FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline

Arpit Gupta; Chenyang Tao; Kartik Mehta; Mohit Bansal; Nanyun Peng; Parker Seegmiller; Shereen Oraby; Soumya Saha; Tagyoung Chung

REVIEW 3 major objections 5 minor 1 cited by

FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline

T0 review · 3 major / 5 minor · reviewed 2026-08-05 · deepseek-v4-flash

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Pith's one-line read A 50-20-20-10 blend of four data-synthesis agents makes a 7B math model reach 81.4% on MATH, beating much larger models.

desk verdict FLAMES is a well-controlled testbed for synthetic math data, but its headline gains over public datasets are likely inflated by eval-set tuning and missing decontamination. read the letter →

arxiv 2508.16514 v1 pith:6K3A5KX6 submitted 2025-08-22 cs.LG cs.AIcs.CL

Parker Seegmiller , Kartik Mehta , Soumya Saha , Chenyang Tao , Shereen Oraby , Arpit Gupta , Tagyoung Chung , Mohit Bansal

show 1 more author

Nanyun Peng

This is my paper

classification cs.LGcs.AIcs.CL

keywords mathreasoningsyntheticdatapipelinesynthesisagentsfine-tuningout-of-domaingeneralizationdistractionrobustnesseasy-to-hardFLAMESdataset

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

FLAMES is a controlled framework for studying the math-data synthesis pipeline one factor at a time: same seed problems, same problem generator, same solution generator, same student model, same evaluation. Using it, the paper claims that the biggest gains come from agents that increase problem complexity, that keeping more problems with imperfect solutions beats strict precision filtering (the tested solvability filter even rejects 30% of real MATH problems), and that GSM8K/MATH-seeded synthetic data transfers to competition-level benchmarks. From those findings it builds FLAMES datasets—a 50/20/20/10 blend of Suggester-Editor, IQC, Taxonomy-Based Key Concepts, and Distraction Insertion—and reports that FLAMES Large outperforms all tested public math datasets on OlympiadBench, CollegeMath, GSMPlus, and MATH, with Qwen2.5-Math-7B reaching 81.4% on MATH. The reason to care: prior synthetic-math works used incomparable setups, so practitioners could not tell which pipeline choices actually drive reasoning gains.

What carries the argument

The load-bearing object is the FLAMES framework: a standardized synthetic-data pipeline with fixed seed datasets (GSM8K and MATH), fixed problem-generation model (Qwen2.5-32B-Instruct), fixed solution-generation model (Qwen2.5-Math-7B-Instruct), fixed student model (DeepSeek-Math-7B), and fixed first-solution quality control. Inside it, the paper compares 12 data agents—prompt-based problem-synthesis strategies—including two new ones: Taxonomy-Based Key Concepts, which generates problems from a curated math taxonomy with no seed problems, and Distraction Insertion, which adds irrelevant details without changing the answer. The framework's one-factor-at-a-time design is what converts a jumble

What would settle it

Retrain a FLAMES mixture with the proportions chosen on only four of the five benchmarks, then evaluate on the held-out benchmark; if the margin over refreshed ScaleQuest shrinks or reverses on the held-out set, the reported superiority is partly benchmark tuning. A second check: replace the Qwen2.5-Math-7B-Instruct solution teacher with a weaker model and see whether the 'coverage beats precision' ordering flips on MATH.

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Extended reading notes

Core claim

On its own terms, the paper's discovery is that the math data synthesis pipeline can be decomposed into controllable factors and that a few simple design rules dominate: complexity-enhancing agents (Suggester-Editor and IQC) give the best overall improvements; coverage of generated problems matters more than the reliability of their solutions, so 'keep the first solution' and 'majority + first' outperform solvability and reward-model filtering; and the choice of solution-generation teacher matters more than the choice of problem-generation model. It then claims that combining 50% Suggester-Editor, 20% IQC, 20% Taxonomy-Based Key Concepts, and 10% Distraction Insertion produces a dataset that

Load-bearing premise

The load-bearing assumption is that the FLAMES mixture proportions, selected by running candidate mixtures on the same five evaluation benchmarks later used to certify the dataset, do not create an unfair advantage over public datasets whose compositions were not tuned on those benchmarks.

Editorial extensions

If this is right

With a fixed generation budget, complexity-enhancing agents should be preferred: they improved in-domain, robustness, and competition metrics simultaneously.
Strict solvability and reward-model filtering can be skipped; keeping first solutions and broader problem coverage performs better and costs less compute.
Synthetic data seeded only by GSM8K and MATH improved OlympiadBench, so easy problems can transfer to hard competition problems.
Investing in a stronger solution-generation teacher yields more student-model improvement than a stronger problem generator.
A small share (10%) of distraction-insertion data improves robustness and overall average without hurting in-domain scores.

Reading between the lines

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

The exact 50/20/20/10 proportions were picked on the same five benchmarks used for the final comparison, so part of the margin over public datasets could be selection artifact; a cleaner test would tune on a subset and hold out one benchmark.
The coverage-beats-precision result was established with Qwen2.5-Math-7B-Instruct as solution teacher; with a weaker teacher, noisy solutions could plausibly reverse the ordering.
The two novel agents suggest a general recipe: explicitly target the failure mode (OOD breadth via taxonomy, distraction robustness via insertion) and add a small portion of that data to a strong base mixture.
The easy-to-hard transfer result is tested only on English benchmarks; applying the same pipeline to other languages or formal math domains would show whether the finding generalizes.

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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

FLAMES is worth reading. It provides a controlled comparison of 12 data agents and 6 quality-control strategies under a single pipeline, with the sensible touch of refreshing public datasets with the same solution teacher. The two new agents—Taxonomy-Based Key Concepts and Distraction Insertion—are modest twists on existing ideas, but they are clearly described and their targeted effects (OOD and robustness) show up in the right places. The dataset blend also lifts small models substantially on competition benchmarks, which is a real finding if it holds.

The central internal comparisons are carefully run: same student model, same 150K scale, same solution generator. The finding that coverage beats precision in quality control is plausible and independently useful, as is the result that solution-teacher quality matters more than problem-teacher quality.

The soft spots are mostly about the external claims. First, decontamination is only reported against GSM8K/MATH test sets. CollegeMath, GSMPlus, and OlympiadBench are not checked, and the Taxonomy agent generates unseeded problems while the Distraction Insertion agent perturbs GSM8K in ways that could resemble GSMPlus. The largest reported gains are precisely on those benchmarks. So the easy-to-hard generalization and 'outperforms public datasets' claims need an overlap audit. Second, the final mixture proportions were chosen by looking at the same five evaluation sets (Table 11), and checkpoints were selected by test-set performance. That doesn't invalidate the relative agent ranking, but it means the margins over public datasets are partly a selection artifact. Third, there are no error bars or seeds, and the dataset is not released, so external validation is impossible right now.

The limitations section acknowledges teacher dependence and bias, but does not mention benchmark overlap or selection on eval sets, which are the more pressing risks.

This paper is aimed at anyone building synthetic math data or comparing data-synthesis methods. The framework itself is a contribution worth citing. It deserves a serious referee—the right outcome is peer review, not desk rejection—but the referee should ask for a contamination check on all five benchmarks, error bars or multiple seeds, and ideally a release of the FLAMES dataset.

Referee Report

3 major / 5 minor

Summary. The paper introduces FLAMES, a standardized framework for controlled comparison of synthetic math data pipelines. It studies 10 existing plus 2 novel data synthesis agents, 6 quality-control strategies, 2 problem-generation and 2 solution-generation models, and mixture proportions. The empirical findings are that complexity-enhancing agents help most, problem coverage matters more than solution precision, easy-to-hard generalization occurs, and a tuned blend (FLAMES Small/Large/XL) outperforms public datasets on MATH, CollegeMath, GSMPlus, and OlympiadBench. The internal comparisons are carefully controlled, but the dataset-level claims depend on decontamination and selection protocols that are currently incomplete.

Significance. If the dataset gains are robust, this is a valuable contribution: the framework enables apples-to-apples comparison of data synthesis strategies, the public baselines are refreshed with the same solution generator as a fairness control, and the final data pipeline uses only open-source models. The two novel agents are plausible and directly tested. The main risk is that the headline superiority over public datasets may be inflated by evaluation-set contamination and by tuning the mixture and checkpoints on the same benchmarks used for certification.

major comments (3)

[§2, Appendix A; Tables 3, 9] Decontamination is described only against the GSM8K and MATH test sets (Appendix A: 'decontaminating synthetic problems against the GSM8K and MATH test sets'). The largest reported gains are on OlympiadBench, CollegeMath, and GSMPlus, and these are exactly the benchmarks not audited. The Distraction Insertion agent (Figure 9) modifies GSM8K problems by inserting misleading details, the same perturbation family as GSMPlus; the Taxonomy-Based Key Concepts agent generates unseeded problems from a web-derived taxonomy and may reproduce or near-duplicate existing competition problems. Please run an overlap audit of FLAMES Large/XL against CollegeMath, GSMPlus, and OlympiadBench, report near-duplicate counts, and re-evaluate after removing them. The Limitations section (Section 7) does not mention this gap.
[§5.3, Appendix D.2, Table 11] The FLAMES mixture proportions were selected by evaluating candidate mixtures on the same five evaluation benchmarks that later certify the dataset (Table 11, Appendix D.2), and checkpoints were selected by highest average on GSM8K/MATH (Appendix A). The public datasets were not tuned in this way. This makes the claimed superiority over public datasets partly a selection artifact. Please provide a holdout evaluation or otherwise quantify the effect of benchmark-guided selection on the reported margins.
[Abstract vs §5.3, Tables 3 and 9] The headline numbers are computed against different baselines. The abstract's +15.7/+4.5/+6.5/+3.1 match the original (non-refreshed) ScaleQuest in Table 9, while Section 5.3's +12.8/+5.8/+4.9/+1.3 appear to be per-column best refreshed baselines from Table 3. This makes the claimed improvements difficult to interpret. Please report all deltas against a single consistent baseline, preferably the best refreshed public dataset at comparable scale.

minor comments (5)

[Appendix D.2] In the text describing mixture-D, 'IDC agent' should be 'IQC agent'.
[Table 5] The label 'DeepSeek-7B' for the solution-generation model should be expanded to 'DeepSeek-Math-7B-RL' to avoid confusion with the student model.
[Table 3] The 'GSM8K/MATH 15K' row should clarify whether this is the combined train split size or a subsample.
[§5.2] The statement 'data agents, while using only GSM8K and MATH as seed sets, lead to improvement over competition level benchmarks' is inaccurate for the QFT and Taxonomy agents, which do not use those seed sets. Please qualify.
[Section 7] The limitations section should also acknowledge the decontamination scope and the benchmark-guided mixture selection as potential threats to the dataset-level claims.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: FLAMES is an empirical evaluation study, and the concerns raised (mixture selection on eval benchmarks, limited decontamination) are validity risks, not self-referential reductions.

full rationale

FLAMES does not contain a derivation chain in which an output is defined in terms of an input, so none of the circularity patterns apply. The reader's main concern is that the FLAMES mixture proportions (50% Suggester-Editor, 20% IQC, 20% Taxonomy Key Concepts, 10% Distraction Insertion) were selected using the same five evaluation benchmarks that later certify FLAMES Large/XL (Section 5.3; Appendix D.2, Table 11). That is a legitimate selection-bias / overfitting concern, but it is not circularity by the standard used here: the mixture is a hyperparameter chosen by validation, and the reported 1M/1.5M results are measurements of the chosen configuration, not predictions derived from the selection criterion. No equation or definition in the paper makes the reported gains equal to the optimization target by construction. Similarly, decontamination only against GSM8K and MATH tests while evaluating on CollegeMath, GSMPlus, and OlympiadBench is a possible contamination risk, but it is an empirical validity gap, not a self-referential reduction. The paper's claims are supported by controlled comparisons and external benchmarks rather than by a self-citation chain or an imported uniqueness theorem. The few citations to prior work by overlapping authors (e.g., Hase et al. 2024; He et al. 2024) are contextual and not load-bearing. Therefore the honest finding is no significant circularity.

Assumptions & free parameters 5 free parameters · 4 assumptions · 4 invented entities

The central empirical claims rest on several hand-picked design choices: the mixture proportions, the quality-control default, the data budget, the checkpoint selection rule, and the solution sampling policy. The paper also assumes domain assumptions about benchmark validity, transfer from synthetic data, and fidelity of agent re-implementations. No new physical or mathematical entities are introduced; the new artifacts are the dataset and two data agents, none of which have independent external validation.

free parameters (5)

FLAMES Small mixture weights (50% Suggester-Editor, 20% IQC, 20% Taxonomy Key Concepts, 10% Distraction Insertion) = 0.5/0.2/0.2/0.1
Chosen manually after evaluating candidate mixtures on the same five evaluation benchmarks (Table 11, Appendix D.2). These weights are tuned to the eval suite that later measures FLAMES performance.
Quality control default: 'First solution' (keep first generated solution, no verification) = First
Selected in Table 1 based on in-domain GSM8K/MATH performance; this choice fixes the default for all subsequent agent and dataset experiments.
Data generation budget per agent = 150K problems (75K GSM8K-seeded + 75K MATH-seeded)
Arbitrary budget chosen for the agent comparison; budget affects absolute performance and may interact with agent quality.
Checkpoint selection rule = best average GSM8K+MATH among 10 saved checkpoints
Reports the best checkpoint, not a fixed epoch or averaged run; inflates reported scores relative to any single checkpoint.
Solution sampling policy = one sample (temperature 0.7), first kept
The 'First solution' policy is chosen after comparing against self-consistency variants; this is a hyperparameter of the pipeline.

assumptions (4)

domain assumption Fine-tuning a base math LLM on the generated synthetic data improves performance on held-out math benchmarks and transfers across model families.
Central to the entire evaluation; assumed because the experimental results consistently show gains, but this is an empirical regularity, not proven.
domain assumption The five evaluation benchmarks (GSM8K, MATH, CollegeMath, GSMPlus, OlympiadBench) are a valid proxy for math reasoning ability.
Section 2 lists them as in-domain, OOD, robustness, and competition measures; no external validation that these benchmarks capture the intended capabilities beyond standard practice.
domain assumption The solution generation model's outputs are mostly correct and can serve as training targets; inaccurate solutions remain useful up to a point.
Section 5.1 conclusion 'coverage matters more than accuracy' depends on this assumption that noisy solutions still teach useful reasoning.
domain assumption Data agents listed in Table 7 faithfully reproduce the strategies from their source papers.
The authors implemented 10 existing agents based on descriptions in prior work; fidelity to the originals is assumed and not verified against official code.

invented entities (4)

FLAMES dataset (Small 150K, Large 1M, XL 1.5M)
purpose: Training data for fine-tuning math LLMs; the paper's main artifact.
Not released with the preprint; its claimed benefits rest only on the paper's own evaluations.
Taxonomy-Based Key Concepts agent
purpose: Generates OOD problems from a curated math taxonomy without seed problems.
Evaluated only in this paper; no external validation or release of the taxonomy.
Distraction Insertion agent
purpose: Adds misleading details to problems to improve robustness.
Only evaluated in this paper; no external reproduction yet.
Math taxonomy curated from several sources
purpose: Drives the Taxonomy-Based Key Concepts agent's problem generation.
The taxonomy itself is not released and its coverage and quality are not independently measured.

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Cite this review

Pith. "Pith review of FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline." pith.science (2026). https://pith.science/paper/6K3A5KX6

@misc{pith2026250816514,
  author       = {Pith},
  title        = {Pith review of: FLAMES: Improving LLM Math Reasoning via a Fine-Grained Analysis of the Data Synthesis Pipeline},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/6K3A5KX6}},
  note         = {Machine review of arXiv:2508.16514}
}

read the original abstract

Recent works improving LLM math reasoning with synthetic data have used unique setups, making comparison of data synthesis strategies impractical. This leaves many unanswered questions about the roles of different factors in the synthetic data pipeline, such as the impact of filtering low-quality problems. To address this gap, we introduce FLAMES, a Framework for LLM Assessment of Math rEasoning Data Synthesis, and perform a systematic study of 10 existing data synthesis strategies and multiple other factors impacting the performance of synthetic math reasoning data. Our FLAMES experiments provide several valuable insights about the optimal balance of difficulty and diversity of synthetic data. First, data agents designed to increase problem complexity lead to best improvements on most math metrics. Second, with a fixed data generation budget, keeping higher problem coverage is more important than keeping only problems with reliable solutions. Third, GSM8K- and MATH-based synthetic data can lead to improvements on competition-level benchmarks, showcasing easy-to-hard generalization. Leveraging insights from our FLAMES experiments, we design two novel data synthesis strategies for improving out-of-domain generalization and robustness. Further, we develop the FLAMES dataset, an effective blend of our novel and existing data synthesis strategies, outperforming public datasets on OlympiadBench (+15.7), CollegeMath (+4.5), GSMPlus (+6.5), and MATH (+3.1). Fine-tuning Qwen2.5-Math-7B on the FLAMES dataset achieves 81.4% on MATH, surpassing larger Llama3 405B, GPT-4o and Claude 3.5 Sonnet.

Figures

Figures reproduced from arXiv: 2508.16514 by the authors.

**Figure 1.** MATH benchmark scores for popular LLMs. Qwen2.5-Math-7B + X (FLAMES or OrcaMath) denotes results obtained by finetuning Qwen2.5-Math-7B model with X dataset. Comparison of FLAMES data with other public Math datasets is shown in Tables 3, 4. Hendrycks et al., 2021). Due to the challenges of creating a large-scale human-crafted dataset, LLMbased generation of synthetic data has been explored and proven effective in… view at source ↗

**Figure 2.** Landscape of recent math data synthesis works. Each work uses non standardized setups, such as different synthesis models, student models, and quality control, making comparison across works impractical. Detailed version is shown in Appendix [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** Overview of the FLAMES framework, showing fine-grained components of the Math data synthesis [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (7 more)

**Figure 4.** Figure 4: Examples of our novel Distraction Insertion [PITH_FULL_IMAGE:figures/full_fig_p014_4.png]

**Figure 5.** Figure 5: The full landscape of several recently-proposed math data synthesis works. Each work uses different [PITH_FULL_IMAGE:figures/full_fig_p017_5.png]

**Figure 6.** Figure 6: Prompt for extracting key concepts from existing GSM8K and MATH problems. Used in both Key [PITH_FULL_IMAGE:figures/full_fig_p019_6.png]

**Figure 7.** Figure 7: Prompt for using key concepts to generate synthetic problem. Used by Key Concepts agent ( [PITH_FULL_IMAGE:figures/full_fig_p020_7.png]

**Figure 8.** Figure 8: Prompt for using problem and key concepts to generate synthetic problem. Used by Seeded Key Concepts [PITH_FULL_IMAGE:figures/full_fig_p020_8.png]

**Figure 9.** Figure 9: Prompt used to generate synthetic problems using the novel Distraction Insertion agent (see Section [PITH_FULL_IMAGE:figures/full_fig_p021_9.png]

**Figure 10.** Figure 10: Prompt used to filter unsolvable synthetic problems ( [PITH_FULL_IMAGE:figures/full_fig_p021_10.png]

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Reference graph

Works this paper leans on

7 extracted references · 5 canonical work pages · cited by 1 Pith paper

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Your response is about generic concept and does not use specifics like numbers or words or object from the problem, so that the key concept can be used to generate related but different problems

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[2]

[https://huggingface.co/ AI-MO/NuminaMath-CoT](https://github.com/ project-numina/aimo-progress-prize/blob/ main/report/numina_dataset.pdf)

Numinamath. [https://huggingface.co/ AI-MO/NuminaMath-CoT](https://github.com/ project-numina/aimo-progress-prize/blob/ main/report/numina_dataset.pdf). Qintong Li, Leyang Cui, Xueliang Zhao, Lingpeng Kong, and Wei Bi. 2024. Gsm-plus: A comprehen- sive benchmark for evaluating the robustness of llms as mathematical problem solvers. arXiv preprint arXiv:24...

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[5]

Your response provide granular details so that this response can be independently used to create a similar problem for teaching this key concept. Below are few examples : Problem : In how many ways can 5 students be selected from a group of 6 students? Solution : We can choose 5 students out of a group of 6 students without regard to order in binom{6}{5} ...

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[6]

The given problem is a math problem

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Please reason step by step and conclude with either ‘Yes’ or ‘No’

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work page 2024
[2021]

small- size

and MATH (Hendrycks et al., 2021) training sets. These agents interact with the Qwen2.5-32B- Instruct model (Yang et al., 2024b) to generate new problems, an open-source instruction-tuned Factor Value Controlled/PriorLocation Problem Generation Data Synthesis Agent 10 Existing, 2 Novel Controlled Section 5.2 Problem Generation Model Qwen2.5-32B-Instruct C...

work page 2021
[2024]

arXiv preprint arXiv:2406.11704

Nemotron-4 340b technical report. arXiv preprint arXiv:2406.11704. Zheng Cai, Maosong Cao, Haojiong Chen, Kai Chen, Keyu Chen, Xin Chen, Xun Chen, Zehui Chen, Zhi Chen, Pei Chu, et al. 2024. Internlm2 technical re- port. arXiv preprint arXiv:2403.17297. Zui Chen, Tianqiao Liu, Mi Tian, Qing Tong, Weiqi Luo, and Zitao Liu. 2025. Advancing math reasoning in...

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Pith tools

Reviewed August 5, 2026 · model on record in the stance chip above.

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Your response is about generic concept and does not use specifics like numbers or words or object from the problem, so that the key concept can be used to generate related but different problems

work page

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[https://huggingface.co/ AI-MO/NuminaMath-CoT](https://github.com/ project-numina/aimo-progress-prize/blob/ main/report/numina_dataset.pdf)

Numinamath. [https://huggingface.co/ AI-MO/NuminaMath-CoT](https://github.com/ project-numina/aimo-progress-prize/blob/ main/report/numina_dataset.pdf). Qintong Li, Leyang Cui, Xueliang Zhao, Lingpeng Kong, and Wei Bi. 2024. Gsm-plus: A comprehen- sive benchmark for evaluating the robustness of llms as mathematical problem solvers. arXiv preprint arXiv:24...

arXiv 2024

[3] [5]

Your response provide granular details so that this response can be independently used to create a similar problem for teaching this key concept. Below are few examples : Problem : In how many ways can 5 students be selected from a group of 6 students? Solution : We can choose 5 students out of a group of 6 students without regard to order in binom{6}{5} ...

work page

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The given problem is a math problem

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Please reason step by step and conclude with either ‘Yes’ or ‘No’

The given math problem can be solved based on the conditions provided in the problem (You can first try to solve it and then judge its solvability). Please reason step by step and conclude with either ‘Yes’ or ‘No’. Given Problem: {problem} Figure 10: Prompt used to filter unsolvable synthetic problems (Ding et al., 2024), see Section 4

work page 2024

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small- size

and MATH (Hendrycks et al., 2021) training sets. These agents interact with the Qwen2.5-32B- Instruct model (Yang et al., 2024b) to generate new problems, an open-source instruction-tuned Factor Value Controlled/PriorLocation Problem Generation Data Synthesis Agent 10 Existing, 2 Novel Controlled Section 5.2 Problem Generation Model Qwen2.5-32B-Instruct C...

work page 2021

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arXiv preprint arXiv:2406.11704

Nemotron-4 340b technical report. arXiv preprint arXiv:2406.11704. Zheng Cai, Maosong Cao, Haojiong Chen, Kai Chen, Keyu Chen, Xin Chen, Xun Chen, Zehui Chen, Zhi Chen, Pei Chu, et al. 2024. Internlm2 technical re- port. arXiv preprint arXiv:2403.17297. Zui Chen, Tianqiao Liu, Mi Tian, Qing Tong, Weiqi Luo, and Zitao Liu. 2025. Advancing math reasoning in...

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