arxiv: 2511.09907 · v5 · submitted 2025-11-13 · 💻 cs.AI · cs.CV

Learning to Pose Problems: Reasoning-Driven and Solver-Adaptive Data Synthesis

Yongxian Wei , Yilin Zhao , Zixuan Hu , Li Shen , Xinrui Chen , Runxi Cheng , Sinan Du , Hao Yu

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Chun Yuan Dian Li

This is my paper

Pith reviewed 2026-05-17 22:57 UTC · model grok-4.3

classification 💻 cs.AI cs.CV

keywords problem synthesisreasoning modelsadaptive data generationsolver feedbackchain of thoughtmathematical reasoningvision-language modelsdifficulty calibration

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The pith

A problem generator reasons explicitly about directions then adapts difficulty using solver feedback to synthesize high-value training data.

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

The paper introduces a problem generator for training large reasoning models that first plans problem directions through explicit reasoning and then adjusts difficulty based on how well the current solver performs. It starts by building related problem pairs and enriching them with chain-of-thought traces from a reasoning model to learn effective design strategies. The generator then treats the solver's success or failure on newly created problems as a reward signal, steering future synthesis toward problems that sit near the edge of the solver's current competence. This targets two common shortcomings in prior data synthesis: generating problems that ignore the solver's ability or relying on elaborate pipelines to balance difficulty. The approach is tested on ten mathematical and general reasoning benchmarks.

Core claim

By constructing related problem pairs, augmenting them with intermediate problem-design chain-of-thought, and using the solver's feedback as a reward signal, the generator learns to plan directions and calibrate difficulty so that it produces complementary problems near the solver's competence edge, resulting in a cumulative average improvement of 3.4 percent across ten benchmarks and generalization to both language and vision-language models.

What carries the argument

The solver-adaptive problem generator that bootstraps design strategies from augmented chain-of-thought on related problem pairs and treats solver feedback as a reward to adjust difficulty.

If this is right

Yields a cumulative 3.4 percent average improvement on ten mathematical and general reasoning benchmarks.
Generalizes across both language models and vision-language models.
Produces problems that are complementary to those a solver already handles well, rather than indiscriminate variants.
Bootstraps problem-design strategies from explicit reasoning traces without complex external pipelines.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The method could support iterative self-improvement where a model repeatedly generates and solves its own training problems.
Similar feedback-driven adaptation might apply to synthesizing code problems or scientific questions beyond the tested domains.
Combining the generator with existing data-augmentation techniques could further increase the efficiency of creating training sets.

Load-bearing premise

The solver's performance on the generated problems provides a reliable, unbiased signal for calibrating future problem difficulty.

What would settle it

An ablation that disables the solver-feedback reward and instead uses random or fixed difficulty targets, then measures whether the 3.4 percent benchmark gains disappear.

Figures

Figures reproduced from arXiv: 2511.09907 by Chun Yuan, Dian Li, Hao Yu, Li Shen, Runxi Cheng, Sinan Du, Xinrui Chen, Yilin Zhao, Yongxian Wei, Zixuan Hu.

**Figure 1.** Figure 1: Training pipeline for our problem generator. First, we employ a reasoning model with the reverse-engineered problem-design prompt to elicit latent CoT from constructed problem pairs. These traces bootstrap the generator’s initial ability to harden seed problems. Next, conditioned on a seed set, the generator proposes problems that the solver answers multiple times. We apply majority voting to form pseudo-l… view at source ↗

**Figure 3.** Figure 3: Performance comparison across iterations on all ten benchmarks. As the generator and solver are trained alternately in an iterative manner, the solver continues to improve, as evidenced by the expanding area of the radar chart. MathVista MathVision MathVerse 20 30 40 50 60 70 80 Accuracy (%) 68.4 23.35 43.53 69.0 29.28 45.23 69.8 29.60 46.40 69.3 27.63 45.58 69.3 26.64 44.72 70.3 27.63 46.17 69.1 28.29 45.… view at source ↗

**Figure 4.** Figure 4: Performance comparison on multimodal reasoning benchmarks. The VLM evaluated is Qwen2.5-VL-7B-Instruct, and the seed set is the MMK12 training split. erator’s reasoning on open-ended tasks, while the solver improves its mathematical ability using the generator’s synthetic problems. Both models are initially identical. After each training round, the solver’s enhanced ability alters its difficulty feedback,… view at source ↗

**Figure 5.** Figure 5: Training dynamics across iterations: the problem generator’s reward score, flip success rates (%) for the original and new problems, and changes in difficulty (%) for the original and new problems [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗

**Figure 6.** Figure 6: Self-Instruct prompt template for problem synthesis. Please create a new problem based on: <question>{Seed Question}</question>. Please reason step by step inside <think>...</think> and output only the final problem inside <question>...</question> [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 8.** Figure 8: Solver prompt template for problem solving. Please reason step by step, and put your final answer within \boxed{}. {Question}. B. Case Study We conduct a case study to illustrate the generator’s reasoning process. In [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗

**Figure 9.** Figure 9: The case study illustrates how two problem generators reason step by step, informed by the student’s performance, to create a new problem, and compares their responses to the same prompt. C. Co-evolutionary We co-train the problem generator and solver in an iterative manner: the generator leverages solver feedback as a reward to produce increasingly challenging problems, while the solver improves its reaso… view at source ↗

**Figure 10.** Figure 10: The contour density plot illustrating the relationship between Consistency and Accuracy across the MATH dataset. The color map represents the probability density estimated via Gaussian KDE, with lighter regions indicating a higher concentration of data points. The dashed red line shows the best-fit linear regression, and the yellow dotted line denotes the perfect correlation reference (y = x). Statistical… view at source ↗

read the original abstract

Data synthesis for training large reasoning models offers a scalable alternative to limited, human-curated datasets, enabling the creation of high-quality data. However, existing approaches face several challenges: (i) indiscriminate generation that ignores the solver's ability and yields low-value problems, or reliance on complex data pipelines to balance problem difficulty; and (ii) a lack of reasoning in problem generation, leading to shallow problem variants. In this paper, we develop a problem generator that reasons explicitly to plan problem directions before synthesis and adapts difficulty to the solver's ability. Specifically, we construct related problem pairs and augment them with intermediate problem-design CoT produced by a reasoning model. These data are used to bootstrap problem-design strategies in the generator. Then, we treat the solver's feedback on synthetic problems as a reward signal, enabling the generator to calibrate difficulty and produce complementary problems near the edge of the solver's competence. Extensive experiments on 10 mathematical and general reasoning benchmarks show that our proposed framework achieves a cumulative average improvement of 3.4%, demonstrating robust generalization across both language and vision-language models.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note private letter to a colleague

The paper builds a generator that plans problems with explicit CoT and adapts difficulty via solver feedback, but the 3.4% gains rest on thin experimental reporting so far.

read the letter

The main thing here is a synthesis method that first trains a generator on related problem pairs augmented with problem-design chain-of-thought, then uses the solver's own performance as a reward to steer toward problems near the competence edge. This directly targets the two issues called out in the abstract: generation that ignores what the solver already knows and variants that lack real reasoning structure behind them. The loop is straightforward and avoids some of the heavier pipelines in earlier work. The reported 3.4% average lift across ten benchmarks, with some carry-over to vision-language models, is the concrete outcome they highlight. That number is modest but could still matter if the gains hold under tighter controls. The soft spot is that the abstract gives almost no information on baselines, variance, exclusion rules, or statistical checks, so it is hard to tell how much of the lift traces to the new components versus other choices. The stress-test worry about noisy or biased feedback also lands: if the reward mixes prompt sensitivity or model-specific quirks rather than clean difficulty, the adaptation could reinforce narrow distributions instead of producing broadly useful data. Readers working on scalable reasoning data pipelines would find the most value, especially if they already use solver signals or CoT-style planning. The work shows clear thinking on the problem and honest engagement with prior limitations, so it deserves a serious referee to verify the experiments and see whether the adaptation delivers what the abstract claims.

Referee Report

2 major / 2 minor

Summary. The manuscript proposes a data synthesis framework for training reasoning models. It first constructs related problem pairs augmented with problem-design Chain-of-Thought produced by a reasoning model to bootstrap explicit planning strategies in a generator. It then treats solver feedback on generated problems as a reward signal to calibrate difficulty and synthesize complementary problems near the solver's competence boundary. Experiments across 10 mathematical and general reasoning benchmarks report a cumulative average improvement of 3.4% with generalization to both language and vision-language models.

Significance. If validated, the explicit reasoning step for problem planning combined with solver-adaptive difficulty calibration could improve the quality and relevance of synthetic data over indiscriminate generation or complex balancing pipelines. The approach credits the use of external solver performance as an adaptive signal rather than purely internal fitting, which is a constructive direction for scalable reasoning data synthesis.

major comments (2)

[§3.3] §3.3 (Difficulty Adaptation): Treating solver feedback (accuracy or error signals) as a reward for calibrating difficulty implicitly assumes this signal is a reliable, low-bias proxy for competence edge. The construction does not address how prompt sensitivity, model-specific failure modes, or sampling stochasticity are mitigated; if unaddressed, the adaptation loop risks reinforcing narrow distributions instead of producing genuinely complementary problems, which would undermine the generalization claim across 10 benchmarks.
[§5] §5 (Experiments): The reported 3.4% cumulative average improvement lacks any description of the baselines, number of independent runs, statistical significance tests, or data exclusion criteria. Without these controls it is impossible to determine whether the gains are attributable to the reasoning-driven generator and solver-adaptive loop or to uncontrolled factors in the evaluation setup.

minor comments (2)

[Abstract] The abstract uses 'cumulative average improvement' without clarifying whether this is an unweighted mean, a weighted sum, or aggregated across specific metrics; a precise definition would aid interpretation.
[§3] Notation for the reward signal derived from solver feedback should be introduced explicitly (e.g., as r(s) or similar) when first defined in the method section to improve readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We are grateful to the referee for the careful review and the recommendation for major revision. We believe the suggested changes will improve the paper, and we address the comments point-by-point below.

read point-by-point responses

Referee: [§3.3] §3.3 (Difficulty Adaptation): Treating solver feedback (accuracy or error signals) as a reward for calibrating difficulty implicitly assumes this signal is a reliable, low-bias proxy for competence edge. The construction does not address how prompt sensitivity, model-specific failure modes, or sampling stochasticity are mitigated; if unaddressed, the adaptation loop risks reinforcing narrow distributions instead of producing genuinely complementary problems, which would undermine the generalization claim across 10 benchmarks.

Authors: We thank the referee for this comment. The current version of the paper does not detail mitigations for prompt sensitivity, model-specific failure modes, or sampling stochasticity in the difficulty adaptation loop. We will revise the manuscript to include a discussion of these issues in §3.3, explaining our approach to using averaged feedback from multiple prompts and generations to reduce bias and stochastic effects. We believe this addition will support the generalization claims. revision: yes
Referee: [§5] §5 (Experiments): The reported 3.4% cumulative average improvement lacks any description of the baselines, number of independent runs, statistical significance tests, or data exclusion criteria. Without these controls it is impossible to determine whether the gains are attributable to the reasoning-driven generator and solver-adaptive loop or to uncontrolled factors in the evaluation setup.

Authors: We agree with the referee that the experimental section would benefit from more details on the evaluation protocol. The revised manuscript will expand §5 to describe the baselines compared against, the number of independent runs, the statistical significance tests performed, and any data exclusion criteria used in the experiments. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation grounded in external solver feedback and benchmark evaluation

full rationale

The paper's core construction bootstraps a generator from related problem pairs augmented with external reasoning-model CoT, then calibrates difficulty via solver feedback treated as a reward signal. Neither the claimed 3.4% cumulative improvement nor the adaptation loop reduces by construction to quantities defined solely by the generator's own fitted parameters or self-citations. Evaluation occurs on 10 independent mathematical and general reasoning benchmarks, providing external falsifiability. This satisfies the criteria for a self-contained empirical method with no load-bearing self-definition or fitted-input-as-prediction steps.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on two domain assumptions about the utility of reasoning-model-generated CoT for bootstrapping problem design and the informativeness of solver performance as a difficulty signal; no free parameters or invented entities are described.

axioms (2)

domain assumption A reasoning model can produce useful intermediate problem-design chain-of-thought from related problem pairs.
Invoked to bootstrap problem-design strategies in the generator.
domain assumption Solver feedback on synthetic problems provides a reliable signal for calibrating difficulty near the edge of competence.
Central to the reward-based adaptation step that produces complementary problems.

pith-pipeline@v0.9.0 · 5514 in / 1501 out tokens · 54372 ms · 2026-05-17T22:57:05.150346+00:00 · methodology

discussion (0)

Reference graph

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