Prejudge-Before-Think: Enhancing Large Language Models at Test-Time by Process Prejudge Reasoning

Jianing Wang; Jin Jiang; Mengdi Zhang; Xunliang Cai; Yang Liu

REVIEW 5 major objections 9 minor 15 references

Prejudge-Before-Think: Enhancing Large Language Models at Test-Time by Process Prejudge Reasoning

T0 review · 5 major / 9 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Inserting 'prejudge' warnings about upcoming errors into a reasoning chain lifts LLM accuracy on eight competition-level math and logic benchmarks, with average gains of 3.5 and 2.4 points for a 7B and a 32B model.

desk verdict A genuinely new data-synthesis mechanism for inserting 'prejudge' hints into reasoning trajectories, with consistent but partly contaminated empirical support. read the letter →

arxiv 2504.13500 v1 pith:MZVLMUW5 submitted 2025-04-18 cs.CL

Jianing Wang , Jin Jiang , Yang Liu , Mengdi Zhang , Xunliang Cai This is my paper · ORCID

classification cs.CL

keywords processprejudgenodedynamictreesearchLLMreasoningtest-timereinforcementlearningchain-of-thoughtself-correction

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 claims that a language model can be taught to 'prejudge before thinking': to pause at a reasoning step, anticipate the error a later step is about to make, and insert a short warning hint before proceeding. The authors build an automated pipeline that locates these pauses—called prejudge nodes—by tree search, generates the hint with a critic, verifies it with a second search, and then fine-tunes the model on the resulting rationales. On eight competition-level benchmarks, the resulting model beats chain-of-thought and self-refine baselines for both a 7B and a 32B backbone, by 3.5 and 2.4 average points, with further gains from reinforcement learning. The point of the exercise is to show that anticipatory error avoidance, not just trial-and-error correction, is a learnable and transferable reasoning skill for LLMs.

What carries the argument

The central object is the 'prejudge node': a reasoning step $z_i$ that is itself on a correct path ($v(z_i)=1$) but has at least one sampled child that is a dead end ($\min_j v(z_{i+1}^j)=0$). The prejudge value $v_p(z_i)=v(z_i)\cdot \mathbf{1}(\min_j v(z_{i+1}^j)=0)$ identifies these nodes. Around this definition the paper builds a one-LLM dynamic tree search that estimates node values with an LLM-as-judger using hard estimation, produces error analysis and a prejudge hint through an LLM-as-critic, re-searches with the hint to confirm it leads to a correct completion, and writes accepted trajectories with "<|think|>", "<|verify|>", and "<|prejudge|>" boundary tags. That data then feeds a two-phase post-training scheme: cold-start SFT on about 39k searched rationales, distillation to about 195k rationales, and then GRPO or DPO reinforcement learning.

What would settle it

Take a sample of the synthesized prejudge trajectories, re-run the tree search with a much larger sampling budget (e.g., tens of thousands of paths per node instead of 1024), and measure how often a child that was marked $v=0$ actually leads to a correct answer. If a substantial fraction of 'dead-end' children are resurrected, the prejudge-node definition is flagging sampling artifacts rather than genuine errors, and the training signal is largely noise.

Watch

Extended reading notes

Core claim

The central claim is that a reasoning model trained on rationales that contain prejudge hints—short self-oriented warnings such as 'the denominator cannot be 0' placed just before the step that would otherwise commit the error—learns to foresee and sidestep mistakes, and that this transferable 'prejudge before think' behavior improves test-time accuracy beyond what chain-of-thought or self-corrective pipelines achieve. The paper operationalizes the claim as follows: with the same backbone, PBT#1 outperforms CoT and Self-Refine on all eight benchmarks, with average gains of 3.5% and 2.4% for Qwen2.5-7B and Qwen2.5-32B respectively; adding GRPO reinforcement learning raises the 7B average from 59.0% to 63.9%. The authors also show that removing the verification component degrades performance, that prejudge hints improve pass@N by about 3% in a thought-completion task, and that mixing prejudge data with long-CoT (o1-style) data is compatible and often additive.

Load-bearing premise

The pipeline assumes that a node marked as a dead end by the LLM-as-judger inside the truncated tree search (at most 1024 paths and 14 steps) truly has no path to the correct answer; if a dead-end child is merely undersampled, then the prejudge positions and hints are built on a false premise and the training data contains misleading prejudge positions.

Editorial extensions

If this is right

Across all eight benchmarks, PBT#1 beats both CoT training and Self-Refine for Qwen2.5-7B and Qwen2.5-32B; removing the verification step degrades results, so verification is load-bearing for the prejudge recipe.
Adding GRPO reinforcement learning after SFT raises the 7B average from 59.0% to 63.9%, outperforming DPO by about 2 points.
Increasing the number of prejudge hints per rationale improves accuracy on GSM8K and MATH-500, and prejudge hints improve pass@N by about 3% in the thought-completion test.
Mixing prejudge data with o1-style LIMO data keeps or improves most benchmarks, suggesting the prejudge mode is compatible with existing long-chain reasoning styles.

Reading between the lines

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

If the effect is real, it suggests that part of chain-of-thought's value is anticipatory error avoidance rather than merely more tokens; a testable extension is ablating the specificity of hints (generic warnings vs. problem-specific ones) to isolate what the model learns.
Because the dead-end labels come from a bounded tree search, a natural stress test is measuring how much of the training signal is an artifact of undersampling; the paper's own reported search limits (1024 paths, 14 steps) make this the empirical hinge of the method.
The same 'prejudge node + hint + verify' template could transfer to other verifiable step-structured domains, such as code generation or theorem proving, where a hint before a risky operation can be generated and checked automatically.
The paper's stated limitation (about 5 minutes per query for search) points to a practical next step: distilling the prejudge-hint generation itself into a lightweight model that can emit hints at inference time without search.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Short version: the prejudge-node idea is new and the pipeline is clearly described, but the evaluation is muddier than the abstract claims. The paper defines a prejudge node as a step with a child that has no path to the correct answer, then uses tree search to find such nodes, generate hints, verify them, and distill the rationales into SFT and RL. That mechanism is not in the prior self-refine/verification literature, and the single-LLM dynamic tree-search pipeline is a legitimate engineering contribution. The code and data release helps reproducibility.

What is good: the method beats CoT and Self-Refine on average by 3.5 and 2.4 points (7B/32B), and the w/o Verify ablation points to the verification component mattering. The two-phase SFT+RL scaling is standard but executed cleanly. The case studies look plausible.

The soft spots are real. First and most important: the benchmark suite is largely contaminated. GSM8K, MATH-500, AQuA, SVAMP, and AIME-2024 all come from the same sources used to build the training data (Table 4). So those columns are not independent. The only clean benchmarks are TheoremQA, GAOKAO-2023, and GPQA-Diamond; gains there are smaller but still mostly positive. Second, the 'consistently outperforms Self-Refine' claim in Section 4.4 is factually wrong: 7B SVAMP 90.3 vs 90.7, 32B GSM8K 92.4 vs 92.6, and 32B GAOKAO 78.6 vs 79.4 all go the other direction. It is a 3-of-16-cell point, but the text overstates. Third, the dead-end labels in Eq. 1-2 are sampled under a fixed 1024-path/14-step budget with a 14B generator; a child marked v=0 may be under-searched, not genuinely dead. No sensitivity analysis is provided, so the prejudge nodes could be partly spurious. That is a moderate concern, not fatal, because the method still seems to help. Fourth, the main ablations are length-confounded: removing verify shortens rationales, and increasing prejudge count lengthens them, so the 'prejudge helps' conclusion is entangled with test-time compute.

My take: the mechanism is worth a serious look, but the current evaluation does not establish that the gains come from prejudging per se rather than longer rationales and contaminated training overlap. A referee should ask for a held-out evaluation on non-overlapping benchmarks, error bars or at least variance across seeds, and an ablation that controls for rationale length. This paper deserves a revise-and-resubmit, not a desk reject.

Referee Report

5 major / 9 minor

Summary. This paper introduces 'process prejudge' (PBT), a training-time strategy that conditions LLM reasoning on anticipatory error-avoidance hints. The authors define a prejudge node as a step whose next-step children contain at least one child with no sampled path to a correct answer (Eqs. 1-2). They synthesize rationales containing such prejudge hints via a dynamic tree-search framework in which a single LLM (Qwen2.5-14B-Instruct) generates thoughts, judges answers, critiques incorrect paths, and verifies corrected steps. A two-phase post-training recipe (Phase 1: cold-start SFT on roughly 39k searched rationales from about 21k queries; Phase 2: self-distillation with the cold-start model on roughly 195k rationales, followed by SFT and optionally GRPO/DPO RL) is evaluated on eight reasoning benchmarks with Qwen2.5-7B and 32B backbones. Table 1 reports PBT#1 outperforming CoT on all sixteen benchmark/backbone pairs and improved averages over Self-Refine, with Phase-2 and RL variants adding further gains; ablations (w/o Verify, w. CoT, number of prejudge hints, pass@N with/without hints) are used to attribute the gains.

Significance. If the reported gains hold, PBT is a useful contribution to the growing self-training and self-correction literature: it proposes a concrete, automated way to inject anticipatory error-avoidance into rationales, it is backbone-agnostic, and the two-phase recipe produces meaningful average gains on small open models (e.g., +3.5 and +2.4 points over CoT for the 7B and 32B backbones). The paper's strengths include released code and data, broad benchmark coverage, internal ablations (w/o Verify, w. CoT, hint-count, RL), and a separate analysis showing that the synthesized prejudge hints improve pass@N when given at test time. The significance is moderated, however, by the fact that several per-benchmark deltas are within a few questions of one another, by the unsupported claim of universal superiority over Self-Refine, and by the reliance on budget-relative 'dead-end' labels without sensitivity analysis. The conceptual distinction between prejudging and reactive correction is interesting and worth validating with the strengthened evidence requested below.

major comments (5)

[§3.1, Eqs. (1)-(2); §4.1; Appendix B.1] The definition of a prejudge node ('no paths toward the correct answer') is operationalized only within the sampled subtree built by Qwen2.5-14B-Instruct under a 14-step horizon and a 1,024-path budget. A child marked v=0 in Eq. (1) means 'no correct leaf was found within budget,' not 'no correct continuation exists,' so Eq. (2) can mark as prejudge nodes positions whose children are merely undersampled or beyond the horizon, and the error analysis and hints of Section 3.2 are then built on those possibly false premises. The paper provides no sensitivity analysis showing label stability under larger budgets or a longer horizon. I ask for (i) an explicit restatement that all 'no path' claims are budget-relative; (ii) a label-stability study (e.g., the fraction of v=0 children that become v=1 as the path budget is doubled or the horizon is extended); and, if labels flip materially, a re-synthesis or restriction to stable prejudge positions. Since the generator (14B) is weaker than the trained 32B model, a correct branch that the 14B fails to discover will also be mislabeled as a dead end.
[Table 4 and Table 1 (SVAMP)] SVAMP is listed as a Phase-1 training source (700 queries sampled, 700 trained) and also appears as one of the eight evaluation benchmarks in Table 1, with no statement that the 700 training queries were excluded from the SVAMP evaluation set. Under the standard usage of SVAMP as a 1,000-question test set, up to 70% of the evaluation set could have been seen during SFT, which would make the SVAMP rows in Table 1 (and the all-eight-benchmarks claim) uninterpretable. Please clarify the exact split used, remove the 700 training queries from the evaluation set (or re-evaluate on a disjoint subset), and report the resulting SVAMP numbers for all methods.
[§4.4] The sentence 'PBT consistently outperforms CoT training and Self-Refine across all benchmarks using both 7B and 32B backbones' is contradicted by Table 1 itself: Self-Refine#1 is higher than PBT#1 on 7B SVAMP (90.7 vs 90.3), 32B GSM8K (92.6 vs 92.4), and 32B GAOKAO (79.4 vs 78.6). The claim should be weakened to PBT being better on average and better than CoT on all sixteen benchmark/backbone pairs; the three exceptions should be acknowledged, and the Abstract's 'significantly enhance' should be made consistent with the per-benchmark results.
[Table 1 and Table 2] No error bars, significance tests, or random-seed information are reported, and several headline deltas are at the resolution of the benchmark. For example, AIME-2024 contains 30 problems, so 13.3% vs 6.7% is 4 vs 2 correct answers; TheoremQA and GAOKAO deltas of roughly 1-2 points correspond to a handful of questions. The average gains of 3.5 and 2.4 points aggregate these small per-benchmark differences. Please report variance over at least three seeds (or bootstrap confidence intervals over sampled responses) and indicate which per-benchmark differences exceed chance; the consistent sign of the PBT-vs-CoT differences is informative, but the magnitude claims need statistical support.
[§4.3] The training data used for the CoT and Self-Refine baselines is not described: no query counts, rationale counts, or sampling procedure are given. Since the PBT pipeline synthesizes a large corpus (234k rationales), the PBT-vs-CoT comparison could conflate the prejudge format with data volume. Please report the dataset sizes for all baselines and add a data-matched control (identical query set and rationale count, plain CoT format); the 'w. CoT' row in Table 1 suggests such controls are feasible.

minor comments (9)

[§4.3 / References] Section 4.3 cites the Self-Refine baseline as '(Kumar et al., 2024)', but the described behavior (iterative refinement with feedback) is the Self-Refine method of (Madaan et al., 2023); the reference list's Kumar et al. (2024) entry is a different method. Please correct the attribution.
[Abstract / Table 4] The Abstract states that the work 'construct[s] 234k data', while the body reports approximately 39k Phase-1 and 195k Phase-2 rationales and Table 4's #Train query counts sum to about 110k. Please state explicitly that 234k refers to rationales rather than queries, and clarify how the #Search/#Train query counts relate to the final rationale counts.
[§5.3] Section 5.3 does not state whether the five sets D_k (k=1,...,5) contain the same queries with k prejudge hints or contain different sampled queries. If the queries differ across sets, the upward trend in Figure 4 may reflect query difficulty rather than hint count; please clarify the construction and report run-level variance for the SFT accuracies.
[§5.3] The sentence '...the more likely the model will make prejudges, which can better guide the model to make incorrect prejudges before thinking' appears garbled; the intended meaning is presumably that more prejudge hints guide the model to avoid the anticipated mistakes.
[§1, §5.4] Please fix the typos: 'Monto Carlo Tree Search' should be 'Monte Carlo Tree Search' (Introduction), and 'prejudge before use' (Introduction and Section 5.4) should be 'prejudge before think' to match the title.
[§4.2 / Figure 5] State explicitly whether the LLM-as-a-judger inside the dynamic tree search is the same Qwen2.5-14B-Instruct model used for the other three roles, with Qwen2.5-72B-Instruct used only for final benchmark evaluation; this would make the Abstract's 'requires only one LLM' claim precise and reproducible.
[§5.2 / Figure 3] Define Pass@N precisely (empirical fraction correct at N sampled completions versus a pass@k estimator), and report the completion temperature, the seed, and the variance across the 2,000 queries for the curves in Figure 3.
[§2.2 / §4.1] The symbol N denotes the number of repeated samples per layer in tree search (Section 2.2) and also the self-consistency count (N=32) in Phase 2 (Section 4.1); please use distinct symbols for these two quantities to avoid confusion.
[Limitations] Please report the total compute of the data-synthesis pipeline (e.g., GPU-hours for the 21k-query tree search and the Phase-2 distillation), since the per-query cost ('about 5 minutes') alone does not allow cost-based comparison with existing self-training methods.

Circularity Check

1 steps flagged · score 2.0 of 10

Main results are externally grounded; only the Section 5.2 hint-usefulness check is self-fulfilling via the rejected-sampling selection of hints.

fitted input called prediction [Section 3.2 (Prejudge Estimating) and Section 5.2 (Effect of Prejudge in Test-time)]
"we employ tree-searching to sample all reasoning steps to determine if the prejudge hint enables the LLM to arrive at the correct answer, utilizing the rejected sampling method to select the appropriate prejudge hint. Figure 3 shows that the Pass@N value is, on average, 3% higher with prejudge hints than without, suggesting that the rationale provided by the prejudge hint can better assist the LLM in avoiding mistakes."

The 'effect of prejudge' in Section 5.2 is measured on hints that were admitted into the training data only when the pipeline's tree-search procedure, after inserting the hint, reached a ground-truth-correct answer (rejected sampling). Removing such already-vetted hints and observing that completion accuracy drops is a property of the acceptance filter, not independent evidence that an autonomously reasoning model has learned to prejudge. The measured Pass@N advantage is therefore partly forced by construction: unhelpful hints were discarded before the comparison. This step is peripheral to the central benchmark comparison in Table 1, which is judged externally against ground truth, so it does not make the main result circular.

full rationale

The central claim of the paper — that models trained with process-prejudge rationales improve on complex reasoning benchmarks — is evaluated on standard external benchmarks with ground-truth answers, and the LLM-as-a-judger used for evaluation checks generated answers against that ground truth. The two-phase SFT/RL training is a bootstrap loop, but bootstrap self-training is not circularity when the final evaluation is external, which it is here. The definition of a prejudge node via Equations (1) and (2) is operational, not self-referential: it labels nodes based on sampled tree search and judger checks, and any concern that 'no path toward the correct answer' may really mean 'no path found within the sampling budget' is a correctness/robustness limitation, not a circular derivation. I found no load-bearing self-citation: the citations to prior work, including Math-Shepherd's hard estimation, are external and not used to define away the central result. The only reduction I can exhibit is the secondary Section 5.2 analysis, where the hints being tested were selected precisely because they led to correct answers under rejected sampling, making the subsequent 'hints help' comparison partly self-fulfilling. I therefore score this as a minor, peripheral circularity rather than a central one. I also note the text's claim that PBT 'consistently outperforms' Self-Refine is not fully supported by its own Table 1 (e.g., 32B GSM8K 92.4 vs 92.6; 7B SVAMP 90.3 vs 90.7), but that is an empirical inconsistency, not circularity, and is excluded from this score.

Assumptions & free parameters 4 free parameters · 4 assumptions · 2 invented entities

The ledger contains no fitted physical constants. The listed free parameters are procedural hyperparameters that shape the synthetic data distribution. The axioms capture the load-bearing assumptions about judger reliability, tree-search exhaustiveness, hint transfer, and benchmark labels. Invented entities are the paper's conceptual and formatting constructs, all defined internally.

free parameters (4)

Tree search path budget = 1024 paths maximum
Search is truncated so that the number of root-to-leaf paths does not exceed 1024 (Appendix B.1). This budget determines which children receive v=0.
Maximum reasoning step length in search = 14 steps
Each sampled path is stopped after 14 steps; open branches are treated as terminal for value estimation (Section 4.1).
Self-consistency sample count = 32
Phase 2 distillation samples N=32 responses and keeps the most reliable rationale (Section 4.1).
Number of prejudge hints per rationale in the D_k ablation = k = 1, 2, 3, 4, 5
SFT ablations vary the count of prejudge nodes per rationale (Section 5.3); the effect is confounded with rationale length.

assumptions (4)

domain assumption The LLM-as-a-judger correctly maps a final answer to TRUE/FALSE against the ground truth.
Used in Equation 1 for tree node values and in evaluation (Appendix C.2). If the judger is unreliable, v(z) values and prejudge-node detection are wrong.
domain assumption A child with value 0 in the searched tree has no path to the correct answer.
Equation 2's indicator on min child value = 0 defines a prejudge node. The tree is truncated at 1024 paths and 14 steps, so v=0 only means 'no correct path found'.
domain assumption Prejudge hints generated from error analysis of incorrect branches transfer to guide the next step.
The critic prompt (Figure 7) produces hints from observed mistakes; the second tree search filters them, but the filter uses the same LLM family.
standard math Benchmark ground-truth answers are correct.
All filtering and evaluation use these labels (Section 4.2).

invented entities (2)

Prejudge node
purpose: A position in the rationale where at least one sampled next step has no correct path; this is where the model inserts a prejudge hint.
Defined by Equation 2 using tree-search values; it is a paper-internal construct with no external validation.
Special tokens <|think|>, <|verify|>, <|prejudge|>
purpose: Format delimiters for thinking, verification, and prejudge segments in synthetic training data.
Introduced as a training format; their utility is shown only through the paper's experiments.

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Cite this review

Pith. "Pith review of Prejudge-Before-Think: Enhancing Large Language Models at Test-Time by Process Prejudge Reasoning." pith.science (2026). https://pith.science/paper/MZVLMUW5

@misc{pith2026250413500,
  author       = {Pith},
  title        = {Pith review of: Prejudge-Before-Think: Enhancing Large Language Models at Test-Time by Process Prejudge Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/MZVLMUW5}},
  note         = {Machine review of arXiv:2504.13500}
}

read the original abstract

In this paper, we introduce a new \emph{process prejudge} strategy in LLM reasoning to demonstrate that bootstrapping with process prejudge allows the LLM to adaptively anticipate the errors encountered when advancing the subsequent reasoning steps, similar to people sometimes pausing to think about what mistakes may occur and how to avoid them, rather than relying solely on trial and error. Specifically, we define a prejudge node in the rationale, which represents a reasoning step, with at least one step that follows the prejudge node that has no paths toward the correct answer. To synthesize the prejudge reasoning process, we present an automated reasoning framework with a dynamic tree-searching strategy. This framework requires only one LLM to perform answer judging, response critiquing, prejudge generation, and thought completion. Furthermore, we develop a two-phase training mechanism with supervised fine-tuning (SFT) and reinforcement learning (RL) to further enhance the reasoning capabilities of LLMs. Experimental results from competition-level complex reasoning demonstrate that our method can teach the model to prejudge before thinking and significantly enhance the reasoning ability of LLMs. Code and data is released at https://github.com/wjn1996/Prejudge-Before-Think.

Figures

Figures reproduced from arXiv: 2504.13500 by the authors.

**Figure 2.** The automated reasoning framework for synthesizing process prejudge with the dynamic tree-searching. [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗

**Figure 3.** Effect of prejudge in complex reasoning with [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Effect of the number of prejudge hints over [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]

**Figure 5.** Figure 5: The prompt for LLM-as-a-Judger. Let's think step by step, and put the final answer within \boxed{}. <|im_end|> <|im_start|>assistant where “{Question}” is the placeholder for complex query, “<|im_start|>”, “<|im_end|>” are the special tokens in vocabulary set of Qwen2.…

**Figure 6.** Figure 6: The prompt for prejudge estimating. utilized in dynamic tree searching to produce error analysis for all incorrect rationales and construct a prejudge hint for the prejudge node. C.4 Prompt for Prejudge Estimating The prompt for prejudge estimating is shown in [PITH_F…

**Figure 7.** Figure 7: The prompt for LLM-as-a-Critic [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]

**Figure 8.** Figure 8: The case of prejudge reasoning (part 1). [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

**Figure 9.** Figure 9: The case of prejudge reasoning (part 2). [PITH_FULL_IMAGE:figures/full_fig_p016_9.png]

**Figure 10.** Figure 10: The case of prejudge reasoning (part 3). [PITH_FULL_IMAGE:figures/full_fig_p017_10.png]

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Reference graph

Works this paper leans on

15 extracted references · 10 canonical work pages

[1]

Completion #1

Errors Analysis: Each incorrect completion reaches an incorrect answer due to misconception, please list the specific mistakes details. Cautions: - DO NOT disclose the complete number (e.g., "Completion #1")

work page
[2]

I should double-check

Prejudge: You will start reasoning from the given initialized step, please generate some detailed prejudge information to ask yourself to avoid making errors. Cautions: - The generated prediction information is intended to guide the next step of reasoning to avoid errors, it should be closed to the possible errors and the detailed error analysis; - The ge...

work page
[3]

If we round down $a_2 = 2.61$ and $a_3 = 2.65$ to 2: \[ \lvert A_2 - a_2 \rvert = \lvert 2 - 2.61 \rvert = 0.61 \] \[ \lvert A_3 - a_3 \rvert = \lvert 2 - 2.65 \rvert = 0.65 \] Maximum error is 0.65.<|think|> We see that rounding down $a_1 = 2.56$ and $a_2 = 2.61$ to 2 results in a maximum error of 0.61, which is the smallest among the evaluated combinati...

work page
[6]

Associa- tion for Computational Linguistics

Are NLP models really able to solve simple math word problems? InNAACL, Online. Associa- tion for Computational Linguistics. Aske Plaat, Annie Wong, Suzan Verberne, Joost Broekens, Niki van Stein, and Thomas Bäck. 2024. Reasoning with large language models, a survey. CoRR, abs/2407.11511. Zhenting Qi, Mingyuan Ma, Jiahang Xu, Li Lyna Zhang, Fan Yang, and ...

arXiv 2024
[7]

Chaojie Wang, Yanchen Deng, Zhiyi Lv, Zeng Liang, Jujie He, Shuicheng Yan, and Bo An

Solving math word problems with process- and outcome-based feedback.CoRR, abs/2211.14275. Chaojie Wang, Yanchen Deng, Zhiyi Lv, Zeng Liang, Jujie He, Shuicheng Yan, and Bo An. 2024a. Q*: Improving multi-step reasoning for llms with deliber- ative planning.CoRR, abs/2406.14283. Jianing Wang, Qiushi Sun, Xiang Li, and Ming Gao. 2024b. Boosting language mode...

arXiv
[11]

If we round down $a_1 = 2.56$ and $a_2 = 2.61$ to 2: \[ 2 + 2 + 3 + 3 + 3 + 3 + 3 = 19 \] Errors: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_2 - a_2 \rvert = \lvert 2 - 2.61 \rvert = 0.61 \] Maximum error is 0.61

work page
[12]

If we try rounding down $a_1 = 2.56$ and $a_3 = 2.65$ to 2: \[ 2 + 2 + 3 + 3 + 3 + 3 + 3 = 19 \] Errors: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_3 - a_3 \rvert = \lvert 2 - 2.65 \rvert = 0.65 \] Maximum error is 0.65. We should continue this process and consider other combinations to ensure the error is minimized.<|verify...

work page
[13]

If we round down $a_1 = 2.56$ and $a_2 = 2.61$ to 2: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_2 - a_2 \rvert = \lvert 2 - 2.61 \rvert = 0.61 \] Maximum error is 0.61

work page

Show all 15 references

[14]

If we round down $a_1 = 2.56$ and $a_3 = 2.65$ to 2: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_3 - a_3 \rvert = \lvert 2 - 2.65 \rvert = 0.65 \] Maximum error is 0.65
[293]

Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yu- taka Matsuo, and Yusuke Iwasawa

Springer. Takeshi Kojima, Shixiang Shane Gu, Machel Reid, Yu- taka Matsuo, and Yusuke Iwasawa. 2022. Large lan- guage models are zero-shot reasoners. InNeurIPS. Aviral Kumar, Vincent Zhuang, Rishabh Agarwal, Yi Su, John D. Co-Reyes, Avi Singh, Kate Baumli, Shariq Iqbal, Colton...

2022 arXiv
[2020]

In NeurIPS

Language models are few-shot learners. In NeurIPS. Sijia Chen and Baochun Li. 2024. Toward adaptive reasoning in large language models with thought roll- back. InICML. OpenReview.net. Wenhu Chen, Ming Yin, Max Ku, Pan Lu, Yixin Wan, Xueguang Ma, Jianyu Xu, Xinyi Wang, and Tony...

2024
[2021]

Bofei Gao, Zefan Cai, Runxin Xu, Peiyi Wang, Ce Zheng, Runji Lin, Keming Lu, Junyang Lin, Chang Zhou, Wen Xiao, Junjie Hu, Tianyu Liu, and Baobao Chang

Training verifiers to solve math word prob- lems.CoRR, abs/2110.14168. Bofei Gao, Zefan Cai, Runxin Xu, Peiyi Wang, Ce Zheng, Runji Lin, Keming Lu, Junyang Lin, Chang Zhou, Wen Xiao, Junjie Hu, Tianyu Liu, and Baobao Chang. 2024a. LLM critics help catch bugs in mathematics: To...

arXiv
[2022]

InNeurIPS

Training language models to follow instruc- tions with human feedback. InNeurIPS. Joon Sung Park, Joseph C. O’Brien, Carrie Jun Cai, Meredith Ringel Morris, Percy Liang, and Michael S. Bernstein. 2023. Generative agents: Interactive sim- ulacra of human behavior. InUIST, pages...

2023
[2024]

Let’s verify step by step. InICLR. Open- Review.net. Wang Ling, Dani Yogatama, Chris Dyer, and Phil Blun- som. 2017. Program induction by rationale genera- tion: Learning to solve and explain algebraic word problems. InACL, pages 158–167. Association for Computational Linguist...

2017 arXiv
[4981]

2-4-1-3” is located at the fourth layer in the tree, and it is one of the child nodes of “2-4-1

Association for Computational Linguistics. Jianing Wang, Junda Wu, Yupeng Hou, Yao Liu, Ming Gao, and Julian J. McAuley. 2024c. Instructgraph: Boosting large language models via graph-centric instruction tuning and preference alignment. InACL, pages 13492–13510. Association fo...

arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [1]

Completion #1

Errors Analysis: Each incorrect completion reaches an incorrect answer due to misconception, please list the specific mistakes details. Cautions: - DO NOT disclose the complete number (e.g., "Completion #1")

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[2] [2]

I should double-check

Prejudge: You will start reasoning from the given initialized step, please generate some detailed prejudge information to ask yourself to avoid making errors. Cautions: - The generated prediction information is intended to guide the next step of reasoning to avoid errors, it should be closed to the possible errors and the detailed error analysis; - The ge...

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[3] [3]

If we round down $a_2 = 2.61$ and $a_3 = 2.65$ to 2: \[ \lvert A_2 - a_2 \rvert = \lvert 2 - 2.61 \rvert = 0.61 \] \[ \lvert A_3 - a_3 \rvert = \lvert 2 - 2.65 \rvert = 0.65 \] Maximum error is 0.65.<|think|> We see that rounding down $a_1 = 2.56$ and $a_2 = 2.61$ to 2 results in a maximum error of 0.61, which is the smallest among the evaluated combinati...

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[4] [6]

Associa- tion for Computational Linguistics

Are NLP models really able to solve simple math word problems? InNAACL, Online. Associa- tion for Computational Linguistics. Aske Plaat, Annie Wong, Suzan Verberne, Joost Broekens, Niki van Stein, and Thomas Bäck. 2024. Reasoning with large language models, a survey. CoRR, abs/2407.11511. Zhenting Qi, Mingyuan Ma, Jiahang Xu, Li Lyna Zhang, Fan Yang, and ...

arXiv 2024

[5] [7]

Chaojie Wang, Yanchen Deng, Zhiyi Lv, Zeng Liang, Jujie He, Shuicheng Yan, and Bo An

Solving math word problems with process- and outcome-based feedback.CoRR, abs/2211.14275. Chaojie Wang, Yanchen Deng, Zhiyi Lv, Zeng Liang, Jujie He, Shuicheng Yan, and Bo An. 2024a. Q*: Improving multi-step reasoning for llms with deliber- ative planning.CoRR, abs/2406.14283. Jianing Wang, Qiushi Sun, Xiang Li, and Ming Gao. 2024b. Boosting language mode...

arXiv

[6] [11]

If we round down $a_1 = 2.56$ and $a_2 = 2.61$ to 2: \[ 2 + 2 + 3 + 3 + 3 + 3 + 3 = 19 \] Errors: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_2 - a_2 \rvert = \lvert 2 - 2.61 \rvert = 0.61 \] Maximum error is 0.61

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[7] [12]

If we try rounding down $a_1 = 2.56$ and $a_3 = 2.65$ to 2: \[ 2 + 2 + 3 + 3 + 3 + 3 + 3 = 19 \] Errors: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_3 - a_3 \rvert = \lvert 2 - 2.65 \rvert = 0.65 \] Maximum error is 0.65. We should continue this process and consider other combinations to ensure the error is minimized.<|verify...

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[8] [13]

If we round down $a_1 = 2.56$ and $a_2 = 2.61$ to 2: \[ \lvert A_1 - a_1 \rvert = \lvert 2 - 2.56 \rvert = 0.56 \] \[ \lvert A_2 - a_2 \rvert = \lvert 2 - 2.61 \rvert = 0.61 \] Maximum error is 0.61

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