Pith. sign in

REVIEW 5 major objections 5 minor 5 cited by

ThinkDial claims the first open-recipe training pipeline that gives one LLM three stable reasoning modes, switched by system prompt alone: High at full capability, Medium halving thinking with <10% loss, Low cutting 75% with <15%.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

An open training recipe that teaches a 32B LLM to reason in three adjustable modes, cutting token use by half or three quarters with small accuracy losses.

T0 review reviewed 2026-08-05 challenge →

load-bearing objection Plausible, honest engineering recipe with a genuinely useful leak-penalty finding, but the headline compression/degradation numbers are never tabulated and the 'open' claim ships no artifacts. the 5 major comments →

arxiv 2508.18773 v1 pith:HFO3MWE7 submitted 2025-08-26 cs.CL

ThinkDial: An Open Recipe for Controlling Reasoning Effort in Large Language Models

Qianyu He , Siyu Yuan , Xuefeng Li , Mingxuan Wang , Jiangjie Chen This is my paper
classification cs.CL
keywords controllable reasoningreasoning effortchain-of-thought compressionbudget-aware reinforcement learningreward shapingreasoning length hackingdiscrete operational modestoken efficiency
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

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's claim is that reasoning effort can be made a user-facing dial: the same model can be instructed, through a system prompt alone, to reason at full depth, at half depth, or at a quarter depth, and it will keep accuracy losses inside promised bounds while cutting thinking tokens by roughly 50% and 75%. This matters because the obvious alternative—letting users set a token budget—requires technical knowledge, while the proprietary gpt-oss-style mode system that offers this control has no open recipe. ThinkDial's recipe has three load-bearing parts: budget-mode supervised fine-tuning that teaches the model to associate each mode label with a reasoning depth; a warm-up reinforcement-learning phase that locks in the performance ceiling before any compression is introduced; and a budget-aware reward-shaping phase with a leak penalty that stops the model from hiding its reasoning in the answer section instead of actually compressing. The authors report that the full system matches the accuracy-versus-token curves of the closed gpt-oss models on math benchmarks, beats naive inference-time truncation by a wide margin, and transfers out of distribution to GPQA.

Core claim

The central claim: controllable reasoning is trainable end-to-end. A model can read a mode label (Low/Medium/High) as an instruction about how deeply to reason, so its thinking-token count tracks the mode while accuracy clears defined thresholds. On math benchmarks, Medium halves thinking tokens with under 10% degradation and Low cuts them to a quarter with under 15%, relative to the post-training peak that High preserves or exceeds. Truncating a peak model's chains at inference collapses accuracy; RL compression alone makes modes interfere and crushes High-mode performance; only the two-phase design plus the leak penalty keeps the three distributions separate. Transfer to out-of-distributio

What carries the argument

Three training stages carry it. (1) Budget-mode SFT: full reasoning chains are truncated to half and quarter of their thinking tokens, patched and re-answered, and bound to distinct system prompts, teaching the mode-label-to-depth mapping before RL. (2) Warm-up RL: decoupled-clip policy-gradient training on the full-data mode fixes the performance ceiling compression must not erode. (3) Budget-aware RL: the same optimizer, reward R = R_task + α(m)·R_length + R_leak — mode-scaled compression, a normalized length reward positive only when the answer is correct, and a ±0.5 penalty on metacognitive words in the answer section, blocking 'Reasoning Length Hacking' (reasoning slipped past ⟨/think⟩)

Load-bearing premise

The load-bearing premise is that the compressed training data teaches genuine compressed reasoning: full chains truncated to 50% and 25% of their thinking tokens, patched with connective text, and re-answered are kept only when they stay logically coherent—and because the source chains and the filtering are in-house and unreleased, that trustworthiness cannot be checked externally. If truncated traces teach the model wrong or incoherent reasoning, the mode control collapses e

What would settle it

Reproduce the pipeline with open components: build the budget-mode SFT set by truncating public long-CoT traces at the same 50%/25% ratios, keep the same SFT and RL schedule, and check whether the three-mode separation and the <10%/<15% degradation bounds survive. If mode control blurs or collapses with public traces, the recipe's success depends on the proprietary filtering rather than the training design. A cheaper check: strip the ⟨think⟩ sections from Medium/Low outputs and have independent judges score the answers alone—if the answer sections carry the reasoning, much of the apparent comp

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • Users can pick a reasoning-effort level per request through a system prompt, without knowing anything about token economics.
  • Open-weight models could reproduce the efficiency-versus-accuracy behavior of closed gpt-oss-style systems, at least on math-heavy workloads.
  • Because High mode holds or exceeds the post-RL peak, adding controllability need not cost peak capability when the warm-up phase is present.
  • The amount of budget-mode SFT data is itself a control: roughly 6K compressed samples help while 12K depress the ceiling and shrink High-mode output, so the recipe includes a data-composition constraint.
  • Mode control carries over to out-of-distribution questions (GPQA), suggesting the learned behavior is a general responsiveness-to-prompt policy rather than memorized benchmark formatting.

Where Pith is reading between the lines

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

  • Editorial: the three fixed modes look like an accident of the reward coefficients (0.0/0.5/1.0) rather than a design bound; the same machinery could plausibly produce more than three effort levels or a continuous slider, since nothing in the reward construction ties α to a specific mode count.
  • Editorial: the compressed SFT traces are in-house and unreleased, so the recipe's portability is untested; rebuilding the same pipeline from public long-CoT data would show whether the mode control belongs to the training design or to the specific filtered traces.
  • Editorial: the leak penalty reveals that part of the measured compression is format discipline rather than reasoning-depth reduction; if the model can move work into the answer section without trigger words, the reported thinking-token savings could overstate true effort saved.
  • Editorial: the GPQA transfer raises a plausible next step—applying the same three-stage recipe to non-math long-CoT data (code, agentic planning) might yield the same mode separation, turning 'controllable reasoning' from a math-benchmark result into a general training option.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

5 major / 5 minor

Summary. This paper presents ThinkDial, an end-to-end training framework for LLM reasoning control with three discrete operational modes (High, Medium, Low) in the style of OpenAI's gpt-oss. The method comprises (i) budget-mode supervised fine-tuning, in which complete reasoning chains are truncated to 50% and 25% of original thinking-token length, given connective text, and answer-regenerated, and (ii) two-phase budget-aware RL built on DAPO, with a warm-up phase to preserve peak performance and a second phase adding mode-dependent length rewards and a 'leak penalty' that discourages reasoning from leaking into answer sections. Experiments are reported on AIME 2024, AIME 2025, GSM8K, and GPQA, using Qwen2.5-Instruct-32B as the base model. The abstract claims 50%/75% token reductions with <10%/<15% performance degradation for Medium/Low modes. The main evidence is a composite ACT score (Table 1) and accuracy-vs-thinking-token plots (Figures 1-5), but per-mode accuracy and token-cost values are not tabulated.

Significance. If the claimed thresholds were verified, this would be a practically valuable open-recipe for controllable reasoning effort, with potential deployment benefits. The paper's contribution would be the integration of mode-conditioned SFT with two-phase RL reward shaping, and the identification of 'reasoning length hacking' as a failure mode. However, the manuscript as submitted does not provide sufficient evidence to verify the central quantitative claims: the headline numbers are not directly reported, no uncertainty estimates are given, and the compression targets are partly set by the SFT truncation ratios. The paper also omits comparisons with existing open controllable-reasoning baselines and does not release code, data, or weights, which weakens the 'open-recipe' positioning. If the missing evidence is supplied in revision, the contribution could be solid.

major comments (5)
  1. [Section 4.1, Eq. (6), Table 1] The abstract's central quantitative claim (50%/75% token reduction and <10%/<15% degradation) is not directly verifiable. Table 1 reports only ACT scores, which combine accuracy retention and compression into a single scalar, and Figures 1-5 plot accuracy against thinking-token cost without numerical per-mode values. The paper never reports Acc_m, Cost_m, Acc_base, Cost_base per benchmark. Without these, the thresholds in the abstract cannot be checked. Please add a table with raw per-mode accuracy, thinking-token count, and base values, along with sampling uncertainty.
  2. [Section 3.1, 3.2.3, Appendix D] The target compression ratios used in the evaluation are the same as the SFT truncation ratios (r_med=0.5, r_low=0.25) and are further reinforced by the length-reward coefficients. Hence the observed ~50%/75% token reductions are partly a consequence of the training objective, not an independent discovery. To support the claim of learned controllability, the paper should report actual per-mode thinking-token counts and show behavior when target ratios are varied or when the model is tested on data not seen in SFT.
  3. [Section 4.1] The reported results have no error bars even though evaluations use stochastic sampling (32/4/8 samples per query). For the abstract's inequalities (<10%, <15% degradation) to be meaningful, confidence intervals or standard errors are needed. As it stands, one cannot tell whether deviations are within the stated thresholds across runs.
  4. [Section 2 and 4.1] The 'first open-recipe' claim is not tested against existing open controllable-reasoning methods cited in the paper itself (e.g., L1 [8], CoT-Valve [12], TokenSkip [11], C3oT [13]). The baseline list only includes internal ablations and proprietary systems. A comparison with these open methods is required to substantiate the novelty and effectiveness claim.
  5. [Appendix B.1, Section 3.1] The 'open-recipe' positioning is not supported by released artifacts. The 6K budget-mode SFT data are derived from in-house, unreleased reasoning data; no code, model weights, or datasets are provided. The construction steps for truncation, connective text, and answer regeneration are described, but without the source data or filtering criteria the recipe cannot be reproduced. Please either release the necessary artifacts or clearly state the accessibility conditions.
minor comments (5)
  1. [Eq. (6)] For High mode beta=1, so ACT_High reduces to 100*Acc_High/Acc_base; naming it a 'trade-off score' is misleading, since compression is ignored. Clarify the metric and the role of C_m for High mode.
  2. [Figure 5 caption] 'Total Tokens include both Thinking Tokens and Summary Tokens' - what are 'Summary Tokens'? The text in Section 4.3 uses 'answer tokens' or 'summary tokens' interchangeably; use consistent terminology.
  3. [Section 4.2] The phrase 'original model baseline' is not defined in Section 4.1; is it the same as the 'peak-performance checkpoint'? Please clarify.
  4. [Appendix B.1] The statement 'incorporate 800 GSM8K samples with empty thinking into the low mode' is unclear: are these also truncated from high-quality chains or a separate construction, and how are they combined with r_low=0.25 samples?
  5. [Abstract, Section 3.1] Minor typos: 'ourThinkDial' and 'The detailed construction details' should be cleaned up.

Circularity Check

1 steps flagged

Compression percentages in the abstract are the training truncation ratios restated; accuracy/OOD claims remain measured.

specific steps
  1. self definitional [Abstract; §3.1; §4.1; §4.2]
    ""Medium mode (50 percent token reduction with <10 percent performance degradation), and Low mode (75 percent token reduction with <15 percent performance degradation)." ... "We set truncation ratios rmed = 0.5 and rlow = 0.25 for Medium and Low mode, respectively" ... "achieving the target compression rates while maintaining specified performance thresholds.""

    The abstract's headline reductions are the training-data truncation ratios. §3.1 constructs Medium/Low samples by 'targeted truncation at approximately rmed and rlow of the original thinking token length', and §4.1 fixes rmed = 0.5 and rlow = 0.25. The paper then presents '50% token reduction' and '75% token reduction' as results, but these are the same preset ratios, and §4.2 explicitly calls them 'target compression rates'. The evaluation reports only the composite ACT score (Eq. 6), which folds compression into the scalar, and never tabulates raw Acc_m or Cost_m per mode, so the claimed reduction percentages cannot be verified independently of the construction choices. The central compression figures therefore reduce to the authors' own design targets rather than being independently mea

full rationale

The core methodological novelty—mode-conditioned SFT, two-phase RL, and leak penalty—is not itself circular: the model is trained with rewards and then evaluated on accuracy and OOD generalization, which are measured rather than fitted. There is no load-bearing self-citation chain; the external references (DAPO, Kimi k1.5, gpt-oss) are used as prior frameworks, not as justifications of ThinkDial's own claims. However, the paper's most prominent quantitative claims—Medium at 50% token reduction and Low at 75%—are exactly the truncation ratios used to build the training data, and the paper openly describes itself as 'achieving the target compression rates while maintaining specified performance thresholds.' Because no raw per-mode token counts or accuracies are reported, only the composite ACT score, those headline percentages are presently indistinguishable from the authors' own settings. The <10%/<15% degradation bounds and the OOD generalization results retain independent empirical content, which keeps the circularity partial rather than total. The in-house, unreleased data also prevents independent replication, but that is a reproducibility gap rather than a circularity step.

Axiom & Free-Parameter Ledger

6 free parameters · 4 axioms · 0 invented entities

The central claim depends on hand-chosen compression targets (r_med, r_low, alpha_m) and on the unverified assumption that truncated, answer-regenerated SFT samples faithfully represent correct low/medium effort reasoning. The data and code are not released, so these assumptions cannot be checked.

free parameters (6)
  • r_med (Medium mode truncation ratio) = 0.5
    Hand-set target for Medium mode compression; directly defines the claimed 50% token reduction.
  • r_low (Low mode truncation ratio) = 0.25
    Hand-set target for Low mode compression; directly defines the claimed 75% token reduction.
  • alpha_med (Medium mode length reward coefficient) = 0.5
    Chosen reward scaling that controls Medium mode compression intensity.
  • alpha_low (Low mode length reward coefficient) = 1.0
    Chosen reward scaling that controls Low mode compression intensity.
  • Leak penalty magnitude = +/-0.5
    Hand-chosen reward constants for detecting reasoning leakage via transition keywords.
  • ACT beta weights = beta(High)=1, beta(Med/Low)=0.5
    Evaluation metric weights chosen by the authors; they shape the reported composite scores.
axioms (4)
  • domain assumption Truncating a correct high-quality reasoning trace to r_med/r_low of its thinking tokens and regenerating the answer yields a correct, coherent compressed reasoning sample.
    Used in Budget-Mode SFT data construction (Section 3.1, Appendix B.1); if compressed traces teach wrong or incoherent low/medium reasoning, mode control fails.
  • ad hoc to paper Exact answer matching is a sufficient task reward, and the fixed transition-keyword list detects all meaningful reasoning leakage into answer sections.
    Assumed in Equations 3-5 and Section 3.2.3; leakage expressed in other phrasing would evade the Leak Penalty.
  • domain assumption The unreleased in-house 20K problem set plus 12K light-R1 traces is representative enough to train peak reasoning that transfers to AIME, GSM8K, and GPQA.
    Section 4.1 and Appendix B.1; all results depend on this private training data.
  • domain assumption Mode-specific system prompts elicit stable, distinct reasoning distributions after SFT/RL, without needing explicit token budgets.
    Core controllability premise in Section 3.3 and Appendix A; if prompts do not generalize, the discrete-mode interface fails.

reviewed 2026-08-05 · how reviews work

0 comments
Cite this review

Pith. "Pith review of ThinkDial: An Open Recipe for Controlling Reasoning Effort in Large Language Models." pith.science (2026). https://pith.science/paper/HFO3MWE7

@misc{pith2026250818773,
  author       = {Pith},
  title        = {Pith review of: ThinkDial: An Open Recipe for Controlling Reasoning Effort in Large Language Models},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HFO3MWE7}},
  note         = {Machine review of arXiv:2508.18773}
}
Share X Bluesky LinkedIn Reddit HN
read the original abstract

Large language models (LLMs) with chain-of-thought reasoning have demonstrated remarkable problem-solving capabilities, but controlling their computational effort remains a significant challenge for practical deployment. Recent proprietary systems like OpenAI's gpt-oss series have introduced discrete operational modes for intuitive reasoning control, but the open-source community has largely failed to achieve such capabilities. In this paper, we introduce ThinkDial, the first open-recipe end-to-end framework that successfully implements gpt-oss-style controllable reasoning through discrete operational modes. Our system enables seamless switching between three distinct reasoning regimes: High mode (full reasoning capability), Medium mode (50 percent token reduction with <10 percent performance degradation), and Low mode (75 percent token reduction with <15 percent performance degradation). We achieve this through an end-to-end training paradigm that integrates budget-mode control throughout the entire pipeline: budget-mode supervised fine-tuning that embeds controllable reasoning capabilities directly into the learning process, and two-phase budget-aware reinforcement learning with adaptive reward shaping. Extensive experiments demonstrate that ThinkDial achieves target compression-performance trade-offs with clear response length reductions while maintaining performance thresholds. The framework also exhibits strong generalization capabilities on out-of-distribution tasks.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 5 Pith papers

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

  1. CLORE: Content-Level Optimization for Reasoning Efficiency

    cs.AI 2026-05 unverdicted novelty 6.0

    CLORE augments correct on-policy rollouts by deleting repetitive and irrelevant segments then optimizes with auxiliary DPO to improve accuracy-efficiency trade-off on math benchmarks.

  2. CODA: Difficulty-Aware Compute Allocation for Adaptive Reasoning

    cs.CL 2026-03 unverdicted novelty 6.0

    CODA uses rollout-based difficulty signals to drive two gates that penalize verbosity on easy instances and promote deliberation on hard ones, cutting token use over 60% on simple tasks while maintaining accuracy.

  3. SLAT: Segment-Level Adaptive Trimming for Efficient CoT Reasoning

    cs.AI 2026-05 unverdicted novelty 5.0

    SLAT applies segment-level adaptive trimming in RL to reduce CoT reasoning length by 50% while maintaining competitive accuracy on benchmarks.

  4. SuCo: Sufficiency-guided Continuous Adaptive Reasoning

    cs.CL 2026-06 unverdicted novelty 4.0

    SuCo defines minimal sufficient CoT and applies a two-stage fine-tuning plus RL framework to enable continuous adaptive reasoning control, claiming gains in both accuracy and token efficiency on math, code, and science tasks.

  5. A Survey of Reinforcement Learning for Large Reasoning Models

    cs.CL 2025-09 accept novelty 3.0

    A survey compiling RL methods, challenges, data resources, and applications for enhancing reasoning in large language models and large reasoning models since DeepSeek-R1.

Reference graph

Works this paper leans on

30 extracted references · 9 canonical work pages · cited by 5 Pith papers

  1. [1]

    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, Shaochen Zhong, Hanjie Chen, et al. Stop overthinking: A survey on efficient reasoning for large language models. arXiv preprint arXiv:2503.16419, 2025

    Pith/arXiv arXiv 2025

  2. [2]

    Efficient reasoning models: A survey.arXiv preprint arXiv:2504.10903, 2025

    Sicheng Feng, Gongfan Fang, Xinyin Ma, and Xinchao Wang. Efficient reasoning models: A survey.arXiv preprint arXiv:2504.10903, 2025

    arXiv 2025

  3. [3]

    gpt-oss-120b & gpt-oss-20b model card, 2025

    OpenAI. gpt-oss-120b & gpt-oss-20b model card, 2025

    2025

  4. [4]

    Building with extended thinking, 2025

    Anthropic. Building with extended thinking, 2025

    work page 2025

  5. [5]

    Adacot: Pareto-optimal adaptive chain-of-thought triggering via reinforcement learning.arXiv preprint arXiv:2505.11896, 2025

    Chenwei Lou, Zewei Sun, Xinnian Liang, Meng Qu, Wei Shen, Wenqi Wang, Yuntao Li, Qingping Yang, and Shuangzhi Wu. Adacot: Pareto-optimal adaptive chain-of-thought triggering via reinforcement learning.arXiv preprint arXiv:2505.11896, 2025

    Pith/arXiv arXiv 2025

  6. [6]

    s1: Simple test-time scaling

    Niklas Muennighoff, Zitong Yang, Weijia Shi, Xiang Lisa Li, Li Fei-Fei, Hannaneh Hajishirzi, Luke Zettlemoyer, Percy Liang, Emmanuel Candès, and Tatsunori Hashimoto. s1: Simple test-time scaling. arXiv preprint arXiv:2501.19393, 2025

    Pith/arXiv arXiv 2025

  7. [7]

    An empirical study of llm reasoning ability under strict output length constraint.arXiv preprint arXiv:2504.14350, 2025

    Yi Sun, Han Wang, Jiaqiang Li, Jiacheng Liu, Xiangyu Li, Hao Wen, Yizhen Yuan, Huiwen Zheng, Yan Liang, Yuanchun Li, et al. An empirical study of llm reasoning ability under strict output length constraint.arXiv preprint arXiv:2504.14350, 2025

    Pith/arXiv arXiv 2025

  8. [8]

    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

    Pith/arXiv arXiv 2025

  9. [9]

    Adaptthink: Reasoning models can learn when to think

    Jiajie Zhang, Nianyi Lin, Lei Hou, Ling Feng, and Juanzi Li. Adaptthink: Reasoning models can learn when to think. arXiv preprint arXiv:2505.13417, 2025

    Pith/arXiv arXiv 2025

  10. [10]

    Qwen technical report.arXiv preprint arXiv:2309.16609, 2023

    Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, et al. Qwen technical report.arXiv preprint arXiv:2309.16609, 2023

    Pith/arXiv arXiv 2023

  11. [11]

    Tokenskip: Controllable chain-of-thought compression in llms.arXiv preprint arXiv:2502.12067, 2025

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

    arXiv 2025

  12. [12]

    Cot-valve: Length-compressible chain-of-thought tuning.arXiv preprint arXiv:2502.09601, 2025

    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

    Pith/arXiv arXiv 2025

  13. [13]

    C3oT: Generating Shorter Chain-of-Thought Without Compromising Effectiveness

    Yu Kang, Xianghui Sun, Liangyu Chen, and Wei Zou. C3oT: Generating Shorter Chain-of-Thought Without Compromising Effectiveness. Proceedings of the AAAI Conference on Artificial Intelligence, 39(23):24312–24320, 2025

    work page 2025

  14. [14]

    Lightthinker: Thinking step-by-step compression.ArXiv, abs/2502.15589, 2025

    Jintian Zhang, Yuqi Zhu, Mengshu Sun, Yujie Luo, Shuofei Qiao, Lun Du, Da Zheng, Huajun Chen, and Ningyu Zhang. Lightthinker: Thinking step-by-step compression.ArXiv, abs/2502.15589, 2025

    arXiv 2025

  15. [15]

    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, Zhaoxiang Liu, and Shiguo Lian. Dast: Difficulty-adaptive slow-thinking for large reasoning models. arXiv preprint arXiv:2503.04472, 2025

    arXiv 2025

  16. [16]

    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

    Pith/arXiv arXiv 2025

  17. [17]

    O1-pruner: Length-harmonizing fine-tuning for o1-like reasoning pruning.arXiv preprint arXiv:2501.12570, 2025

    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

    Pith/arXiv arXiv 2025

  18. [18]

    Optimizing test-time compute via meta reinforcement fine-tuning.arXiv preprint arXiv:2503.07572, 2025

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

    Pith/arXiv arXiv 2025

  19. [19]

    S-grpo: Early exit via reinforcement learning in reasoning models

    Muzhi Dai, Chenxu Yang, and Qingyi Si. S-grpo: Early exit via reinforcement learning in reasoning models. arXiv preprint arXiv:2505.07686, 2025. 11

    Pith/arXiv arXiv 2025

  20. [20]

    Retro-search: Exploring untaken paths for deeper and efficient reasoning.arXiv preprint arXiv:2504.04383, 2025

    Ximing Lu, Seungju Han, David Acuna, Hyunwoo Kim, Jaehun Jung, Shrimai Prabhumoye, Niklas Muennighoff, Mostofa Patwary, Mohammad Shoeybi, Bryan Catanzaro, et al. Retro-search: Exploring untaken paths for deeper and efficient reasoning.arXiv preprint arXiv:2504.04383, 2025

    Pith/arXiv arXiv 2025

  21. [21]

    Dapo: An open-source llm reinforcement learning system at scale

    Qiying Yu, Zheng Zhang, Ruofei Zhu, Yufeng Yuan, Xiaochen Zuo, Yu Yue, Weinan Dai, Tiantian Fan, Gaohong Liu, Lingjun Liu, et al. Dapo: An open-source llm reinforcement learning system at scale. arXiv preprint arXiv:2503.14476, 2025

    Pith/arXiv arXiv 2025

  22. [22]

    Towards thinking-optimal scaling of test-time compute for llm reasoning.arXiv preprint arXiv:2502.18080, 2025

    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

    arXiv 2025

  23. [23]

    Light-r1: Curriculum sft, dpo and rl for long cot from scratch and beyond.arXiv preprint arXiv:2503.10460, 2025

    Liang Wen, Yunke Cai, Fenrui Xiao, Xin He, Qi An, Zhenyu Duan, Yimin Du, Junchen Liu, Lifu Tang, Xiaowei Lv, et al. Light-r1: Curriculum sft, dpo and rl for long cot from scratch and beyond.arXiv preprint arXiv:2503.10460, 2025. 12 /* Low Mode */ You have extremely limited time to think and respond to the users query. Every additional second of processing...

    Pith/arXiv arXiv 2025

  24. [24]

    This power is also equal to|BO2|2 − r2 2

    Power of a Point: For pointB on the first circle, the power with respect to the second circle is given by BA · BD = 5 · 9 = 45. This power is also equal to|BO2|2 − r2 2

    work page

  25. [25]

    Common Tangent: The length of the common tangentBC can be related to the radii and the distance between centers using the Pythagorean theorem for the external tangent:BC 2 = (O1O2)2 − (r1 − r2)2

    work page

  26. [26]

    Calculations: • Using the power of pointB, we findr1 = 5 and solve forr2 using the lengthAD = 4

    Coordinate Geometry: Placing A at the origin,O1 at (−r1, 0), and O2 at (r2, 0), we use the coordinates of B and C on the tangent line to relate the radii and solve forr1 and r2. Calculations: • Using the power of pointB, we findr1 = 5 and solve forr2 using the lengthAD = 4. • The common tangent lengthBC is found using the radii and the distance between ce...

    work page

  27. [27]

    Here,|BA| = 5 and |AD| = 4, so |BD| = |BA| + |AD| = 9

    Power of Point B: The power of pointB with respect to the circle centered atO2 is equal to the product of the lengths of the segments fromB to the points of intersection with the circle. Here,|BA| = 5 and |AD| = 4, so |BD| = |BA| + |AD| = 9. Thus, the power ofB is |BA| · |BD| = 5 · 9 = 45

    work page

  28. [28]

    Since BC is a common tangent,O1B ⊥ BC and O2C ⊥ BC, so O1B ∥ O2C

    Distance from B to O2: Let r1 and r2 be the radii of the circles centered atO1 and O2, respectively. Since BC is a common tangent,O1B ⊥ BC and O2C ⊥ BC, so O1B ∥ O2C. The distance betweenO1 and O2 is r1 + r2

    work page

  29. [29]

    Using Coordinates and Similar Triangles : By setting up coordinates and using the fact thatBA intersects the second circle atD, we find that the power ofB gives |BO2|2 − r2 2 = 45

    work page

  30. [30]

    However, using the power of pointB and the fact thatBC is a common tangent, we find that |CD | = 6

    Length of CD: Since CD is a tangent segment fromC to D on the circle, and using the properties of the tangent and the circle, we find thatCD can be determined by the power of pointC or by recognizing similar triangles. However, using the power of pointB and the fact thatBC is a common tangent, we find that |CD | = 6. Answer: 6 Table 6 A case study of supe...

    work page

This paper was first reviewed by deepseek-v4-flash on August 5, 2026.