

    2025 arXiv

  18. [25]

    Fast inference from transformers via speculative decoding

    Yaniv Leviathan, Matan Kalman, and Yossi Matias. Fast inference from transformers via speculative decoding. In International Conference on Machine Learning, pages 19274–19286. PMLR, 2023

    2023

  19. [26]

    Adaptive group policy optimization: Towards stable training and token-efficient reasoning

    Chen Li, Nazhou Liu, and Kai Yang. Adaptive group policy optimization: Towards stable training and token-efficient reasoning. arXiv preprint arXiv:2503.15952, 2025

    2025

  20. [27]

    Mixed distillation helps smaller language model better reasoning

    Chenglin Li, Qianglong Chen, Liangyue Li, Caiyu Wang, Yicheng Li, Zulong Chen, and Yin Zhang. Mixed distillation helps smaller language model better reasoning. arXiv preprint arXiv:2312.10730, 2023

    2023 arXiv

  21. [28]

    Imagine while reasoning in space: Multimodal visualization-of-thought

    Chengzu Li, Wenshan Wu, Huanyu Zhang, Yan Xia, Shaoguang Mao, Li Dong, Ivan Vuli´c, and Furu Wei. Imagine while reasoning in space: Multimodal visualization-of-thought. arXiv preprint arXiv:2501.07542, 2025

    2025 arXiv

  22. [29]

    Numinamath

    Jia LI, Edward Beeching, Lewis Tunstall, Ben Lipkin, Roman Soletskyi, Shengyi Costa Huang, Kashif Ra- sul, Longhui Yu, Albert Jiang, Ziju Shen, Zihan Qin, Bin Dong, Li Zhou, Yann Fleureau, Guillaume Lample, and Stanislas Polu. Numinamath. [https://huggingface.co/AI-MO/NuminaMa...

    2024

  23. [30]

    Eagle: Speculative sampling requires rethinking feature uncertainty

    Yuhui Li, Fangyun Wei, Chao Zhang, and Hongyang Zhang. Eagle: Speculative sampling requires rethinking feature uncertainty. arXiv preprint arXiv:2401.15077, 2024

    2024 arXiv

  24. [31]

    Reward-guided speculative decoding for efficient llm reasoning

    Baohao Liao, Yuhui Xu, Hanze Dong, Junnan Li, Christof Monz, Silvio Savarese, Doyen Sahoo, and Caiming Xiong. Reward-guided speculative decoding for efficient llm reasoning. arXiv preprint arXiv:2501.19324, 2025

    2025 arXiv

  25. [32]

    Let’s verify step by step

    Hunter Lightman, Vineet Kosaraju, Yuri Burda, Harrison Edwards, Bowen Baker, Teddy Lee, Jan Leike, John Schulman, Ilya Sutskever, and Karl Cobbe. Let’s verify step by step. In The Twelfth International Conference on Learning Representations, 2023

    2023

  26. [33]

    Video-t1: Test-time scaling for video generation

    Fangfu Liu, Hanyang Wang, Yimo Cai, Kaiyan Zhang, Xiaohang Zhan, and Yueqi Duan. Video-t1: Test-time scaling for video generation. arXiv preprint arXiv:2503.18942, 2025

    2025 arXiv

  27. [34]

    Quantization hurts reasoning? an empirical study on quantized reasoning models

    Ruikang Liu, Yuxuan Sun, Manyi Zhang, Haoli Bai, Xianzhi Yu, Tiezheng Yu, Chun Yuan, and Lu Hou. Quantization hurts reasoning? an empirical study on quantized reasoning models. arXiv preprint arXiv:2504.04823, 2025. 11

    2025 arXiv

  28. [35]

    Can language models learn to skip steps? arXiv preprint arXiv:2411.01855, 2024

    Tengxiao Liu, Qipeng Guo, Xiangkun Hu, Cheng Jiayang, Yue Zhang, Xipeng Qiu, and Zheng Zhang. Can language models learn to skip steps? arXiv preprint arXiv:2411.01855, 2024

    2024 arXiv

  29. [36]

    Thought manipulation: External thought can be efficient for large reasoning models

    Yule Liu, Jingyi Zheng, Zhen Sun, Zifan Peng, Wenhan Dong, Zeyang Sha, Shiwen Cui, Weiqiang Wang, and Xinlei He. Thought manipulation: External thought can be efficient for large reasoning models. arXiv preprint arXiv:2504.13626, 2025

    2025 arXiv

  30. [37]

    Adar1: From long-cot to hybrid-cot via bi-level adaptive reasoning optimization

    Haotian Luo, Haiying He, Yibo Wang, Jinluan Yang, Rui Liu, Naiqiang Tan, Xiaochun Cao, Dacheng Tao, and Li Shen. Adar1: From long-cot to hybrid-cot via bi-level adaptive reasoning optimization. arXiv preprint arXiv:2504.21659, 2025

    2025 arXiv

  31. [38]

    O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning

    Haotian Luo, Li Shen, Haiying He, Yibo Wang, Shiwei Liu, Wei Li, Naiqiang Tan, Xiaochun Cao, and Dacheng Tao. O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning. arXiv preprint arXiv:2501.12570, 2025

    2025 arXiv

  32. [39]

    Non-myopic generation of language models for reasoning and planning

    Chang Ma, Haiteng Zhao, Junlei Zhang, Junxian He, and Lingpeng Kong. Non-myopic generation of language models for reasoning and planning. arXiv preprint arXiv:2410.17195, 2024

    2024 arXiv

  33. [40]

    Inference-time scaling for diffusion models beyond scaling denoising steps

    Nanye Ma, Shangyuan Tong, Haolin Jia, Hexiang Hu, Yu-Chuan Su, Mingda Zhang, Xuan Yang, Yandong Li, Tommi Jaakkola, Xuhui Jia, et al. Inference-time scaling for diffusion models beyond scaling denoising steps. arXiv preprint arXiv:2501.09732, 2025

    2025 arXiv

  34. [41]

    Cot-valve: Length- compressible chain-of-thought tuning

    Xinyin Ma, Guangnian Wan, Runpeng Yu, Gongfan Fang, and Xinchao Wang. Cot-valve: Length- compressible chain-of-thought tuning. arXiv preprint arXiv:2502.09601, 2025

    2025 arXiv

  35. [42]

    Simpo: Simple preference optimization with a reference-free reward

    Yu Meng, Mengzhou Xia, and Danqi Chen. Simpo: Simple preference optimization with a reference-free reward. Advances in Neural Information Processing Systems, 37:124198–124235, 2024

    2024

  36. [43]

    Self-training elicits concise reasoning in large language models

    Tergel Munkhbat, Namgyu Ho, Seo Hyun Kim, Yongjin Yang, Yujin Kim, and Se-Young Yun. Self-training elicits concise reasoning in large language models. arXiv preprint arXiv:2502.20122, 2025

    2025 arXiv

  37. [44]

    Skeleton-of-thought: Prompting llms for efficient parallel generation

    Xuefei Ning, Zinan Lin, Zixuan Zhou, Zifu Wang, Huazhong Yang, and Yu Wang. Skeleton-of-thought: Prompting llms for efficient parallel generation. arXiv preprint arXiv:2307.15337, 2023

    2023 arXiv

  38. [45]

    Learning adaptive parallel reasoning with language models

    Jiayi Pan, Xiuyu Li, Long Lian, Charlie Snell, Yifei Zhou, Adam Yala, Trevor Darrell, Kurt Keutzer, and Alane Suhr. Learning adaptive parallel reasoning with language models. arXiv preprint arXiv:2504.15466, 2025

    2025 arXiv

  39. [46]

    Specreason: Fast and accurate inference-time compute via speculative reasoning

    Rui Pan, Yinwei Dai, Zhihao Zhang, Gabriele Oliaro, Zhihao Jia, and Ravi Netravali. Specreason: Fast and accurate inference-time compute via speculative reasoning. arXiv preprint arXiv:2504.07891, 2025

    2025 arXiv

  40. [47]

    Deepspeed: System optimizations enable training deep learning models with over 100 billion parameters

    Jeff Rasley, Samyam Rajbhandari, Olatunji Ruwase, and Yuxiong He. Deepspeed: System optimizations enable training deep learning models with over 100 billion parameters. In Proceedings of the 26th ACM SIGKDD international conference on knowledge discovery & data mining, pages 3...

    2020

  41. [48]

    Efficient reasoning with hidden thinking

    Xuan Shen, Yizhou Wang, Xiangxi Shi, Yanzhi Wang, Pu Zhao, and Jiuxiang Gu. Efficient reasoning with hidden thinking. arXiv preprint arXiv:2501.19201, 2025

    2025 arXiv

  42. [49]

    Dast: Difficulty-adaptive slow-thinking for large reasoning models, 2025

    Yi Shen, Jian Zhang, Jieyun Huang, Shuming Shi, Wenjing Zhang, Jiangze Yan, Ning Wang, Kai Wang, and Shiguo Lian. Dast: Difficulty-adaptive slow-thinking for large reasoning models, 2025. URL https://arxiv. org/abs/2503.04472

    2025

  43. [50]

    Towards reasoning ability of small language models

    Gaurav Srivastava, Shuxiang Cao, and Xuan Wang. Towards reasoning ability of small language models. arXiv preprint arXiv:2502.11569, 2025

    2025

  44. [51]

    Fast best-of-n decoding via speculative rejection

    Hanshi Sun, Momin Haider, Ruiqi Zhang, Huitao Yang, Jiahao Qiu, Ming Yin, Mengdi Wang, Peter Bartlett, and Andrea Zanette. Fast best-of-n decoding via speculative rejection. arXiv preprint arXiv:2410.20290, 2024

    2024 arXiv

  45. [52]

    Time up! an empirical study of llm reasoning ability under output length constraint

    Yi Sun, Han Wang, Jiaqiang Li, Jiacheng Liu, Xiangyu Li, Hao Wen, Huiwen Zheng, Yan Liang, Yuanchun Li, and Yunxin Liu. Time up! an empirical study of llm reasoning ability under output length constraint. arXiv preprint arXiv:2504.14350, 2025

    2025 arXiv

  46. [53]

    Kimi Team, Angang Du, Bofei Gao, Bowei Xing, Changjiu Jiang, Cheng Chen, Cheng Li, Chenjun Xiao, Chenzhuang Du, Chonghua Liao, et al. Kimi k1. 5: Scaling reinforcement learning with llms. arXiv preprint arXiv:2501.12599, 2025

    2025 arXiv

  47. [54]

    https://qwenlm.github.io/blog/qwq-32b-preview/, 2024

    Qwen Team. https://qwenlm.github.io/blog/qwq-32b-preview/, 2024. 12

    2024

  48. [55]

    Think deep, think fast: Investigating efficiency of verifier-free inference-time-scaling methods

    Junlin Wang, Shang Zhu, Jon Saad-Falcon, Ben Athiwaratkun, Qingyang Wu, Jue Wang, Shuaiwen Leon Song, Ce Zhang, Bhuwan Dhingra, and James Zou. Think deep, think fast: Investigating efficiency of verifier-free inference-time-scaling methods. arXiv preprint arXiv:2504.14047, 2025

    2025 arXiv

  49. [56]

    Self-consistency improves chain of thought reasoning in language models

    Xuezhi Wang, Jason Wei, Dale Schuurmans, Quoc Le, Ed Chi, Sharan Narang, Aakanksha Chowdhery, and Denny Zhou. Self-consistency improves chain of thought reasoning in language models. arXiv preprint arXiv:2203.11171, 2022

    2022 arXiv

  50. [58]

    Chain-of-thought prompting elicits reasoning in large language models

    Jason Wei, Xuezhi Wang, Dale Schuurmans, Maarten Bosma, Fei Xia, Ed Chi, Quoc V Le, Denny Zhou, et al. Chain-of-thought prompting elicits reasoning in large language models. Advances in neural information processing systems, 35:24824–24837, 2022

    2022

  51. [59]

    Tokenskip: Controllable chain-of-thought compression in llms

    Heming Xia, Yongqi Li, Chak Tou Leong, Wenjie Wang, and Wenjie Li. Tokenskip: Controllable chain-of-thought compression in llms. arXiv preprint arXiv:2502.12067, 2025

    2025

  52. [60]

    Unlocking efficiency in large language model inference: A comprehensive survey of speculative decoding

    Heming Xia, Zhe Yang, Qingxiu Dong, Peiyi Wang, Yongqi Li, Tao Ge, Tianyu Liu, Wenjie Li, and Zhifang Sui. Unlocking efficiency in large language model inference: A comprehensive survey of speculative decoding. arXiv preprint arXiv:2401.07851, 2024

    2024 arXiv

  53. [61]

    Sana 1.5: Efficient scaling of training-time and inference-time compute in linear diffusion transformer

    Enze Xie, Junsong Chen, Yuyang Zhao, Jincheng Yu, Ligeng Zhu, Chengyue Wu, Yujun Lin, Zhekai Zhang, Muyang Li, Junyu Chen, et al. Sana 1.5: Efficient scaling of training-time and inference-time compute in linear diffusion transformer. arXiv preprint arXiv:2501.18427, 2025

    2025 arXiv

  54. [62]

    Llava-o1: Let vision language models reason step-by-step

    Guowei Xu, Peng Jin, Li Hao, Yibing Song, Lichao Sun, and Li Yuan. Llava-o1: Let vision language models reason step-by-step. arXiv preprint arXiv:2411.10440, 2024

    2024 arXiv

  55. [63]

    Phi-4-mini-reasoning: Exploring the limits of small reasoning language models in math

    Haoran Xu, Baolin Peng, Hany Awadalla, Dongdong Chen, Yen-Chun Chen, Mei Gao, Young Jin Kim, Yunsheng Li, Liliang Ren, Yelong Shen, et al. Phi-4-mini-reasoning: Exploring the limits of small reasoning language models in math. arXiv preprint arXiv:2504.21233, 2025

    2025 arXiv

  56. [64]

    Chain of draft: Thinking faster by writing less

    Silei Xu, Wenhao Xie, Lingxiao Zhao, and Pengcheng He. Chain of draft: Thinking faster by writing less. arXiv preprint arXiv:2502.18600, 2025

    2025 arXiv

  57. [65]

    An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, et al. Qwen2. 5-math technical report: Toward mathematical expert model via self-improvement. arXiv preprint arXiv:2409.12122, 2024

    2024 arXiv

  58. [66]

    Dynamic early exit in reasoning models

    Chenxu Yang, Qingyi Si, Yongjie Duan, Zheliang Zhu, Chenyu Zhu, Zheng Lin, Li Cao, and Weiping Wang. Dynamic early exit in reasoning models. arXiv preprint arXiv:2504.15895, 2025

    2025

  59. [67]

    Think when you need: Self-adaptive chain-of-thought learning

    Junjie Yang, Ke Lin, and Xing Yu. Think when you need: Self-adaptive chain-of-thought learning. arXiv preprint arXiv:2504.03234, 2025

    2025 arXiv

  60. [68]

    Towards thinking-optimal scaling of test-time compute for llm reasoning

    Wenkai Yang, Shuming Ma, Yankai Lin, and Furu Wei. Towards thinking-optimal scaling of test-time compute for llm reasoning. arXiv preprint arXiv:2502.18080, 2025

    2025

  61. [69]

    Limo: Less is more for reasoning

    Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. Limo: Less is more for reasoning. arXiv preprint arXiv:2502.03387, 2025

    2025 arXiv

  62. [70]

    Demystifying long chain-of- thought reasoning in llms

    Edward Yeo, Yuxuan Tong, Morry Niu, Graham Neubig, and Xiang Yue. Demystifying long chain-of- thought reasoning in llms. arXiv preprint arXiv:2502.03373, 2025

    2025 arXiv

  63. [71]

    Introducing visual perception token into multimodal large language model

    Runpeng Yu, Xinyin Ma, and Xinchao Wang. Introducing visual perception token into multimodal large language model. arXiv preprint arXiv:2502.17425, 2025

    2025 arXiv

  64. [72]

    When reasoning meets compression: Bench- marking compressed large reasoning models on complex reasoning tasks.arXiv preprint arXiv:2504.02010, 2025

    Nan Zhang, Yusen Zhang, Prasenjit Mitra, and Rui Zhang. When reasoning meets compression: Bench- marking compressed large reasoning models on complex reasoning tasks.arXiv preprint arXiv:2504.02010, 2025

    2025

  65. [73]

    Improving mathematical reasoning capabilities of small language models via feedback-driven distillation

    Xunyu Zhu, Jian Li, Can Ma, and Weiping Wang. Improving mathematical reasoning capabilities of small language models via feedback-driven distillation. arXiv preprint arXiv:2411.14698, 2024. 13 In this document, we provide supplementary materials that extend beyond the scope of...

    2024 arXiv

  66. [74]

    So, 49 is 7 times 7

    Now, 49 is a number I recognize; it's 7 squared. So, 49 is 7 times 7. Therefore, putting it all together, the prime factorization of 196 is 2 squared times 7 squared. In mathematical terms, that's \\( 2^2 \\times 7^2 \\).\n\nNow, I recall that the formula for finding the numbe...

  67. [75]

    So scaling by 12 gives the direction vector \\( (2, -12, -3) \\).\n\nAlternatively, maybe I could have found the direction vector differently

    Yeah, that's correct. So scaling by 12 gives the direction vector \\( (2, -12, -3) \\).\n\nAlternatively, maybe I could have found the direction vector differently. Let me see:\n\nFrom the symmetric equations, the direction ratios are the denominators. So for the second line, ...

Pith tools

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