WarriorMath: Enhancing the Mathematical Ability of Large Language Models with a Defect-aware Framework

Dongmei Zhang; Fangkai Yang; Hao Sun; Lu Wang; Minghua He; Pu Zhao; Qingwei Lin; Saravan Rajmohan; Yifei Dong; Yue Chen

WarriorMath: Enhancing the Mathematical Ability of Large Language Models with a Defect-aware Framework

T0 review · 4 major / 3 minor · reviewed 2026-08-06 · deepseek-v4-flash

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

Pith's one-line read A defect-aware framework has LLMs generate problems they fail to solve, then trains on those weaknesses, claiming a 12.57% average gain over strong baselines on six math benchmarks.

desk verdict The framework is coherent and worth a look, but the 12.57% claim is a single unverified number that needs a contamination audit before it can be taken seriously. read the letter →

arxiv 2508.01245 v1 pith:GMIWUEXE submitted 2025-08-02 cs.CL

Yue Chen , Minghua He , Fangkai Yang , Pu Zhao , Lu Wang , Yu Kang , Yifei Dong , Yuefeng Zhan

show 4 more authors

Hao Sun Qingwei Lin Saravan Rajmohan Dongmei Zhang

This is my paper

classification cs.CL

keywords defect-awaredatasynthesisprogressivetrainingmathematicalreasoninglargelanguagemodelsmulti-expertcollaborationfine-tuning

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

WarriorMath tries to show that large language models can become substantially better at mathematical problem solving if the training data is built around the model's own failure modes rather than around rephrased or progressively harder problems. The authors propose a defect-aware synthesis stage where multiple expert LLMs generate, critique, and refine problems, focusing on questions the base model cannot solve. They then add a progressive training stage that fine-tunes the model on increasingly challenging data matched to its weaknesses. The paper claims this approach outperforms strong baselines by 12.57% on average across six mathematical benchmarks, setting a new state-of-the-art. A sympathetic reader would take the core claim to be that targeting defects directly, instead of generic augmentation, yields measurable gains in mathematical ability.

What carries the argument

The central mechanism is the defect-aware data synthesis loop: expert LLMs generate candidate problems, another expert critiques them, and refinement produces questions that expose and target the base model's specific mistakes. These questions are then used in a progressive training curriculum that escalates difficulty according to the model's weaknesses. The machinery works by converting the model's failures into training signal, so each fine-tuning round is aimed at the gap between current ability and required competence.

What would settle it

A concrete check would be to train WarriorMath on problems that are deliberately disjoint from the evaluation benchmarks in style and topic, then measure whether the reported 12.57% average improvement persists; if the gain largely disappears on such held-out benchmarks, the central claim of improved mathematical ability would be undermined.

Watch

Extended reading notes

Core claim

The paper's central claim is that LLM mathematical ability improves most when training data is generated adversarially to the model's current deficiencies. WarriorMath's synthesis stage uses multiple expert LLMs in a collaborative generate-critique-refine loop, and only questions that the base LLM fails to solve are kept and iteratively improved through expert feedback. The training stage then uses progressive fine-tuning, feeding the model increasingly challenging defect-aware data. The authors report that this defect-aware, multi-expert framework outperforms strong baselines by 12.57% on average over six mathematical benchmarks, which they describe as a new state-of-the-art.

Load-bearing premise

The paper assumes that the generated defect-aware problems are not leaked from or too similar to the six evaluation benchmarks, so that the measured gains reflect genuine mathematical reasoning rather than memorization of test-like questions.

Editorial extensions

If this is right

If the claimed 12.57% average improvement holds, defect-aware synthesis could become a standard component of LLM math training pipelines, reducing reliance on rephrasing-based augmentation.
Progressive training on defect-matched data may let smaller or weaker base models reach performance levels comparable to larger models on mathematical benchmarks.
The generate-critique-refine loop could be adapted to other reasoning domains where failure modes are identifiable, such as code generation or logical deduction.
The framework suggests that the quality of synthetic data is less about raw diversity and more about whether it targets the model's current limitations.

Reading between the lines

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

A testable extension would be to evaluate WarriorMath on held-out benchmarks that are temporally and topically disjoint from the training data, to confirm that the gains are from reasoning rather than from overfitting to benchmark-style problem distributions.
The defect-aware principle could be combined with process supervision: critiques generated during synthesis might double as step-by-step rationales, further boosting the training signal beyond just the final answer.
The progressive training schedule implies that the order of training data matters beyond its content, which suggests that curriculum design for LLMs may be as important as data volume.
One implicit consequence is that the same defect-aware loop could be run iteratively after each fine-tuning round, creating a self-improving cycle where the model's new failures become the next training batch.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Here's my read, based only on the abstract. The idea is actually decent: instead of blindly rephrasing or cranking up difficulty, generate problems that the base model currently fails, use multiple experts to critique and refine them, then train progressively on the harder failures. That is a plausible way to spend synthetic data budget, and the multi-expert critique step is a nice addition over the usual single-generator pipeline. The writing is clear about what the framework does, which counts for something.

The soft spot is exactly the one the stress test flags. The headline 12.57% average gain over strong baselines is an assertion, not evidence. There are no error bars, no baseline names, no benchmark details, and no code or data. More importantly, the contamination risk is load-bearing. The synthesis stage uses LLMs that were trained on web-scale corpora, and public math benchmarks are all over those corpora. If the generate-critique-refine loop produces near-duplicates of evaluation items, the progressive training stage could be concentrating on exactly the content that later shows up on the test sets. Without an overlap analysis between the synthetic training data and the six evaluation benchmarks, the 12.57% number is uninterpretable. That is not a minor omission; it is central to the claim.

I want to be fair though. Abstract-only reviews are inherently limited. The lack of detail is normal for an abstract, and the leakage concern is a concern, not a demonstrated flaw. The real question is whether the full paper ships with the necessary checks. If the authors provide code, data, and a contamination audit, the framework could be a useful contribution to synthetic data generation for math LLMs. If they don't, the result is just another unverifiable SOTA claim.

My verdict: the paper deserves a serious referee, because the method is coherent, the combination is new enough, and the empirical claim is strong enough that checking it is worthwhile. But I would want the referee to push hard on the leakage issue and on error bars. I would not cite this yet, since the evidence is too thin. I might bring it to reading group mainly to discuss the contamination methodology, which is a useful cautionary example.

Referee Report

4 major / 3 minor

Summary. The paper proposes WarriorMath, a defect-aware framework for improving LLM mathematical problem solving. The synthesis stage uses multiple expert LLMs to generate, critique, and refine problems that base LLMs fail, while the training stage progressively fine-tunes the model on increasingly challenging data. The abstract reports that on six mathematical benchmarks, WarriorMath outperforms strong baselines by 12.57% on average and claims a new state-of-the-art. Only the abstract was available for review, so the assessment is based on the claims and descriptions in that abstract.

Significance. If the reported results are reproducible and free of contamination, WarriorMath would offer a useful contribution by directly targeting LLM failure modes rather than merely increasing data volume. The multi-expert critique-and-refine loop is a plausible and well-motivated mechanism for generating high-quality training data. However, the abstract alone provides no experimental details, no error bars, no benchmark or baseline specifications, no ablation results, and no contamination analysis. The central empirical claim of a 12.57% average improvement is therefore currently unverifiable. The paper would be substantially strengthened by releasing the synthetic data and code, and by including an overlap audit between generated training data and evaluation benchmarks.

major comments (4)

[Abstract] The headline result, 'outperforms strong baselines by 12.57% on average,' is presented without error bars, number of runs, or any statistical significance measure. Since the evaluation spans six benchmarks with likely different scales, the aggregation method (e.g., simple average versus weighted) is undefined. Without this information, the reported improvement is not interpretable and cannot be independently verified.
[Abstract, synthesis stage] The defect-aware generation pipeline uses expert LLMs trained on web-scale corpora, which very likely include public math benchmarks that overlap with the six evaluation benchmarks. The abstract does not report any n-gram, embedding, or human-level overlap audit between generated training questions and benchmark test sets. Because the progressive training stage selects questions that the base model fails—which are often benchmark-like hard problems—any test-set leakage would be amplified. Without a contamination check, the 12.57% gain cannot be attributed to improved mathematical reasoning rather than memorization.
[Abstract, training stage] The progressive learning framework is described only qualitatively as 'iteratively fine-tunes the model using increasingly challenging data tailored to its weaknesses.' The abstract omits the number of iterations, the precise difficulty metric, the fine-tuning protocol (e.g., learning rates, batch sizes, number of epochs), and the base model architecture. These details are necessary to evaluate the framework's novelty, reproducibility, and incremental contribution over standard curriculum learning.
[Abstract, benchmarks and baselines] The six mathematical benchmarks are not named, and the 'strong baselines' are not specified. The evaluation metric and prompting protocol (e.g., chain-of-thought, tool use, answer extraction) are also absent. As a result, the claim of a 'new state-of-the-art' is unfalsifiable from the submitted material.

minor comments (3)

[Abstract] The term 'defect-aware' is used informally; please provide a formal definition, such as the exact criterion for identifying a defect or failure mode.
[Abstract, synthesis stage] The phrase 'questions that base LLMs fail to solve' lacks a failure criterion; specify, for example, whether failure means an incorrect final answer, a flawed reasoning chain, or a low confidence score.
[General] Please include a reproducibility statement with data and code availability, since the contribution is an empirical pipeline whose value depends on the synthetic data and training code being accessible.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity identified in the abstract-only material; the central claim rests on an external empirical comparison, not on a self-referential derivation.

full rationale

This review is based solely on the abstract; no full text, equations, or derivation chain are available. The abstract describes a synthesis stage that generates, critiques, and refines problems, followed by progressive training, and then reports improvements on six benchmarks. No step in this description defines the claimed output in terms of its inputs, fits a parameter and then calls it a prediction, or imports a conclusion from a self-citation. The only identifiable risk is potential benchmark contamination from LLM-generated training data, but that is a data-leakage and validity concern, not a circularity concern under the specified definitions. Without access to the method details, data filtering procedures, or benchmark overlap checks, no circular step can be quoted or exhibited. Therefore the appropriate finding is no significant circularity, with a score of 0.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim is an empirical performance claim; it rests on benchmark choice, the reliability of expert LLM critiques, and the absence of training/evaluation leakage. No new entities are introduced.

free parameters (2)

number of generate-critique-refine iterations = not reported
The synthesis pipeline repeats expert generation and critique some number of times; the abstract does not state this count, which is a tuning choice that affects data quality and compute cost.
failure criterion for base model = not reported
The framework selects problems that base LLMs fail to solve; the exact criterion (e.g., wrong final answer vs. incomplete reasoning) is a modeling decision not described in the abstract.

assumptions (3)

domain assumption The six selected benchmarks are a valid and representative measure of mathematical ability.
The claim of state-of-the-art performance rests on these benchmarks being the right yardstick, which is an evaluative choice, not a mathematical fact.
domain assumption Expert LLMs can reliably identify and refine flaws in generated math problems without introducing errors or leaking solutions.
The whole synthesis pipeline depends on the quality of critique from these LLMs.
domain assumption The progressive training schedule does not overfit to the synthetic data distribution.
If it overfits, the benchmark gains could be spurious.

how reviews work

0 comments

Cite this review

Pith. "Pith review of WarriorMath: Enhancing the Mathematical Ability of Large Language Models with a Defect-aware Framework." pith.science (2026). https://pith.science/paper/GMIWUEXE

@misc{pith2026250801245,
  author       = {Pith},
  title        = {Pith review of: WarriorMath: Enhancing the Mathematical Ability of Large Language Models with a Defect-aware Framework},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GMIWUEXE}},
  note         = {Machine review of arXiv:2508.01245}
}

read the original abstract

Large Language Models (LLMs) excel in solving mathematical problems, yet their performance is often limited by the availability of high-quality, diverse training data. Existing methods focus on augmenting datasets through rephrasing or difficulty progression but overlook the specific failure modes of LLMs. This results in synthetic questions that the model can already solve, providing minimal performance gains. To address this, we propose WarriorMath, a defect-aware framework for mathematical problem solving that integrates both targeted data synthesis and progressive training. In the synthesis stage, we employ multiple expert LLMs in a collaborative process to generate, critique, and refine problems. Questions that base LLMs fail to solve are identified and iteratively improved through expert-level feedback, producing high-quality, defect-aware training data. In the training stage, we introduce a progressive learning framework that iteratively fine-tunes the model using increasingly challenging data tailored to its weaknesses. Experiments on six mathematical benchmarks show that WarriorMath outperforms strong baselines by 12.57% on average, setting a new state-of-the-art. Our results demonstrate the effectiveness of a defect-aware, multi-expert framework for improving mathematical ability.

Discussion (0). Sign in to comment.

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.