Pith. sign in

REVIEW 4 major objections 5 minor 1 cited by

Don't Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models

T0 review · 4 major / 5 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 The paper introduces DTO, a framework that reduces overthinking in large reasoning models by segmenting reasoning into thinking patterns, pruning unhelpful ones, and using preference optimization to make models stop at the right time…

desk verdict A solid, incrementally novel method for making reasoning models cheaper; the oracle-based offline analysis is a construction, not a prediction, and the real open question is whether preference learning transfers those oracle decisions to test time. read the letter →

arxiv 2505.21765 v1 pith:JZ26PCMP submitted 2025-05-27 cs.AI

Sohyun An , Ruochen Wang , Tianyi Zhou , Cho-Jui Hsieh This is my paper
classification cs.AI
keywords largereasoningmodelsoverthinkingthinkingpatternsefficiencypreferenceoptimizationdynamictokenreductionmathematical
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 tries to show that the main source of inefficiency in large reasoning models is not simply long output but a failure to dynamically choose the right modular reasoning moves, which it calls thinking patterns. It proposes DTO, a framework that cuts a model's reasoning path into thinking patterns, finds the earliest point where the model already has enough information to answer correctly, prunes unhelpful segments, and then trains the model with preference optimization on the resulting concise trajectories. Across mathematical reasoning benchmarks, the paper reports that this reduces token use from roughly 5,000 to 3,000 and improves accuracy by up to 12%, including on problems that were originally answered incorrectly. A sympathetic reader would care because it suggests efficiency and accuracy can be improved together rather than traded off.

What carries the argument

The central object is the thinking pattern, a modular segment of a reasoning trace that serves a distinct cognitive function such as verification, summarization, or exploration, usually identifiable by cues like "Wait". DTO's machinery is the pipeline that manipulates these patterns: for each prefix it constructs $\tau_i = \delta_1 \oplus \cdots \oplus \delta_i \oplus \delta_{\text{exit}}$, samples $M$ completions, estimates $p_i = |\{r \in R_i : a^* \in r\}|/|R_i|$, and stops at the earliest $i$ with $p_i \ge T$. A binary selection function keeps only patterns up to that point, a finalization pattern and shortest correct completion are appended, and a pruning function $g$ removes segments judged redundant by an auxiliary LLM after a decoding check. These optimized trajectories become the winning responses in a pairwise dataset trained with a reference-free preference objective, so the model learns the stop-and-prune behavior directly.

What would settle it

Concrete test: train DTO only on problems where the Monte Carlo estimate $p_i$ never reaches the threshold $T$, then compare accuracy and token counts against the base model on unseen problems. If the gains disappear or accuracy drops, the improvement comes from oracle truncation rather than a learnable thinking-pattern policy.

Watch

Extended reading notes

Core claim

The paper's central claim is that large reasoning models can reason both more cheaply and more accurately if their reasoning process is optimized at the level of thinking patterns instead of at the level of whole trajectories. For each generated solution, DTO segments the trace by linguistic cues, appends a special exit pattern at each candidate position, and estimates the probability that Monte Carlo completions reach the ground-truth answer; the first position where this probability crosses a threshold becomes the truncation point. It then appends a finalization phrase, keeps the shortest correct completion, uses an auxiliary LLM to judge which remaining segments can be removed, and finally builds a pairwise dataset that contrasts these optimized trajectories with the longest unoptimized ones for preference training. The paper reports that this dynamic selection not only preserves accuracy for originally correct responses while cutting attention FLOPs by up to 47%, but also converts a non-trivial fraction of incorrect responses into correct ones. If the claim holds, overthinking is not a fixed cost of strong reasoning but a controllable behavior.

Load-bearing premise

The load-bearing premise is that trajectories optimized offline using the ground-truth answer, with early termination and pruning decisions made with oracle knowledge, can be learned by preference optimization and will transfer to test-time reasoning where no ground truth exists.

Editorial extensions

If this is right

  • If DTO is right, language models can be made noticeably cheaper to run without sacrificing accuracy: the paper reports token counts dropping from roughly 5,000 to 3,000 on hard math benchmarks.
  • Reasoning errors are partly recoverable: the method's early-termination and pruning procedure turns some originally wrong solutions into correct ones, with reported accuracy gains of 15.6% and 7.8% on two 1.5B models before preference training.
  • Preference optimization over optimized trajectories gives the largest gains on difficult competition problems, with about a 7% accuracy improvement over the base model on AMC and AIME while shortening outputs.
  • The behavior of thinking-pattern transitions changes: DTO-trained models use the cue "Wait" less often, indicating fewer unproductive reasoning shifts at similar or better accuracy.

Reading between the lines

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

  • The same segment-level machinery could be transferred to other reasoning-heavy domains, such as coding or legal analysis, where intermediate verification and summarization patterns are identifiable; the paper's MMLU-Pro results provide partial evidence but leave open-ended tasks untested.
  • A natural extension is to make the pruning judge and the preference data generation lighter, since the current pipeline needs multiple samples and an auxiliary LLM per problem; a version that learns the pruning decision entirely from the base model would make the method practical at deployment scale.
  • If the learned policy genuinely captures when to stop, it should compose with test-time compute scaling: the model could dynamically allocate more patterns to hard problems and fewer to easy ones, which the paper's formulation hints at but does not directly evaluate.
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

4 major / 5 minor

Summary. The paper hypothesizes that overthinking in large reasoning models stems from poor dynamic selection of 'thinking patterns' (modular reasoning segments). It introduces DTO, a framework that (i) segments a model-generated reasoning trajectory, (ii) uses ground-truth answers to find the earliest safe termination point via Monte Carlo estimation of correctness probability, (iii) appends a finalization pattern and selects the shortest completion containing the correct answer, and (iv) prunes redundant segments using an auxiliary LLM. These optimized trajectories are then used to build a pairwise preference dataset, and SimPO is applied to train the base model. Experiments on MATH, GSM8K, Gaokao, AMC, AIME, and MMLU-Pro report reduced token usage and improved or maintained accuracy, with the headline claim of up to 12% accuracy improvement and token reduction from about 5,000 to 3,000 tokens.

Significance. If the central transfer claim held, the work would be a useful contribution to reasoning-efficiency research: it proposes a segment-level objective rather than length heuristics, provides an explicit optimization algorithm (Algorithm 1), and includes a preference-optimization pipeline with detailed prompts. The empirical comparisons across six benchmarks and a generalization study on MMLU-Pro are valuable. However, the evidence currently rests on an oracle-guided trajectory construction whose learnability at test time is not demonstrated, and the offline analysis in Section 3.3 is partly circular as evidence of accuracy improvement. The strengths are the concrete framework and the transparent algorithm; the weaknesses are the missing statistical support and the lack of an oracle-free ablation.

major comments (4)
  1. [Section 3.3, Eqs. (6)–(12)] The claimed offline 'accuracy improvement' on originally incorrect responses is constructed rather than predicted. For each incorrect response, the pipeline selects the earliest index i for which the Monte Carlo estimate p_i reaches the threshold T=1.0, samples K completions after appending δ_finalize, keeps the shortest completion containing the ground-truth answer a*, and prunes segments only when the remaining trajectory still yields a*. Every decision uses a*. Therefore the statement that 'a non-trivial portion of originally incorrect responses are transformed into correct ones' is true by construction, not a property of the base model's learned behavior. Please reframe Section 3.3 as a data-construction validation, and add a no-oracle baseline (e.g., termination by a fixed token budget or by the model's own confidence score) to quantify what the oracle contributes.
  2. [Section 4.1, Eq. (13) and Tables 1–2] The central test-time claim depends on SimPO learning to reproduce the oracle's termination and pruning decisions, but the paper provides no evidence of such transfer. The authors do not analyze whether the trained model's self-chosen termination points align with the oracle's i′, nor do they ablate the oracle by training on non-oracle curated trajectories (e.g., random truncation or shortest correct completions without ground-truth pruning). Given that the pairwise dataset D′ is built entirely from ground-truth-answer-dependent trajectories, Tables 1–2 could reflect length regularization or memorization of the training distribution rather than the proposed 'thinking pattern' optimization. Please add an ablation removing the oracle from data construction, an analysis of termination-point agreement, and statistical significance tests.
  3. [Section 3.2 and Algorithm 1] The segmentation of a reasoning trajectory y into thinking patterns [δ_1, ..., δ_n_y] is never specified. The paper mentions linguistic cues such as 'Wait' and 'Alternatively', but no algorithm, prompt, or rule is given for producing the segment boundaries that every downstream step (Eqs. (4)–(12) and Algorithm 1) relies on. This makes the method underspecified and not reproducible. Please provide the segmentation procedure, or state explicitly that the auxiliary LLM µϕ performs segmentation and include the full prompt used for that step.
  4. [Section 3.3, threshold T and hyperparameters] The threshold T=1.0 is an extreme choice: it requires all M=10 Monte Carlo continuations to contain the ground-truth answer before termination. This makes the estimated termination point i′ sensitive to M and to the sampling distribution, and no sensitivity analysis is reported for T, M, or K. Since the termination index is the central mechanism of DTO, the paper should report how results vary with these parameters, or justify T=1.0 theoretically. Without this, the reader cannot tell whether the reported efficiency gains are robust or a consequence of a particular, unexamined threshold.
minor comments (5)
  1. [Eq. (7)] Equation (7) writes f(δ_i) = 1 if δ_i ≤ i′, but δ_i is a reasoning segment and i′ is an index; the comparison is undefined. It should likely be f(δ_i) = 1 if i ≤ i′. Please correct this typo.
  2. [Section 3.3 and Figure 2] The paper reports reductions in 'attention FLOPs' but never defines how attention FLOPs are computed or normalized. Please specify the calculation, including whether it counts only attention operations or all transformer FLOPs, and how the numbers in Figure 2 are aggregated.
  3. [Table 3 and Appendix B] The qualitative comparison refers to segments 'highlighted in yellow' and 'in green', but these colors are not visible in plain-text rendering. Please use explicit labels or bracketed annotations so the claimed redundancy is clear to all readers.
  4. [Section 4.3, Table 4] The generalization experiment on MMLU-Pro uses 100 randomly sampled questions per domain. With such small samples, the accuracy differences (e.g., 17.50 vs. 16.75 for Law) are within sampling noise. Please report standard errors or confidence intervals for these results, or increase the sample size.
  5. [Appendix A.2] The implementation details state that SGLang raises an error when max_tokens exceeds 4096 and that 'we adjusted our settings accordingly,' but it is not clear which models and experiments use the reduced limit. Please clarify whether the 8192-token setting applies to the main DTO experiments and whether the Qwen2.5-Math Instruct baselines use a different maximum.

Circularity Check

1 steps flagged · score 6.0 of 10

Section 3.3's FLOPs/accuracy 'validation' is self-definitional: the optimized trajectories are constructed using the ground-truth answer to select the shortest correct completion, so the reported gains re-express the selection criterion rather than constitute an independent prediction; the held-out preference-optimization results remain non-circular.

  1. self definitional [Abstract; Section 3.3 Results; Algorithm 1 and Eqs. (6), (10), (11)]
    "Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length."

    The measured trajectories are not predictions; they are built by Algorithm 1 with oracle access to a*. Eq. (6) defines pi by checking 'a* in r' and stops at the first i' with pi = T = 1.0, Eq. (10) keeps only the shortest completion s* with a* in it, and Eq. (11) prunes a segment only if decoding the remaining trajectory still yields a*. Hence shorter length and preserved or improved accuracy are imposed by construction. The 'empirical confirmation' in Section 3.3 therefore restates the optimization criterion rather than validating the framework's transferable benefit. This does not invalidate the separate held-out SimPO evaluation in Tables 1-2, which tests a trained model without oracle access.

full rationale

The paper's derivation chain contains one load-bearing circular step: the Section 3.3 analysis (and the abstract's 47% FLOPs reduction and 15.6% accuracy improvement) evaluates trajectories produced by an oracle procedure that uses the ground-truth answer to choose the termination point, the shortest correct completion, and the pruned segments. Those numbers are consequences of the selection rules in Eqs. (6), (10), and (11), so presenting them as 'empirical analysis confirms' is self-definitional rather than an independent test. The central test-time claim, however, is supported by held-out evaluations: after SimPO training on the oracle-curated pairwise dataset, the model is evaluated on MATH, GSM8K, Gaokao, AMC, and AIME test sets without access to ground-truth answers. Those results are not forced by the training-data construction, though they inherit the usual risk that oracle-selected trajectories may not be reproducible by the model at inference. There are no load-bearing self-citations, uniqueness arguments, or renamed known results. The circularity is therefore partial, confined to the oracle-based analysis, and does not make the entire paper's derivation equivalent to its inputs.

Assumptions & free parameters 5 free parameters · 4 assumptions · 1 invented entities

The DTO construction relies on several domain assumptions (segmentability, reliability of Monte Carlo correctness estimates, auxiliary LLM judgment) and free hyperparameters (T=1.0, M=10, K=4, SimPO beta/gamma) that are not justified by sensitivity analysis. The central trained-model claim does not depend on invented physical entities, but the concept of a 'thinking pattern' is an unmeasured categorization.

free parameters (5)
  • threshold T = 1.0
    Controls the earliest termination index; requires all M=10 Monte Carlo samples to contain the correct answer. No sensitivity analysis; a core hyperparameter for trajectory compression.
  • M = 10
    Number of completions for exit probability estimation. Chosen without justification.
  • K = 4
    Number of completions for finalize sampling. Chosen without justification.
  • SimPO beta and gamma/beta = 10.0 / 0.3
    Standard hyperparameters for SimPO, but no tuning details or sensitivity analysis are provided.
  • Sampling temperature and top_p = 0.6 / 0.95
    Fixed sampling parameters for all experiments; no ablation on their effect.
assumptions (4)
  • domain assumption Reasoning trajectories can be segmented into thinking patterns with distinct cognitive functions, detectable via linguistic cues.
    Section 3 defines thinking patterns and uses cues like 'Wait' to segment trajectories; this is a structural assumption about reasoning text.
  • domain assumption The base model's Monte Carlo estimate pi correctly predicts whether the model can complete the answer from a given prefix.
    Equation (6) uses pi to select termination points; if the estimate is noisy, the constructed trajectories may not be optimal.
  • domain assumption The auxiliary LLM µphi's judgments about segment contribution are reliable and align with reasoning quality.
    Section 3.2 relies on µphi to prune segments; if the auxiliary model makes errors, the optimized trajectories lose necessary reasoning steps.
  • domain assumption Preference optimization on the curated pairwise dataset transfers to improved reasoning efficiency at test time.
    Section 4 assumes that training on ground-truth-curated trajectories produces a model that can self-select efficient reasoning without labels.
invented entities (1)
  • thinking pattern
    purpose: To segment reasoning trajectories into modular units for optimization.
    No objective measurement; defined by linguistic cues and auxiliary LLM judgment, not falsifiable independently.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Don't Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models." pith.science (2026). https://pith.science/paper/JZ26PCMP

@misc{pith2026250521765,
  author       = {Pith},
  title        = {Pith review of: Don't Think Longer, Think Wisely: Optimizing Thinking Dynamics for Large Reasoning Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/JZ26PCMP}},
  note         = {Machine review of arXiv:2505.21765}
}
read the original abstract

While recent success of large reasoning models (LRMs) significantly advanced LLMs' reasoning capability by optimizing the final answer accuracy using reinforcement learning, they may also drastically increase the output length due to overthinking, characterized by unnecessarily complex reasoning paths that waste computation and potentially degrade the performance. We hypothesize that such inefficiencies stem from LRMs' limited capability to dynamically select the proper modular reasoning strategies, termed thinking patterns at the right position. To investigate this hypothesis, we propose a dynamic optimization framework that segments model-generated reasoning paths into distinct thinking patterns, systematically identifying and promoting beneficial patterns that improve the answer while removing detrimental ones. Empirical analysis confirms that our optimized thinking paths yield more concise yet sufficiently informative trajectories, enhancing reasoning efficiency by reducing attention FLOPs by up to 47% while maintaining accuracy for originally correct responses. Moreover, a non-trivial portion of originally incorrect responses are transformed into correct ones, achieving a 15.6% accuracy improvement with reduced length. Motivated by the improvement brought by the optimized thinking paths, we apply a preference optimization technique supported by a pairwise dataset contrasting suboptimal and optimal reasoning paths. Experimental evaluations across multiple mathematical reasoning benchmarks reveal that our method notably reduces computational overhead while simultaneously improving reasoning accuracy, achieving up to a 12% accuracy improvement and reducing token usage from approximately 5,000 to 3,000 tokens.

Figures

Figures reproduced from arXiv: 2505.21765 by the authors.

Figure 1
Figure 1. Illustration of DTO. We construct a truncated reasoning trajectory ∆f x by identifying the point where the probability score pi in Equation (6) exceeds a threshold T = 1.0, and then applying the binary selection function f(·) from Equation (7). We then append the finalization pattern δfinalize and sampled answer s ∗ (Equation (9)) to form ∆˜ f x. Finally, the pruning function g(·) (Equation (11)) refines the traject… view at source ↗
Figure 2
Figure 2. Comparison of dynamically optimized vs. original responses, and maxi pi distributions in incorrect cases. (a), (b) Dynamic optimization preserves accuracy for correct responses while reducing attention FLOPs (47%, 40%), and improves accuracy for incorrect ones (15.6%, 7.8%) with lower FLOPs. (c) shows maxi pi, the maximum estimated correctness probability across thinking patterns (Equation (6)). High values suggest … view at source ↗
Figure 3
Figure 3. The average count of “Wait”, which is one of the words signaling a thinking pattern transition. Compared to all baselines, our framework generally results in the lowest average count of “Wait”, suggesting more concise and less interrupted reasoning trajectories. The results are averaged over 4 runs [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Distribution of maxi pi in incorrect responses of DeepScaleR-1.5B-Preview. Due to space limitations, we report the distribution of maxi pi for incorrect responses of the DeepScaleR-1.5B-Preview model in Fig￾ure 4. In Section 3.3, we analyze the distribution of maxi pi …

Discussion (0). Sign in to comment.

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

57 extracted references · 13 canonical work pages · cited by 1 Pith paper

  1. [1]

    L1: Controlling how long a reasoning model thinks with reinforcement learning, 2025

    Pranjal Aggarwal and Sean Welleck. L1: Controlling how long a reasoning model thinks with reinforcement learning, 2025. URL https://arxiv.org/abs/2503.04697

    arXiv 2025

  2. [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

  3. [3]

    Large language monkeys: Scaling inference compute with repeated sampling

    Bradley Brown, Jordan Juravsky, Ryan Ehrlich, Ronald Clark, Quoc V Le, Christopher Ré, and Azalia Mirhoseini. Large language monkeys: Scaling inference compute with repeated sampling. arXiv preprint arXiv:2407.21787, 2024

    arXiv 2024

  4. [4]

    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

  5. [5]

    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

  6. [6]

    Efficiently serving llm reasoning programs with certaindex

    Yichao Fu, Junda Chen, Siqi Zhu, Zheyu Fu, Zhongdongming Dai, Aurick Qiao, and Hao Zhang. Efficiently serving llm reasoning programs with certaindex. arXiv preprint arXiv:2412.20993, 2024

    arXiv 2024

  7. [7]

    Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective stars

    Kanishk Gandhi, Ayush Chakravarthy, Anikait Singh, Nathan Lile, and Noah D Goodman. Cognitive behaviors that enable self-improving reasoners, or, four habits of highly effective stars. arXiv preprint arXiv:2503.01307, 2025

    arXiv 2025

  8. [8]

    The llama 3 herd of models

    Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. The llama 3 herd of models. arXiv preprint arXiv:2407.21783, 2024

    arXiv 2024

Show all 57 references
  1. [9]

    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

  2. [10]

    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

  3. [11]

    Thinkprune: Pruning long chain-of-thought of llms via reinforcement learning, 2025

    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, 2025. URL https://arxiv.org/abs/2504.01296

    2025 arXiv

  4. [12]

    Reinforce++: A simple and efficient approach for aligning large language models

    Jian Hu. Reinforce++: A simple and efficient approach for aligning large language models. arXiv preprint arXiv:2501.03262, 2025

    2025 arXiv

  5. [13]

    Openai o1 system card

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

    2024 arXiv

  6. [14]

    Graph chain-of-thought: Augmenting large language models by reasoning on graphs

    Bowen Jin, Chulin Xie, Jiawei Zhang, Kashob Kumar Roy, Yu Zhang, Zheng Li, Ruirui Li, Xianfeng Tang, Suhang Wang, Yu Meng, et al. Graph chain-of-thought: Augmenting large language models by reasoning on graphs. arXiv preprint arXiv:2404.07103, 2024

    2024 arXiv

  7. [15]

    From system 1 to system 2: A survey of reasoning large language models

    Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Jie Wang, Xiuyi 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]

    Understanding r1-zero-like training: A critical perspective

    Zichen Liu, Changyu Chen, Wenjun Li, Penghui Qi, Tianyu Pang, Chao Du, Wee Sun Lee, and Min Lin. Understanding r1-zero-like training: A critical perspective. arXiv preprint arXiv:2503.20783, 2025. 10

    2025 arXiv

  9. [17]

    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

  10. [18]

    Tang, Manan Roongta, Colin Cai, Jeffrey Luo, Li Erran Li, Raluca Ada Popa, and Ion Stoica

    Michael Luo, Sijun Tan, Justin Wong, Xiaoxiang Shi, William Y . Tang, Manan Roongta, Colin Cai, Jeffrey Luo, Li Erran Li, Raluca Ada Popa, and Ion Stoica. Deepscaler: Surpassing o1-preview with a 1.5b model by scaling rl, 2025. Notion Blog

    2025

  11. [19]

    Deepseek-r1 thoughtology: Let’s< think> about llm reasoning

    Sara Vera Marjanovi ´c, Arkil Patel, Vaibhav Adlakha, Milad Aghajohari, Parishad BehnamGhader, Mehar Bhatia, Aditi Khandelwal, Austin Kraft, Benno Krojer, Xing Han Lù, et al. Deepseek-r1 thoughtology: Let’s< think> about llm reasoning. arXiv preprint arXiv:2504.07128, 2025

    2025

  12. [20]

    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

  13. [21]

    A survey of efficient reasoning for large reasoning models: Language, multimodality, and beyond

    Xiaoye Qu, Yafu Li, Zhaochen Su, Weigao Sun, Jianhao Yan, Dongrui Liu, Ganqu Cui, Daizong Liu, Shuxian Liang, Junxian He, et al. A survey of efficient reasoning for large reasoning models: Language, multimodality, and beyond. arXiv preprint arXiv:2503.21614, 2025

    2025

  14. [22]

    Optimizing test-time compute via meta reinforcement fine-tuning

    Yuxiao Qu, Matthew YR Yang, Amrith Setlur, Lewis Tunstall, Edward Emanuel Beeching, Ruslan Salakhutdinov, and Aviral Kumar. Optimizing test-time compute via meta reinforcement fine-tuning. arXiv preprint arXiv:2503.07572, 2025

    2025 arXiv

  15. [23]

    Proximal policy optimization algorithms

    John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347, 2017

    2017 arXiv

  16. [24]

    Rewarding progress: Scaling automated process verifiers for llm reasoning

    Amrith Setlur, Chirag Nagpal, Adam Fisch, Xinyang Geng, Jacob Eisenstein, Rishabh Agarwal, Alekh Agarwal, Jonathan Berant, and Aviral Kumar. Rewarding progress: Scaling automated process verifiers for llm reasoning. arXiv preprint arXiv:2410.08146, 2024

    arXiv

  17. [25]

    Deepseekmath: Pushing the limits of mathematical reasoning in open language models

    Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Y Wu, et al. Deepseekmath: Pushing the limits of mathematical reasoning in open language models. arXiv preprint arXiv:2402.03300, 2024

    2024 arXiv

  18. [26]

    Hawkeye:efficient reasoning with model collaboration, 2025

    Jianshu She, Zhuohao Li, Zhemin Huang, Qi Li, Peiran Xu, Haonan Li, and Qirong Ho. Hawkeye:efficient reasoning with model collaboration, 2025. URL https://arxiv.org/abs/ 2504.00424

    2025 arXiv

  19. [27]

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

    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. arXiv preprint arXiv:2503.04472, 2025

    2025

  20. [28]

    Scaling llm test-time compute opti- mally can be more effective than scaling model parameters

    Charlie Snell, Jaehoon Lee, Kelvin Xu, and Aviral Kumar. Scaling llm test-time compute opti- mally can be more effective than scaling model parameters. arXiv preprint arXiv:2408.03314, 2024

    2024 arXiv

  21. [29]

    Stop overthinking: A survey on efficient reasoning for large language models

    Yang Sui, Yu-Neng Chuang, Guanchu Wang, Jiamu Zhang, Tianyi Zhang, Jiayi Yuan, Hongyi Liu, Andrew Wen, Hanjie Chen, Xia Hu, et al. Stop overthinking: A survey on efficient reasoning for large language models. arXiv preprint arXiv:2503.16419, 2025

    2025 arXiv

  22. [30]

    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

  23. [31]

    Harnessing the reasoning economy: A survey of efficient reasoning for large language models

    Rui Wang, Hongru Wang, Boyang Xue, Jianhui Pang, Shudong Liu, Yi Chen, Jiahao Qiu, Derek Fai Wong, Heng Ji, and Kam-Fai Wong. Harnessing the reasoning economy: A survey of efficient reasoning for large language models. arXiv preprint arXiv:2503.24377, 2025

    2025 arXiv

  24. [32]

    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. 11

    2022 arXiv

  25. [33]

    Mmlu-pro: A more robust and challenging multi-task language understanding benchmark

    Yubo Wang, Xueguang Ma, Ge Zhang, Yuansheng Ni, Abhranil Chandra, Shiguang Guo, Weiming Ren, Aaran Arulraj, Xuan He, Ziyan Jiang, et al. Mmlu-pro: A more robust and challenging multi-task language understanding benchmark. arXiv preprint arXiv:2406.01574, 2024

    2024 arXiv

  26. [34]

    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

  27. [35]

    Inference scaling laws: An empirical analysis of compute-optimal inference for problem-solving with language models

    Yangzhen Wu, Zhiqing Sun, Shanda Li, Sean Welleck, and Yiming Yang. Inference scaling laws: An empirical analysis of compute-optimal inference for problem-solving with language models. arXiv preprint arXiv:2408.00724, 2024

    2024 arXiv

  28. [36]

    Towards system 2 reasoning in llms: Learning how to think with meta chain-of-though

    Violet Xiang, Charlie Snell, Kanishk Gandhi, Alon Albalak, Anikait Singh, Chase Blagden, Duy Phung, Rafael Rafailov, Nathan Lile, Dakota Mahan, et al. Towards system 2 reasoning in llms: Learning how to think with meta chain-of-though. arXiv preprint arXiv:2501.04682, 2025

    2025 arXiv

  29. [37]

    Qwen2.5-math technical report: Toward mathematical expert model via self-improvement

    An Yang, Beichen Zhang, Binyuan Hui, Bofei Gao, Bowen Yu, Chengpeng Li, Dayiheng Liu, Jianhong Tu, Jingren Zhou, Junyang Lin, Keming Lu, Mingfeng Xue, Runji Lin, Tianyu Liu, Xingzhang Ren, and Zhenru Zhang. Qwen2.5-math technical report: Toward mathematical expert model via se...

    2024 arXiv

  30. [38]

    Think when you need: Self-adaptive chain-of-thought learning, 2025

    Junjie Yang, Ke Lin, and Xing Yu. Think when you need: Self-adaptive chain-of-thought learning, 2025. URL https://arxiv.org/abs/2504.03234

    2025 arXiv

  31. [39]

    Tree of thoughts: Deliberate problem solving with large language models

    Shunyu Yao, Dian Yu, Jeffrey Zhao, Izhak Shafran, Tom Griffiths, Yuan Cao, and Karthik Narasimhan. Tree of thoughts: Deliberate problem solving with large language models. Ad- vances in neural information processing systems, 36:11809–11822, 2023

    2023

  32. [40]

    Limo: Less is more for reasoning, 2025

    Yixin Ye, Zhen Huang, Yang Xiao, Ethan Chern, Shijie Xia, and Pengfei Liu. Limo: Less is more for reasoning, 2025. URL https://arxiv.org/abs/2502.03387

    2025 arXiv

  33. [41]

    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

  34. [42]

    Z1: Efficient test-time scaling with code, 2025

    Zhaojian Yu, Yinghao Wu, Yilun Zhao, Arman Cohan, and Xiao-Ping Zhang. Z1: Efficient test-time scaling with code, 2025. URL https://arxiv.org/abs/2504.00810

    2025 arXiv

  35. [43]

    Eval- uating the performance of large language models on gaokao benchmark

    Xiaotian Zhang, Chunyang Li, Yi Zong, Zhengyu Ying, Liang He, and Xipeng Qiu. Eval- uating the performance of large language models on gaokao benchmark. arXiv preprint arXiv:2305.12474, 2023

    2023 arXiv

  36. [44]

    Processbench: Identifying process errors in mathematical reasoning

    Chujie Zheng, Zhenru Zhang, Beichen Zhang, Runji Lin, Keming Lu, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin. Processbench: Identifying process errors in mathematical reasoning. arXiv preprint arXiv:2412.06559, 2024

    2024 arXiv

  37. [45]

    Hmm, I think this is enough to derive the final answer

    Lianmin Zheng, Liangsheng Yin, Zhiqiang Xie, Chuyue Livia Sun, Jeff Huang, Cody Hao Yu, Shiyi Cao, Christos Kozyrakis, Ion Stoica, Joseph E Gonzalez, et al. Sglang: Efficient execution of structured language model programs. Advances in Neural Information Processing Systems, 37...

    2024

  38. [46]

    A ground-truth answer

  39. [47]

    "" <Clean explanation using only the kept chunks. Minimal edits for flow. End with the boxed final answer.>

    A series of reasoning chunks Your task has two parts: STEP 1: Filtering Decide for each chunk whether to KEEP AS IS or REMOVE. KEEP AS IS if the chunk contributes meaningfully: • Narrowing down possibilities • Showing intermediate calculations • Offering partial insight (even ...

  40. [48]

    Recognize the formula for the angle between two lines: \u03b8 = arctan(|(m2 - m1)/(1 + m1*m2)|)

  41. [49]

    Plug in the slopes m1 = 2 and m2 = 1/3

  42. [50]

    Calculate the numerator and denominator

  43. [51]

    Simplify the expression inside arctan

  44. [52]

    Find that it equals arctan(1) = 45\u00b0

  45. [53]

    Confirm with another method, like computing the individual angles and subtracting them All steps check out, so I 'm pretty sure 45 degrees is the correct answer. **Final Answer** The acute angle formed by the lines is \\boxed{45} degrees.</think> To find the acute angle formed...

  46. [54]

    Compute the numerator: \\[ m_2 - m_1 = \\frac{1}{3} - 2 = \\frac{1}{3} - \\frac{6}{3} = -\\frac{5}{3} \\]

  47. [55]

    Compute the denominator: \\[ 1 + m_1 m_2 = 1 + 2 \\cdot \\frac{1}{3} = 1 + \\frac{2}{3} = \\frac{5}{3} \\]

  48. [56]

    Simplify the argument inside the arctangent: \\[ \\left| \\frac{-\\frac{5}{3}}{\\frac{5}{3}} \\right| = \\left| -1 \\right| = 1 \\]

  49. [57]

    Therefore, the angle \\(\\theta\\) is: \\[ \\theta = \\arctan(1) = 45^\\circ \\] To verify, we can also compute the angles each line makes with the x-axis and find the difference. The angles are: - \\(\\alpha_1 = \\arctan(2) \\approx 63.4349^\\circ\\) - \\(\\alpha_2 = \\arctan...

Pith tools

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