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REVIEW 4 major objections 4 minor 5 cited by

Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective

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

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Pith's one-line read RL for LLM reasoning is domain-dependent: heavily pretrained domains benefit from cross-domain training, while lightly pretrained domains need in-domain data.

desk verdict Useful multi-domain RL dataset, but the 'skill acquisition' headline is confounded by unmeasured pretraining exposure and task difficulty. read the letter →

arxiv 2506.14965 v1 pith:SK4MJSGS submitted 2025-06-17 cs.LG cs.AIcs.CL

Zhoujun Cheng , Shibo Hao , Tianyang Liu , Fan Zhou , Yutao Xie , Feng Yao , Yuexin Bian , Yonghao Zhuang
show 16 more authors
Nilabjo Dey Yuheng Zha Yi Gu Kun Zhou Yuqi Wang Yuan Li Richard Fan Jianshu She Chengqian Gao Abulhair Saparov Haonan Li Taylor W. Killian Mikhail Yurochkin Zhengzhong Liu Eric P. Xing Zhiting Hu
This is my paper
classification cs.LGcs.AIcs.CL
keywords reinforcementlearningLLMreasoningcross-domaintransferverifiablerewardsGURUdatasetPass@kelicitationvsskillacquisitionmulti-domainRL
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

Reinforcement learning (RL) is usually studied on math and code, and a growing consensus says RL mostly elicits reasoning the pretrained model already has. This paper argues that conclusion is domain-dependent. It builds GURU, a 92K-example verifiable RL corpus spanning math, code, science, logic, simulation, and tabular reasoning, and finds that math, code, and science improve even when RL is trained on other domains, while logic, simulation, and tabular reasoning only improve with in-domain training. The paper reads the second pattern as evidence that RL can learn genuinely new skills in domains the base model was not heavily pretrained on. If the finding holds, multi-domain RL training is a practical route to general-purpose reasoning models, not just sharper math tutors.

What carries the argument

The load-bearing artifact is GURU, a 92K-example corpus with a domain-specific binary reward for every sample: rule-based matching for math, logic, simulation, and tabular; execution against test cases for code; and a small verifier model for science. A two-stage filter uses pass rates of a weak and a strong model to remove easy, noisy, and anomalous samples, and a difficulty gap controls learnability. The cross-domain transfer experiments train on 3K examples per domain and compare gain patterns across 13 online tasks; Pass@k curves provide the boundary-expansion evidence.

What would settle it

Measure or reconstruct the Qwen2.5 pretraining composition and verify that logic, simulation, and tabular really are under-represented; alternatively, train a model on a pretraining mixture with equal domain shares and test whether the asymmetric transfer pattern disappears. If a domain the authors classify as lightly pretrained shows robust cross-domain transfer under controlled exposure, the skill-acquisition conclusion would need revision.

Watch

Extended reading notes

Core claim

The central claim is that RL's role in LLM reasoning is not uniformly "elicitation of existing knowledge"; it depends on how much pretraining exposure the domain received. For math, code, and science, cross-domain RL produces clear gains, consistent with RL amplifying latent knowledge. For logic, simulation, and tabular reasoning, only in-domain RL gives meaningful improvement, which the authors interpret as evidence that RL facilitates genuine skill acquisition. The paper also shows that a uniformly mixed multi-domain RL corpus matches or exceeds single-domain training, and that Pass@k expansion—RL widening the set of correct answers a base model can reach—occurs on synthetic tasks like Zebra Puzzle but not on math benchmarks like AIME24. The resulting GURU-7B and GURU-32B models outperform the best open RL-trained baselines by 7.9% and 6.7% across a 17-task suite.

Load-bearing premise

The premise that carries the interpretation is that math, code, and science are heavily represented in the base model's pretraining while logic, simulation, and tabular are not; the paper infers this from the literature and benchmark difficulty rather than measuring the pretraining corpus.

Editorial extensions

If this is right

  • Multi-domain RL training from base models can match or beat single-domain RL, so reasoning data collection should not stop at math and code.
  • RL-trained models can expand the Pass@k reasoning boundary on tasks with low pretraining exposure, such as synthetic Zebra Puzzles, even when they cannot do so on AIME24.
  • Aggressive difficulty filtering improves in-domain math performance but can hurt performance on easier cross-domain tasks like HumanEval and HiTab.
  • General reasoning benchmarks should include under-represented domains if RL research is to learn about skill acquisition rather than about math elicitation.
  • Response-length behavior during RL is domain-dependent: code, logic, and tabular training can shorten outputs while math and science lengthen them.

Reading between the lines

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

  • The elicitation-versus-acquisition distinction may be better framed as a continuum fixed by pretraining exposure; a direct test would train a base model on controlled domain mixtures and rerun the transfer matrix.
  • If in-domain RL truly acquires new skills in lightly pretrained domains, scaling compute and data in those domains could be more valuable than adding harder math; a prediction is that GURU-style training on logic and simulation should continue improving beyond the reported epochs.
  • Pass@k as a boundary measure is sensitive to decoding temperature and top-p, so its use as evidence should be paired with output-entropy reporting to separate exploration from new capability.
  • The mixed-corpus result suggests domain interference is small at six domains, but the paper leaves open whether balancing strategies are needed as domain count grows; that is a natural next experiment with the released corpus.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 4 minor

Summary. The paper introduces GURU, a curated 92K-example reinforcement learning (RL) reasoning corpus spanning six domains (Math, Code, Science, Logic, Simulation, Tabular), with domain-specific reward design, deduplication, and difficulty filtering. Using GRPO on Qwen2.5-7B and Qwen2.5-32B base models, the authors conduct a controlled transfer study with 3K samples per domain and a mixed-domain 18K set. They report that Math, Code, and Science show positive cross-domain transfer, whereas Logic, Simulation, and Tabular require in-domain training, and interpret this as evidence that RL can acquire new skills in under-exposed domains. They further report mixed-domain training matches or exceeds single-domain training, difficulty filtering improves in-domain performance while hurting easy cross-domain transfer, and Pass@k behavior varies by task, scale, and decoding parameters. The authors release data, models, and code, and report state-of-the-art average performance on a 17-task suite among open models trained on public data with RL.

Significance. If the transfer asymmetry is robust, the paper provides a valuable multi-domain RL dataset and challenges the amplifier-only view of RL for reasoning, with open data, models, and code as a strong community contribution. The paper's empirical measurements are extensive and reproducible in principle. However, the central interpretation—that the transfer differences arise from pretraining exposure and that RL facilitates genuine skill acquisition—rests on an unmeasured and confounded domain split, and the key Pass@k evidence is partly circular. The dataset and empirical findings are significant, but the theoretical conclusion currently exceeds what the evidence supports.

major comments (4)
  1. [Sec. 3.1 / Abstract] The central skill-acquisition claim rests on an unmeasured pretraining-exposure split. The paper never measures Qwen2.5's pretraining data composition; the categorization of Math, Code, and Science as heavily pretrained and Logic, Simulation, and Tabular as lightly pretrained is justified by citing prior continual-pretraining literature (Ke et al., 2023; Yang et al., 2024) rather than direct evidence. This split is also correlated with task difficulty and format: ARC-AGI, Zebra Puzzle, and CodeI/O start near 0-16% base accuracy in Table 3, while Math/Code/Science tasks have much higher floors. Under this correlation, the low cross-domain gains on hard tasks are exactly what a difficulty effect predicts, independent of any exposure mechanism. The abstract and introduction assert 'limited pretraining exposure' as a fact, whereas Section 3.1 only states 'We hypothesize.' The skill-acquisition claim is not yet supported; the authors should either measure or otherwise control for pretraining exposure (e.g., match tasks on base accuracy or provide direct data-mixture evidence), or reframe the finding as a domain- and difficulty-dependent transfer effect.
  2. [Sec. 4.3 / B.4] The Pass@k evidence for a 'new reasoning boundary' is confounded by the evaluation and training sharing the same synthetic task family. The Zebra Puzzle evaluation set is generated by the same back-solving pipeline used for training (footnote 1 and Sec. B.4), so the expanded Pass@k on that task can be explained by learning the generator's template rather than a general logical skill. The paper should validate the boundary-expansion claim on held-out logic tasks from different generators or with a different evaluation process, or it should temper the claim accordingly.
  3. [Sec. 3 / Fig. 3 / Sec. 4.1] All reported transfer and main results are single-run, with checkpoint selection based on best average accuracy on online tasks (Sec. 3 and Sec. 4.1). No error bars or significance tests are provided, so the claimed patterns (e.g., 'cold colors on all non-diagonal cells' and the 7.9%/6.7% margins over baselines in Table 3) could be driven by selection noise. The authors should report multiple seeds or at least standard errors for the key cells, and clarify the sensitivity of checkpoint selection.
  4. [Sec. 3.3 / Table 2] The difficulty-filtering ablation compares the full unfiltered Math data (~118K after dedup/domain filters per Table 1) against the smaller difficulty-filtered subset (~54K) for a fixed 200 RL steps. This confounds data difficulty with dataset size and number of exposures per sample. The claimed effect of 'training data difficulty' is therefore not cleanly isolated; the authors should match training exposure (e.g., same number of gradient steps per sample) or otherwise control for dataset size.
minor comments (4)
  1. [Sec. 4.2] The text says GURU-7B outperforms the best baseline by 9.0%, while the abstract and Table 3 report 7.9% (43.29 vs 35.42 = 7.87). Please correct the inconsistency.
  2. [Fig. 3] The heatmap colors are min-max normalized per column, so the visual 'warmth' does not indicate absolute gain magnitude. The caption should report the actual accuracy ranges or include numerical labels, since the qualitative conclusions and the phrase 'significant variation' depend on magnitude.
  3. [Sec. 4.3 / footnote 1] The generation of a new Zebra Puzzle test set is described only in a footnote. This is important for interpreting the Pass@k results and should be described in the evaluation suite section (Sec. 4.1).
  4. [Abstract / Notation] The abstract uses 'Guru' while the rest of the paper uses 'GURU'; please use consistent capitalization.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's central claims are empirical measurements against held-out benchmarks, and the domain-exposure split is a qualitative hypothesis with possible confounds, not a definitional reduction.

full rationale

This is an empirical study, not a derivation chain. The headline results are measured accuracies and Pass@k curves on external or separately generated evaluation sets (Tables 2-3, Figures 3-5); the models are trained with GRPO on the released GURU corpus, and no parameter is fitted to a target result and then reported as a prediction. The Math/Code/Science vs Logic/Simulation/Tabular split is asserted from prior technical reports and continual-pretraining literature, not constructed from the transfer matrix, so it is a hypothesis with a difficulty-based confound (a validity risk) rather than a circular definition. The Zebra Puzzle evaluation uses a newly generated test set from the same synthesis pipeline, which is a distributional-overlap concern for the 'new skill' interpretation, but it is not a reduction of the result to the training labels. The paper's self-citations (HiTab, PrOntoQA/Graph Search) are data-provenance citations and are not load-bearing justifications of the central claim. No equation or fitted parameter collapses into an input, so no circular step can be exhibited.

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

The central conclusions rest on hand-chosen filtering thresholds, a qualitative categorization of pretraining exposure, and assumptions that the evaluation benchmarks are clean and the verifier is reliable. The paper does not introduce new physical or theoretical entities; its contribution is empirical.

free parameters (4)
  • Difficulty filtering thresholds = Pweak>=15/16; Pstrong=0; Pweak>Pstrong; math: Pstrong-Pweak<=6/16 when Pstrong>=0.75; science: Pstrong-Pweak<0.5
    These thresholds determine which samples enter GURU and therefore affect all downstream training and transfer results. They are chosen by the authors and are not derived from a theory.
  • Per-domain training subset size for transfer study = 3,000 examples per domain
    The cross-domain analysis uses 3K examples per domain (GURU-18K). The transfer conclusions may change with different subset sizes.
  • Pass-rate estimation runs = N=16 generations per sample
    The difficulty filter defines Pweak and Pstrong from 16 runs; using more runs could change the classification of borderline samples.
  • Online checkpoint selection = best average over 13 online tasks
    All reported accuracies use the checkpoint with the highest average score on online tasks, which introduces a selection effect and does not reflect a fixed training budget.
assumptions (4)
  • domain assumption Math, Code, and Science are heavily covered in Qwen2.5 pretraining, while Logic, Simulation, and Tabular are not.
    The paper cites continual pretraining literature but does not directly measure the base model's pretraining distribution. The interpretation of the transfer results depends on this categorization.
  • domain assumption The evaluation benchmarks are free of contamination with GURU training data.
    The paper uses public splits (e.g., ARC-AGI evaluation set, a new Zebra Puzzle test set), but no contamination analysis is provided. Leakage would inflate the reported gains.
  • domain assumption The 1.5B model-based verifier for science rewards is sufficiently reliable.
    Science rewards are generated by a small verifier model; its accuracy is not reported. If it is noisy, the science transfer and final model results are affected.
  • standard math GRPO without KL or entropy penalties is a valid RL procedure for the claimed comparisons.
    The training algorithm is standard practice in the field, but the absence of KL regularization affects the dynamics and Pass@k behavior; this is a modeling choice rather than a derived fact.

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Cite this review

Pith. "Pith review of Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective." pith.science (2026). https://pith.science/paper/SK4MJSGS

@misc{pith2026250614965,
  author       = {Pith},
  title        = {Pith review of: Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SK4MJSGS}},
  note         = {Machine review of arXiv:2506.14965}
}
read the original abstract

Reinforcement learning (RL) has emerged as a promising approach to improve large language model (LLM) reasoning, yet most open efforts focus narrowly on math and code, limiting our understanding of its broader applicability to general reasoning. A key challenge lies in the lack of reliable, scalable RL reward signals across diverse reasoning domains. We introduce Guru, a curated RL reasoning corpus of 92K verifiable examples spanning six reasoning domains--Math, Code, Science, Logic, Simulation, and Tabular--each built through domain-specific reward design, deduplication, and filtering to ensure reliability and effectiveness for RL training. Based on Guru, we systematically revisit established findings in RL for LLM reasoning and observe significant variation across domains. For example, while prior work suggests that RL primarily elicits existing knowledge from pretrained models, our results reveal a more nuanced pattern: domains frequently seen during pretraining (Math, Code, Science) easily benefit from cross-domain RL training, while domains with limited pretraining exposure (Logic, Simulation, and Tabular) require in-domain training to achieve meaningful performance gains, suggesting that RL is likely to facilitate genuine skill acquisition. Finally, we present Guru-7B and Guru-32B, two models that achieve state-of-the-art performance among open models RL-trained with publicly available data, outperforming best baselines by 7.9% and 6.7% on our 17-task evaluation suite across six reasoning domains. We also show that our models effectively improve the Pass@k performance of their base models, particularly on complex tasks less likely to appear in pretraining data. We release data, models, training and evaluation code to facilitate general-purpose reasoning at: https://github.com/LLM360/Reasoning360

Figures

Figures reproduced from arXiv: 2506.14965 by the authors.

Figure 1
Figure 1. Left: Absolute accuracy gain (%) over the base model when RL-trained on various domains. Pretrained-heavy domains (Math, Code, Science) benefit from cross-domain training, while others require in-domain data, indicating RL aids skill acquisition. Right: Our GURU-7B/32B models consistently outperform strong open baselines across 17 reasoning tasks when RL-trained with mixed-domain data. 1 arXiv:2506.14965v1 [cs.LG] 1… view at source ↗
Figure 2
Figure 2. Overview of the data curation pipeline of GURU dataset. Datasets used for RL reasoning predominantly focus on narrow domains such as Math (Luo et al., 2025b; Hu et al., 2025a; He et al., 2025; Zeng et al., 2025) and Code (Liu and Zhang, 2025; Luo et al., 2025a). However, applying RL on such single-domain datasets often leads to overfitting to domain-specific structures and heuris￾tics. As illustrated in [PITH_FULL_… view at source ↗
Figure 3
Figure 3. Cross-Domain RL Transfer Performance per Task. The heatmap shows the performance gains (accuracy) from RL training on different domains (rows) when evaluated on the test sets on different domains (columns). Warmer colors indicate higher performance gains, computed by applying min-max normalization to the validation accuracies within each column. Accuracy is reported using the checkpoint with the highest average scor… view at source ↗
Figures from the paper (6 more)
Figure 4
Figure 4. Figure 4: The reward and response length of each domain during RL training with: (top row) single domain data (3k examples each) from GURU-18k; and (bottom row): using the full GURU-18k mixture dataset. The x-axis is the number of gradient update steps [PITH_FULL_IMAGE:figures/…
Figure 5
Figure 5. Figure 5: Pass@k analysis of GURU. (a) Pass@k on AIME24 (Math) and Zebra Puzzle (Logic) for base Qwen2.5-7B/32B vs. RL-tuned GURU-7B/32B. (b) Pass@k under different decoding settings: higher sampling temperature or larger top-p broadens exploration and offsets RL-induced entropy…
Figure 6
Figure 6. Figure 6: The sankey diagram tracing the provenance of all math data included in GURU. By carefully curating these datasets, we aim to provide a robust and varied foundation for training and evaluating advanced mathematical reasoning capabilities in LLMs. We instruct the model t…
Figure 7
Figure 7. Figure 7: The sankey diagram tracing the provenance of all code data included in GURU. only focuses on Python, we leave the inclusion of additional programming languages (e.g., Java, C++, Go, etc.) as future work, to explore both cross-lingual transfer and the necessity of langu…
Figure 8
Figure 8. Figure 8: Cross-Domain RL Transfer Performance per Task with Qwen-32B-Base. This figure replicates the heatmap analysis from [PITH_FULL_IMAGE:figures/full_fig_p023_8.png]
Figure 9
Figure 9. Figure 9: Pass@k performance curves of GURU model at different training steps on the AIME24, ARC-AGI, and Code I/O datasets. We observe that in the early stage of RL training (before 160 steps, i.e., within the first epoch), the Pass@1 score increases, while the Pass@max_k score…

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Forward citations

Cited by 5 Pith papers

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Reference graph

Works this paper leans on

58 extracted references · 57 canonical work pages · cited by 5 Pith papers

  1. [1]

    Jen picks 4 distinct numbers from the set S = {1, 2, 3, . . . ,9, 10}

    work page

  2. [2]

    4 numbers are randomly chosen from S

    work page

  3. [3]

    She wins a prize if at least 2 of her numbers match the randomly chosen numbers

    work page

  4. [4]

    She wins the grand prize if all 4 of her numbers match the randomly chosen numbers

    work page

  5. [5]

    Then, we need to find m + n

    We need to find the probability of her winning the grand prize given that she won a prize, and express it as m n where m and n are relatively prime positive integers. Then, we need to find m + n. First, let’s calculate the total number of ways to choose 4 numbers from 10: 10 4 = 210 Next, we need to find the probability of winning a prize. This means at l...

    work page

  6. [6]

    It then iterates through each contest, checking if the rating update is allowed based on the division and the current rating

    Finally, we need to print the updated rating after all the contests.</think> Here is the Python code to solve the problem: ```python # Read the input N, R = map(int, input().split()) rating = R # Process each contest for _ in range(N): D, A = map(int, input().split()) if D == 1: if 1600 <= rating <= 2799: rating += A else: # D == 2 if 1200 <= rating <= 23...

    work page 1900

  7. [7]

    The emitter current ( IE) can be calculated using the formula: IE = qDn ND Lne S where Dn is the diffusion coefficient of electrons, ND is the donor concentration in the emitter region, and Lne is the diffusion length of electrons in the emitter region

    work page

  8. [8]

    We need to simulate the rating updates for Takahashi based on the division of each contest and his performance

    work page

Show all 58 references
  1. [9]

    1 and Div

    The rating update rules are different for Div. 1 and Div. 2: • For Div. 1, the rating update is allowed if the rating is between 1600 and 2799. • For Div. 2, the rating update is allowed if the rating is between 1200 and 2399

  2. [10]

    We need to check the current rating before each contest to determine if an update is allowed

  3. [11]

    If an update is allowed, we update the rating based on the performance in the contest

  4. [12]

    We need to repeat this process for each of the N contests

  5. [13]

    Let’s re-evaluate the steps to ensure accuracy

    However, this result seems too close to 1, which might indicate an error in the calculation. Let’s re-evaluate the steps to ensure accuracy

  6. [14]

    We are given a PNP germanium transistor with specific doping concentrations, base width, cross- sectional area, mobilities, and diffusion lengths

  7. [15]

    We need to calculate the common-base current gain ( α)

  8. [16]

    The common-base current gain (α) is given by the ratio of the collector current ( IC) to the emitter current (IE)

  9. [17]

    For a PNP transistor, the current gain (α) can be approximated by the ratio of the collector current density to the emitter current density, considering the recombination and diffusion processes in the base region

  10. [18]

    The current gain ( α) can be calculated using the formula: α = 1 − IRb IE where IRb is the recombination current in the base region and IE is the emitter current. 28

  11. [19]

    The recombination current in the base region ( IRb) can be calculated using the formula: IRb = qNAW S where q is the elementary charge, NA is the acceptor concentration in the base region, W is the base width, and S is the cross-sectional area

  12. [21]

    The diffusion coefficient of electrons ( Dn) can be calculated using the formula: Dn = kT q µne where k is the Boltzmann constant, T is the temperature (room temperature, approximately 300 K), and µne is the mobility of electrons in the emitter region

  13. [22]

    Let’s calculate the recombination current in the base region ( IRb): IRb = qNAW S= (1.602 × 10−19 C) × (1015 cm−3) × (2 × 10−3 cm) × (5 × 10−3 cm2) IRb = (1.602 × 10−19 C) × (1015 cm−3) × (10−2 cm3) IRb = 1.602 × 10−16 A

  14. [23]

    Let’s calculate the diffusion coefficient of electrons ( Dn): Dn = kT q µne = (1.38 × 10−23 J/K) × (300 K) (1.602 × 10−19 C) × (1900 cm2/V · s) Dn = 4.14 × 10−21 J 1.602 × 10−19 C × (1900 cm2/V · s) Dn = 0.0258 V · s × (1900 cm2/V · s) Dn = 49.02 cm2/s

    1900

  15. [24]

    Let’s calculate the emitter current ( IE): IE = qDn ND Lne S = (1.602 × 10−19 C) × (49.02 cm2/s) × 1017 cm−3 0.1 mm × (5 × 10−3 cm2) IE = (1.602 × 10−19 C) × (49.02 cm2/s) × 1017 cm−3 10−4 cm × (5 × 10−3 cm2) IE = (1.602 × 10−19 C) × (49.02 cm2/s) × (1021 cm−2) × (5 × 10−3 cm2...

  16. [25]

    Finally, let’s calculate the common-base current gain ( α): α = 1 − IRb IE = 1 − 1.602 × 10−16 A 3.926 × 10−1 A 29 α = 1 − 1.602 × 10−16 3.926 × 10−1 α = 1 − 4.08 × 10−16 α ≈ 1

  17. [27]

    Upon re-evaluation, it appears that the recombination current in the base region (IRb) is extremely small compared to the emitter current ( IE), leading to a very high current gain ( α)

  18. [28]

    Your task is to analyze puzzles, spot patterns, and provide direct solutions

    Given the options provided, the closest value to our calculated result is E , which is 0.9779.</think> E 30 E.4 Logic Logic Example (Sampled from ARC-AGI) Question: You are a world-class puzzle solver with exceptional pattern recognition skills. Your task is to analyze puzzles...

  19. [29]

    We have several input-output pairs, and we need to identify the pattern or transformation rule applied to each input to produce the corresponding output

  20. [30]

    Observing the output grids, we see that they are all 3 × 3 grids with a single number repeated throughout

  21. [31]

    The output grids are: Example 1:   4 4 4 4 4 4 4 4 4   Example 2:   3 3 3 3 3 3 3 3 3   Example 3:   8 8 8 8 8 8 8 8 8  

  22. [32]

    The transformation rule seems to be identifying a specific pattern or number in the input grid and using it to fill the output grid

  23. [33]

    In each input grid, we need to identify the number that is consistently present in a specific pattern or area

  24. [34]

    For the given input grid, we need to look for a similar pattern or number that stands out

  25. [35]

    Upon closer inspection, we can see that the number 5 is present in a consistent pattern in the lower part of the grid, forming a 3 × 3 pattern

  26. [36]

    This pattern is similar to the patterns we saw in the previous examples, where a specific number was used to fill the output grid

  27. [37]

    p u b l i c _ k e y

    Therefore, the output grid for the given input should be filled with the number 5.</think> <answer>   5 5 5 5 5 5 5 5 5   </answer> 32 E.5 Simulation Simulation Example (Sampled from CodeI/O) Question: You are given a question that requires some input and output variables ...

  28. [38]

    We are given the output of the RSA algorithm, which includes the public key, private key, encrypted message, and decrypted message

  29. [39]

    The public key is (901, 3), which means n = 901 and e = 3

  30. [40]

    The private key is (555, 901), which means d = 555 and n = 901

  31. [41]

    The encrypted message is 316, and the decrypted message is 88, which should be the same as the original message

  32. [42]

    Since n = p × q, we need to find two prime numbers p and q such that p × q = 901

  33. [43]

    The prime factorization of 901 is 17 × 53, so p = 17 and q = 53 (or vice versa)

    We can factorize 901 to find p and q. The prime factorization of 901 is 17 × 53, so p = 17 and q = 53 (or vice versa)

  34. [44]

    The public exponente is given as 3, which is less than bothp and q and coprime with (p−1)×(q−1)

  35. [45]

    We need to verify that d is the modular inverse of e modulo (p − 1) × (q − 1)

  36. [46]

    Calculate (p − 1) × (q − 1) = (17 − 1) × (53 − 1) = 16 × 52 = 832

  37. [47]

    This means 3 × 555 mod 832 = 1

    Check if d = 555 is the modular inverse of e = 3 modulo 832. This means 3 × 555 mod 832 = 1

  38. [48]

    Calculate 3 × 555 = 1665 , and 1665 mod 832 = 1 , which confirms that d = 555 is indeed the modular inverse of e = 3 modulo 832

  39. [49]

    The message message is 88, which is the original message before encryption

  40. [50]

    The encrypted message is 316, which is calculated as 883 mod 901

  41. [51]

    p": 17,

    The decrypted message is 88, which is calculated as 316555 mod 901, and it should be the same as the original message, which it is.</think> Based on the reasoning above, the feasible input for the given output is: ```json {"p": 17, "q": 53, "e": 3, "message": 88} ``` 34 E.6 Ta...

    2009

  42. [52]

    We need to find the Research and development, net values for 2011 and 2012

    2011

  43. [53]

    From the last table, we can see the Research and development, net values: 2011: $428 2012: $453

    2011

  44. [54]

    To calculate the percentage change, we use the formula: Percentage Change = Value in 2012 − Value in 2011 Value in 2011 × 100

    2012

  45. [55]

    Plugging in the values: Percentage Change = 453 − 428 428 × 100

  46. [56]

    Simplifying the equation: Percentage Change = 25 428 × 100

  47. [57]

    Calculating the fraction: 25 428 ≈ 0.0584

  48. [58]

    Multiplying by 100 to get the percentage: 0.0584 × 100 ≈ 5.84% </think> 5.84% 36

  49. [2021]

    More specialized applications emerged with FinQA (Chen et al., 2021b) and ConvFinQA (Chen et al., 2022b), addressing TQA within the financial domain

    and MultiHiertt (Zhao et al., 2022), which focused on hierarchical tables featuring multiple levels of headers, demanding more sophisticated reasoning. More specialized applications emerged with FinQA (Chen et al., 2021b) and ConvFinQA (Chen et al., 2022b), addressing TQA with...

    2025

  50. [2023]

    A is at position 3

    URL https://arxiv.org/abs/2210.01240. Abulhair Saparov, Srushti Pawar, Shreyas Pimpalgaonkar, Nitish Joshi, Richard Yuanzhe Pang, Vishakh Padmakumar, Seyed Mehran Kazemi, Najoung Kim, and He He. Transformers struggle to learn to search, 2025. URL https: //arxiv.org/abs/2412.04...

    2025 arXiv

Pith tools

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