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arxiv: 2509.21743 · v2 · submitted 2025-09-26 · 💻 cs.AI · cs.LG

Retrieval-of-Thought: Efficient Reasoning via Reusing Thoughts

Ammar Ahmed , Azal Ahmad Khan , Ayaan Ahmad , Sheng Di , Zirui Liu , Ali Anwar This is my paper

Pith reviewed 2026-05-18 13:38 UTC · model grok-4.3

classification 💻 cs.AI cs.LG
keywords Retrieval-of-Thoughtthought graphefficient reasoninginference efficiencytoken reductionreasoning benchmarkslarge reasoning models
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The pith

Retrieval-of-Thought reuses past reasoning steps from a graph to direct new solutions, reducing tokens by up to 40 percent and latency by 82 percent with no accuracy loss.

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

The paper tries to establish that reasoning models do not need to generate every step of a solution from scratch for each new question. Instead, they can pull useful pieces from previous solutions that have been stored and connected in a graph structure. A sympathetic reader would care if this holds because it directly attacks the high cost and slow speed that come with long reasoning traces in large models. By retrieving relevant thought nodes and traversing them to build a custom guide, the model gets a head start on the problem and produces shorter outputs. The evaluations across benchmarks and models confirm that accuracy stays intact while efficiency improves markedly.

Core claim

Retrieval-of-Thought builds a thought graph from prior reasoning traces using sequential and semantic edges. At inference time relevant nodes are retrieved and a reward-guided traversal assembles them into a problem-specific template. This template then guides the model's generation process, which reduces redundant exploration in the reasoning trace. As a result output tokens decrease substantially while accuracy on reasoning tasks is maintained.

What carries the argument

The thought graph, which decomposes prior reasoning into nodes connected by sequential and semantic edges to support fast retrieval and flexible recombination into new templates.

Load-bearing premise

The load-bearing premise is that past reasoning traces can be broken into parts that connect meaningfully enough to be recombined accurately for entirely new problems.

What would settle it

Observing whether accuracy falls or token savings disappear when RoT is applied to problems whose required reasoning steps have no close match in the existing thought graph.

Figures

Figures reproduced from arXiv: 2509.21743 by Ali Anwar, Ammar Ahmed, Ayaan Ahmad, Azal Ahmad Khan, Sheng Di, Zirui Liu.

Figure 1
Figure 1. Figure 1: The figure contrasts Chain-of-Thought (CoT) inference in LRMs with our Retrieval￾of-Thought (RoT) approach. In CoT (top), models sequentially explore multiple wrong paths, causing inefficiency and high token usage. RoT (bottom) builds on a structured thought graph where reasoning steps are stored as nodes. First, RoT retrieves relevant nodes and performs reward-guided traversal to assemble a problem-specif… view at source ↗
Figure 2
Figure 2. Figure 2: Key observations motivating the RoT framework. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Average accuracy versus output tokens across Qwen3 models (1.7B, 4B, 8B). Each panel [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average per-sample inference cost (USD) across [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Average end-to-end latency (seconds) per sample [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Average path switches across Qwen3 models comparing CoT with RoT+TI. RoT+TI consistently reduces unnecessary path exploration, achieving up to 81.8% fewer switches. How does RoT reduce unnecessary exploration during reasoning? We measure this effect by analyzing path switching, defined as the number of times a model aban￾dons one reasoning trajectory and begins another within a single response. In practice… view at source ↗
Figure 7
Figure 7. Figure 7: Semantic similarity of steps to solve reasoning questions across datasets. [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Average number of semantically similar nodes for different thresholds. Semantic Edge Threshold. We sweep the seman￾tic threshold τ that determines which semantic edges are retained in the thought graph. The mean seman￾tic degree (y-axis) vs. τ (x-axis) exhibits a clear knee ( [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: First-step selection trade-off on the Thought Graph. [PITH_FULL_IMAGE:figures/full_fig_p016_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Template scalability analysis of RoT+TI. Accuracy is reported using a smaller thought [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
read the original abstract

Large reasoning models improve accuracy by producing long reasoning traces, but this inflates latency and cost, motivating inference-time efficiency. We propose Retrieval-of-Thought (RoT), which reuses prior reasoning as composable ``thought" steps to guide new problems. RoT organizes steps into a thought graph with sequential and semantic edges to enable fast retrieval and flexible recombination. At inference, RoT retrieves query-relevant nodes and applies reward-guided traversal to assemble a problem-specific template that guides generation. This dynamic template reuse reduces redundant exploration and, therefore, reduces output tokens while preserving accuracy. We evaluate RoT on reasoning benchmarks with multiple models, measuring accuracy, token usage, latency, and memory overhead. Findings show small prompt growth but substantial efficiency gains, with RoT reducing output tokens by up to 40%, inference latency by 82%, and cost by 59% while maintaining accuracy. RoT establishes a scalable paradigm for efficient LRM reasoning via dynamic template construction through retrieval.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper proposes Retrieval-of-Thought (RoT), which organizes prior reasoning traces into a thought graph with sequential and semantic edges. At inference, relevant nodes are retrieved and a reward-guided traversal assembles a problem-specific template to guide generation, reducing redundant steps. The central claim is that this yields up to 40% fewer output tokens, 82% lower inference latency, and 59% lower cost while preserving accuracy on reasoning benchmarks across multiple models.

Significance. If the efficiency gains are robust, RoT offers a practical engineering advance for lowering inference costs of large reasoning models through dynamic reuse of prior thoughts rather than full regeneration. The empirical focus on token, latency, and cost metrics with multiple models provides a direct, falsifiable test of the approach.

major comments (2)
  1. [Abstract] Abstract: the headline efficiency claims (40% token reduction, 82% latency reduction, 59% cost reduction while maintaining accuracy) are presented without benchmark names, number of runs, statistical tests, error bars, or explicit controls for prompt-length effects from retrieved context. These omissions make it impossible to verify that the reported gains are not confounded by problem selection or baseline prompt overhead.
  2. [Abstract (method and findings paragraphs)] The accuracy-preservation claim rests on the assumption that retrieved thought nodes recombine correctly for unseen problems via sequential/semantic edges and reward-guided traversal. However, aggregate accuracy numbers alone do not isolate cases where recombination succeeds from those where it silently degrades quality or triggers fallback to full generation; no per-problem similarity analysis or error-injection ablation is described.
minor comments (2)
  1. [Abstract] The abstract states 'small prompt growth' but does not quantify the added token overhead from retrieval or graph construction; a table or figure reporting average prompt length with/without RoT would clarify the net efficiency.
  2. [Abstract] Memory overhead is mentioned as part of the evaluation but receives no numerical results in the summary findings; adding a short table or sentence with peak memory figures would strengthen the practical assessment.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and insightful comments. We address each major comment below and indicate the revisions planned for the updated manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the headline efficiency claims (40% token reduction, 82% latency reduction, 59% cost reduction while maintaining accuracy) are presented without benchmark names, number of runs, statistical tests, error bars, or explicit controls for prompt-length effects from retrieved context. These omissions make it impossible to verify that the reported gains are not confounded by problem selection or baseline prompt overhead.

    Authors: We agree that the abstract would benefit from greater specificity on the headline claims. In the revised version we will name the primary benchmarks (GSM8K, MATH, and others), state that results are averaged over multiple runs with standard deviations, and reference the statistical tests and error bars already reported in Section 4. We will also add a short clause noting that prompt-length effects are controlled by comparing against a no-retrieval baseline that uses equivalent formatting and by separately reporting the incremental token cost of the retrieved context. Full per-benchmark tables, run counts, and controls remain in the experimental section. revision: yes

  2. Referee: [Abstract (method and findings paragraphs)] The accuracy-preservation claim rests on the assumption that retrieved thought nodes recombine correctly for unseen problems via sequential/semantic edges and reward-guided traversal. However, aggregate accuracy numbers alone do not isolate cases where recombination succeeds from those where it silently degrades quality or triggers fallback to full generation; no per-problem similarity analysis or error-injection ablation is described.

    Authors: We acknowledge that aggregate accuracy alone leaves open questions about recombination robustness. We will add a new subsection in the experiments that reports per-problem similarity scores between queries and retrieved nodes, together with an error-injection ablation that perturbs the thought graph and measures resulting fallback frequency and accuracy change. These additions will quantify when the reward-guided traversal succeeds versus when it triggers full regeneration. revision: yes

Circularity Check

0 steps flagged

No circularity; empirical engineering method with independent evaluation

full rationale

The paper presents Retrieval-of-Thought as a practical system that builds a thought graph from prior traces, retrieves nodes via sequential/semantic edges, and uses reward-guided traversal to form templates for generation. No equations, fitted parameters, or predictions are defined in the provided text that reduce by construction to the inputs (e.g., no self-definitional reuse of accuracy metrics or token counts). Efficiency gains are reported from direct benchmark measurements rather than tautological derivations. No self-citation chains or uniqueness theorems are invoked as load-bearing premises. The approach is self-contained as an algorithmic proposal tested empirically on external reasoning benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The approach rests on the premise that reasoning traces are decomposable into reusable units whose connections support accurate recombination; no free parameters or invented entities beyond the graph structure itself are described in the abstract.

axioms (1)
  • domain assumption Reasoning traces from prior problems can be decomposed into composable thought steps connected by sequential and semantic relations that transfer usefully to new problems.
    This premise underpins the construction of the thought graph and the retrieval/recombination process.
invented entities (1)
  • thought graph no independent evidence
    purpose: Organize prior reasoning steps for fast retrieval and flexible recombination via sequential and semantic edges.
    Introduced as the central data structure enabling the RoT method.

pith-pipeline@v0.9.0 · 5707 in / 1254 out tokens · 36018 ms · 2026-05-18T13:38:28.131996+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

33 extracted references · 33 canonical work pages · 8 internal anchors

  1. [1]

    Reflect, retry, reward: Self-improving llms via reinforcement learning.CoRR, abs/2505.24726, 2025

    Shelly Bensal, Umar Jamil, Christopher Bryant, Melisa Russak, Kiran Kamble, Dmytro Mo- zolevskyi, Muayad Ali, and Waseem AlShikh. Reflect, retry, reward: Self-improving llms via reinforcement learning.arXiv preprint arXiv:2505.24726,

    work page arXiv

  2. [2]

    Aspd: Unlocking adaptive serial-parallel decoding by exploring intrinsic parallelism in llms

    Keyu Chen, Zhifeng Shen, Daohai Yu, Haoqian Wu, Wei Wen, Jianfeng He, Ruizhi Qiao, and Xing Sun. Aspd: Unlocking adaptive serial-parallel decoding by exploring intrinsic parallelism in llms. arXiv preprint arXiv:2508.08895,

    work page arXiv

  3. [3]

    Accelerating llm reasoning via early rejection with partial reward modeling.arXiv preprint arXiv:2508.01969,

    Seyyed Saeid Cheshmi, Azal Ahmad Khan, Xinran Wang, Zirui Liu, and Ali Anwar. Accelerating llm reasoning via early rejection with partial reward modeling.arXiv preprint arXiv:2508.01969,

    work page arXiv

  4. [4]

    Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities

    Gheorghe Comanici, Eric Bieber, Mike Schaekermann, Ice Pasupat, Noveen Sachdeva, Inderjit Dhillon, Marcel Blistein, Ori Ram, Dan Zhang, Evan Rosen, et al. Gemini 2.5: Pushing the frontier with advanced reasoning, multimodality, long context, and next generation agentic capa- bilities.arXiv preprint arXiv:2507.06261,

    work page internal anchor Pith review Pith/arXiv arXiv

  5. [5]

    Thinkless: Llm learns when to think.arXiv preprint arXiv:2505.13379,

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

    work page arXiv

  6. [6]

    Efficient reasoning models: A survey

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

    work page arXiv

  7. [7]

    Scaling reasoning, losing control: Evaluating instruction following in large reasoning models.arXiv preprint arXiv:2505.14810,

    Tingchen Fu, Jiawei Gu, Yafu Li, Xiaoye Qu, and Yu Cheng. Scaling reasoning, losing control: Evaluating instruction following in large reasoning models.arXiv preprint arXiv:2505.14810,

    work page arXiv

  8. [8]

    Jina embeddings 2: 8192-token general-purpose text embeddings for long documents.arXiv preprint arXiv:2310.19923,

    Michael Günther, Jackmin Ong, Isabelle Mohr, Alaeddine Abdessalem, Tanguy Abel, Moham- mad Kalim Akram, Susana Guzman, Georgios Mastrapas, Saba Sturua, Bo Wang, et al. Jina embeddings 2: 8192-token general-purpose text embeddings for long documents.arXiv preprint arXiv:2310.19923,

    work page arXiv

  9. [9]

    DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning

    10 Retrieval-of-Thought: Efficient Reasoning via Reusing Thoughts 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,

    work page internal anchor Pith review Pith/arXiv arXiv

  10. [10]

    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,

    work page arXiv

  11. [11]

    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,

    work page internal anchor Pith review Pith/arXiv arXiv

  12. [12]

    Flashthink: An early exit method for efficient reasoning.arXiv preprint arXiv:2505.13949,

    Guochao Jiang, Guofeng Quan, Zepeng Ding, Ziqin Luo, Dixuan Wang, and Zheng Hu. Flashthink: An early exit method for efficient reasoning.arXiv preprint arXiv:2505.13949,

    work page arXiv

  13. [13]

    Enhancing llm reasoning with reward-guided tree search.arXiv preprint arXiv:2411.11694, 2024a

    Jinhao Jiang, Zhipeng Chen, Yingqian Min, Jie Chen, Xiaoxue Cheng, Jiapeng Wang, Yiru Tang, Haoxiang Sun, Jia Deng, Wayne Xin Zhao, et al. Enhancing llm reasoning with reward-guided tree search.arXiv preprint arXiv:2411.11694, 2024a. Yikun Jiang, Huanyu Wang, Lei Xie, Hanbin Zhao, Hui Qian, John Lui, et al. D-llm: A token adaptive computing resource alloc...

    work page arXiv

  14. [14]

    When thinking fails: The pitfalls of reasoning for instruction- following in llms.arXiv preprint arXiv:2505.11423,

    Xiaomin Li, Zhou Yu, Zhiwei Zhang, Xupeng Chen, Ziji Zhang, Yingying Zhuang, Narayanan Sadagopan, and Anurag Beniwal. When thinking fails: The pitfalls of reasoning for instruction- following in llms.arXiv preprint arXiv:2505.11423, 2025a. Zhong-Zhi Li, Duzhen Zhang, Ming-Liang Zhang, Jiaxin Zhang, Zengyan Liu, Yuxuan Yao, Haotian Xu, Junhao Zheng, Pei-Ji...

    work page arXiv 2025

  15. [15]

    Pre- dictive scaling laws for efficient grpo training of large reasoning models.arXiv preprint arXiv:2507.18014,

    Datta Nimmaturi, Vaishnavi Bhargava, Rajat Ghosh, Johnu George, and Debojyoti Dutta. Pre- dictive scaling laws for efficient grpo training of large reasoning models.arXiv preprint arXiv:2507.18014,

    work page arXiv

  16. [16]

    Learning adaptive parallel reasoning with language models.arXiv preprint arXiv:2504.15466, 2025

    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,

    work page arXiv

  17. [17]

    Evidence to generate (e2g): A single-agent two-step prompting for context grounded and retrieval augmented reasoning.arXiv preprint arXiv:2401.05787,

    Md Rizwan Parvez. Evidence to generate (e2g): A single-agent two-step prompting for context grounded and retrieval augmented reasoning.arXiv preprint arXiv:2401.05787,

    work page arXiv

  18. [18]

    Mathbert: A pre-trained model for mathematical formula understanding.arXiv preprint arXiv:2105.00377,

    Shuai Peng, Ke Yuan, Liangcai Gao, and Zhi Tang. Mathbert: A pre-trained model for mathematical formula understanding.arXiv preprint arXiv:2105.00377,

    work page arXiv

  19. [19]

    Measuring and improving bert’s math- ematical abilities by predicting the order of reasoning.arXiv preprint arXiv:2106.03921,

    Piotr Pi˛ ekos, Henryk Michalewski, and Mateusz Malinowski. Measuring and improving bert’s math- ematical abilities by predicting the order of reasoning.arXiv preprint arXiv:2106.03921,

    work page arXiv

  20. [20]

    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, Yang Wu, et al. Deepseekmath: Pushing the limits of mathemati- cal reasoning in open language models.arXiv preprint arXiv:2402.03300,

    work page internal anchor Pith review Pith/arXiv arXiv

  21. [21]

    Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters

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

    work page internal anchor Pith review Pith/arXiv arXiv

  22. [22]

    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,

    work page internal anchor Pith review Pith/arXiv arXiv

  23. [23]

    Value-guided search for efficient chain-of-thought reasoning.arXiv preprint arXiv:2505.17373,

    Kaiwen Wang, Jin Peng Zhou, Jonathan Chang, Zhaolin Gao, Nathan Kallus, Kianté Brantley, and Wen Sun. Value-guided search for efficient chain-of-thought reasoning.arXiv preprint arXiv:2505.17373,

    work page arXiv

  24. [24]

    Self-Consistency Improves Chain of Thought Reasoning in Language Models

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

    work page internal anchor Pith review Pith/arXiv arXiv

  25. [25]

    Rat: Retrieval augmented thoughts elicit context-aware reasoning in long-horizon generation

    Zihao Wang, Anji Liu, Haowei Lin, Jiaqi Li, Xiaojian Ma, and Yitao Liang. Rat: Retrieval augmented thoughts elicit context-aware reasoning in long-horizon generation.arXiv preprint arXiv:2403.05313,

    work page arXiv

  26. [26]

    Wang, and Prateek Mittal

    Tong Wu, Chong Xiang, Jiachen T Wang, G Edward Suh, and Prateek Mittal. Effectively controlling reasoning models through thinking intervention.arXiv preprint arXiv:2503.24370,

    work page arXiv

  27. [27]

    Monte carlo tree search boosts reasoning via iterative preference learning,

    Yuxi Xie, Anirudh Goyal, Wenyue Zheng, Min-Yen Kan, Timothy P Lillicrap, Kenji Kawaguchi, and Michael Shieh. Monte carlo tree search boosts reasoning via iterative preference learning. arXiv preprint arXiv:2405.00451,

    work page arXiv

  28. [28]

    Towards Large Reasoning Models: A Survey of Reinforced Reasoning with Large Language Models

    Fengli Xu, Qianyue Hao, Zefang Zong, Jingwei Wang, Yunke Zhang, Jingyi Wang, Xiaochong Lan, Jiahui Gong, Tianjian Ouyang, Fanjin Meng, et al. Towards large reasoning models: A survey of reinforced reasoning with large language models.arXiv preprint arXiv:2501.09686, 2025a. Zenan Xu, Zexuan Qiu, Guanhua Huang, Kun Li, Siheng Li, Chenchen Zhang, Kejiao Li, ...

    work page internal anchor Pith review Pith/arXiv arXiv

  29. [29]

    Accurate and diverse llm mathematical reasoning via automated prm-guided gflownets.arXiv preprint arXiv:2504.19981,

    Adam Younsi, Abdalgader Abubaker, Mohamed El Amine Seddik, Hakim Hacid, and Salem Lahlou. Accurate and diverse llm mathematical reasoning via automated prm-guided gflownets.arXiv preprint arXiv:2504.19981,

    work page arXiv

  30. [30]

    arXiv preprint arXiv:2505.24863 , year=

    Junyu Zhang, Runpei Dong, Han Wang, Xuying Ning, Haoran Geng, Peihao Li, Xialin He, Yutong Bai, Jitendra Malik, Saurabh Gupta, et al. Alphaone: Reasoning models thinking slow and fast at test time.arXiv preprint arXiv:2505.24863, 2025a. Zhenru Zhang, Chujie Zheng, Yangzhen Wu, Beichen Zhang, Runji Lin, Bowen Yu, Dayiheng Liu, Jingren Zhou, and Junyang Lin...

    work page arXiv 2024

  31. [31]

    OOT” stands for “Out of Tokens,

    0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0Average Query Similarity Figure 9: First-step selection trade-off on the Thought Graph.LeftProbability that the chosen start is a at a step-0 node.RightAverage query–node similarity of the chosen start. Qwen3-1.7B Qwen3-4B Qwen3-8B 0.0 10 20 30 40 50 60Average Accuracy (%) RoT + TI (w/ 0.9k templates) RoT + T...

    work page 2025

  32. [32]

    Out Tokens: 6746 Input:"You are given a template to solve the problem

    Now substitute into the equations: First equation becomes: x·a= 10⇒a= 10 x Second equation becomes: 4y· 1 a = 10⇒ 4y a = 10 Substitutea= 10 x into the second equation: 4y 10 x = 10⇒ 4xy 10 = 10 Multiply both sides by 10: 4xy= 100⇒xy= 25 — Final Answer: 25 21 Retrieval-of-Thought: Efficient Reasoning via Reusing Thoughts RoT: Input and Output for AIME 2024...

    work page 2024

  33. [33]

    Let me take the first equation

    So now we have two equations:1)y x =x 10 2)x 4y =y 10 So maybe we can manipulate these equations. Let me take the first equation.......... I should have noticed that earlier instead of going through all the logarithmic manipulations and numerical solving. **Final Answer**25 </think> To solve the problem: We are given the following equations involving loga...

    work page 2024