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REVIEW 4 major objections 5 minor 2 cited by

Progressive Mastery: Customized Curriculum Learning with Guided Prompting for Mathematical Reasoning

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Customized Curriculum Learning orders post-training data by a model's own measured accuracy, turns too-hard problems into hint-assisted completion tasks, and reports that this beats uniform training on five mathematical reasoning…

desk verdict The 13.8-point GRPO gain is mostly sample filtering, not curriculum ordering or guided prompting, but the paper is honest enough to include the ablation that shows it. read the letter →

arxiv 2506.04065 v1 pith:TIWORS6B submitted 2025-06-04 cs.CL

Muling Wu , Qi Qian , Wenhao Liu , Xiaohua Wang , Zisu Huang , Di Liang , LI Miao , Shihan Dou
show 7 more authors
Changze Lv Zhenghua Wang Zhibo Xu Lina Chen Tianlong Li Xiaoqing Zheng Xuanjing Huang
This is my paper
classification cs.CL
keywords curriculumlearningmathematicalreasoninglargelanguagemodelsguidedpromptingsupervisedfine-tuningreinforcementGRPOdifficultyestimation
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 is trying to establish that post-training a language model on its own custom curriculum — easy problems first, hard problems last — works better than training on all examples uniformly. Difficulty is not taken from predefined labels but measured by asking the model to answer each problem several times and counting how often it gets it right. Problems the model cannot solve are not discarded; the first steps of the reference solution are given as a hint, converting an open-ended generation into a completion task. The paper reports average gains over uniform training in most settings across five mathematical reasoning benchmarks, in both supervised fine-tuning and reinforcement learning.

What carries the argument

The load-bearing object is a per-sample accuracy score, $\mathrm{ACC}_i = \frac{1}{n}\sum_{j=1}^{n}\mathbf{1}\{A_{ij}=A_i^*\}$, computed by sampling $n$ answers at temperature 0.7; its inverse orders the curriculum. Guided Prompting decomposes the golden solution into steps $\{s_{i1},...,s_{ik}\}$, chooses a prefix $P_i=\{s_{i1},...,s_{ip}\}$ short enough that the model's accuracy rises to a threshold $\tau$, and feeds $[Q_i;P_i]$ so the model completes the reasoning. Multi-stage training then applies supervised fine-tuning or Group Relative Policy Optimization (GRPO) sequentially to the easy, medium, and hard splits, mixing a small proportion of easy samples into later stages. Together these pieces convert a static dataset into a per-model course of study.

What would settle it

Retrain the best GRPO setting with the same three data splits and the same hints but with the stage order shuffled; if the shuffled model matches CCL's average accuracy, the reported gains come from data selection and hinting rather than from the easy-to-hard order.

Watch

Extended reading notes

Core claim

The central claim is that a training set should be ordered and rewritten according to the specific model being trained. CCL first computes an accuracy score for every question from $n$ sampled answers, ranks the questions by that score, and splits them into three equal stages; the least-accurate third is treated as difficult. For those difficult questions, the reference solution is decomposed into steps and a prefix is appended to the question as a hint, so the model is asked to complete the rest of the solution. Training proceeds stage by stage under supervised fine-tuning (SFT) or Group Relative Policy Optimization (GRPO), with a small fraction of earlier-stage samples mixed into later stages. On MATH-500, Minerva Math, OlympiadBench, AMC 23, and AIME 24, the paper reports that CCL outperforms uniform training in most of its comparisons, with the largest average gain under GRPO on the 1.5B model: 38.54 versus 24.74.

Load-bearing premise

The method assumes that 16 sampled answers at temperature 0.7 give a stable difficulty estimate for each problem, and that revealing the first steps of the reference solution as a hint teaches the model without simply leaking the answer.

Editorial extensions

If this is right

  • The same raw dataset yields different curricula for different models, so post-training can be customized per base model without hand-labeled difficulty levels.
  • Hard examples that are normally discarded can be kept by converting them into completion tasks, increasing the fraction of usable training data.
  • The staged schedule appears to help under both SFT and GRPO, so the ordering signal is not tied to one optimization objective.
  • Mixing a small proportion of easy samples into later stages is claimed to prevent catastrophic forgetting and is part of the best reported configuration.

Reading between the lines

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

  • The paper leaves implicit that the curriculum costs 16 extra forward passes per training sample before training starts; on very large datasets this precomputation, not the staged training itself, may dominate the added expense.
  • A test the paper does not run is whether the same hint prefix helps when given to a model that already answers the problem correctly; if it does, part of the gain may be a format effect rather than difficulty adaptation.
  • The prefix-hint idea should transfer to any domain with decomposable reference solutions, such as code generation or proof assistants, but the paper only claims evidence for mathematical reasoning.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. The paper proposes Customized Curriculum Learning (CCL), a post-training framework for mathematical reasoning that (i) defines sample difficulty adaptively per model by sampling multiple responses and measuring accuracy, (ii) partitions data into easy/medium/hard stages, (iii) converts hard samples into hint-guided completion tasks via step decomposition of reference solutions, and (iv) trains the model in multiple SFT or GRPO stages with a review mechanism. The empirical section reports results on Qwen2.5-Math-1.5B and 7B across five benchmarks (MATH500, Minerva Math, OlympiadBench, AIME24, AMC23), with main SFT and GRPO comparisons to uniform training and ablations on difficulty definition, hard-sample processing, and mixing strategy.

Significance. The idea of model-adaptive difficulty combined with hint-based reuse of hard samples is a plausible and practically motivated contribution, and the paper includes a reasonable range of benchmarks and both SFT and RL paradigms. The strongest part is the demonstration that discarding hard samples can help (Table 2) and that guided prompting can add a small further gain. However, the paper's central attribution — that the easy-to-hard curriculum ordering and guided prompting, rather than simple data filtering, drive the headline improvements — is not supported by the present experiments. The missing uniform-order-plus-filtered baseline and the unreported hyperparameters (tau, alpha) leave the main claim underdetermined. These issues are fixable within the manuscript's scope, so they warrant a major revision rather than rejection.

major comments (4)
  1. [Section 4.6.2 / Table 2] The ablation conflates curriculum ordering with data filtering and does not support the paper's causal attribution. For Qwen2.5-Math-1.5B GRPO, uniform training (Table 1) gives 24.74; retaining hard samples in a curriculum gives 26.36; discarding the hardest third gives 37.46; and CCL with guided prompting gives 38.54. Thus the dominant effect is dropping the hard third (+12.7 points), while curriculum ordering contributes about +1.6 and guided prompting about +1.1. The paper does not report a uniform-order baseline trained on the same filtered easy+medium dataset; without it, the claim that 'customized curriculum' and 'guided prompting' drive the improvement is not established. I request that this baseline be added, or that the conclusions be reframed to attribute the gains primarily to data filtering.
  2. [Section 4.5 / Table 1] The claim that CCL yields 'consistent performance gains across all test subsets' is contradicted by the paper's own table. Under SFT, MATH500 drops for both models (48.60 to 48.00 for 1.5B; 68.80 to 63.00 for 7B), and AIME24 is flat at 0 for 1.5B SFT. Additionally, no variance or multiple-seed results are reported anywhere, so even the positive differences of 1–2 points in other settings cannot be distinguished from noise. The authors should provide per-seed results or error bars, or temper the consistency claim to match the data.
  3. [Algorithm 1 / Appendix A] The two key hyperparameters of Guided Prompting, the accuracy threshold tau and the hint ratio alpha, are never reported in the paper or the appendix. Algorithm 1 uses them to decide which samples to keep with hints and how much of the solution prefix to reveal, so their values are essential to reproducing the method and to ruling out that they were tuned toward the test benchmarks. The authors should report specific values for tau and alpha for each model and setting, and ideally include a sensitivity analysis over a small grid.
  4. [Section 3.1 / Appendix A.1] The difficulty estimator uses only n=16 sampled answers at temperature 0.7 for each sample. This is a high-variance estimator: for a sample with true accuracy below 0.1, the probability of observing 0/16 is substantial, making the ordering within the difficult third effectively random. The paper does not report the distribution of ACC_i values, nor the fraction of samples with 0/16 or 1/16 accuracy, so the 'easy-to-hard' ordering component of CCL is not empirically verified. If the difficulty signal is too noisy, the observed gains would be explained by which samples are discarded rather than by the curriculum order. The authors should report the ACC_i summary statistics and, if feasible, a check with a larger n or multiple difficulty-estimation seeds.
minor comments (5)
  1. [Abstract / Section 4] The abstract and conclusion say CCL 'significantly outperforms' uniform training, but no significance tests or confidence intervals are reported; please soften to 'outperforms' or add error bars.
  2. [Equation (6)] There is a typo in the advantage formula: 'maen' should be 'mean'.
  3. [Section 3.3.1] The text says multi-stage SFT needs 'm rounds' but the dataset partitions are defined as p subsets in Section 3.1 and Algorithm 1; please use consistent notation.
  4. [Figure 3] The percentages in the Venn diagram are difficult to interpret (they do not sum to 100% and the figure lacks clear labels for each region); please add a clearer explanation, e.g., percentage of all questions in each category.
  5. [Appendix D / Figure 8] The stage-wise accuracy curves show no variance and are reported on the test sets; please add a sentence clarifying whether these are single runs and how much run-to-run variation is expected.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: CCL's adaptive difficulty is self-paced and evaluated on held-out benchmarks; self-citations are not load-bearing.

full rationale

I examined the derivation chain in Sections 3.1, 3.2, Algorithm 1, Tables 1-2, and the cited prior work. The difficulty label in Eq. (1) is the base model's own accuracy on each training problem, so it is a self-paced training signal rather than a hidden fit to test labels. The central comparison is against uniform training on external benchmarks (MATH500, Minerva, OlympiadBench, AIME24, AMC23), so the claimed improvement is not equivalent to the difficulty definition by construction. The ablation in Table 2 shows that most of the GRPO gain comes from discarding difficult samples and a smaller part from guided prompting; this is an attribution concern, not a circular reduction, because the experimental outcomes are measured rather than derived from the method's inputs. Citations to Xi et al. (2024) and Dou et al. (2025) overlap with the authors and motivate the hinting technique, but they are not the evidence for CCL's effectiveness, which is provided by the paper's own experiments; hence the self-citation is not load-bearing. Unreported hyperparameters tau and alpha and missing variance estimates are reproducibility concerns, not circularity. No self-definitional, fitted-input-as-prediction, uniqueness-importation, or ansatz-smuggling step appears in the paper. The derivation chain is therefore self-contained with respect to circularity.

Assumptions & free parameters 6 free parameters · 4 assumptions · 0 invented entities

The central claim rests mainly on hand-chosen hyperparameters (tau, alpha, p, n, temperature, review proportion) and on domain assumptions about difficulty estimation and hint validity; no code or data release.

free parameters (6)
  • accuracy threshold tau = not reported
    Used in Algorithm 1 line 10 to decide whether a hint is sufficient; never specified or swept.
  • hint ratio alpha = not reported
    Fraction of solution steps given as hint prefix; Algorithm 1 line 10; effect unknown, no sensitivity analysis.
  • number of stages p = 3
    Data split into three equal thirds by accuracy; p=3 chosen by hand, not justified.
  • sampling count n for difficulty = 16
    16 responses per question at temperature 0.7 to estimate ACC; small Monte Carlo sample, no variance reported.
  • temperature for difficulty estimation = 0.7
    Used to sample responses for ACC in Appendix A.1; not swept.
  • curriculum review mix proportion = not reported
    Fraction of easier samples mixed into later stages; mentioned in 4.6.3 but proportion not given.
assumptions (4)
  • domain assumption Training on samples far beyond current capability degrades performance.
    Stated in Section 3.2, supported by citing Yu et al. 2025 and Wen et al. 2025a; underpins discarding and hinting of hard samples.
  • domain assumption A prefix of the reference solution steps is a valid hint, and the remaining steps are a valid supervised target.
    Algorithm 1 lines 9-13; if the hint gives away the answer or the completion task differs from real reasoning, the gain is spurious.
  • domain assumption Accuracy over 16 sampled responses approximates true sample difficulty.
    Section 3.1 and Appendix A.1; no reliability check of ACC estimates.
  • ad hoc to paper Sequential training on three accuracy-based splits with review helps learning.
    This is the core CCL design; validated only by the paper's own comparison.

how reviews work

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Cite this review

Pith. "Pith review of Progressive Mastery: Customized Curriculum Learning with Guided Prompting for Mathematical Reasoning." pith.science (2026). https://pith.science/paper/TIWORS6B

@misc{pith2026250604065,
  author       = {Pith},
  title        = {Pith review of: Progressive Mastery: Customized Curriculum Learning with Guided Prompting for Mathematical Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/TIWORS6B}},
  note         = {Machine review of arXiv:2506.04065}
}
read the original abstract

Large Language Models (LLMs) have achieved remarkable performance across various reasoning tasks, yet post-training is constrained by inefficient sample utilization and inflexible difficulty samples processing. To address these limitations, we propose Customized Curriculum Learning (CCL), a novel framework with two key innovations. First, we introduce model-adaptive difficulty definition that customizes curriculum datasets based on each model's individual capabilities rather than using predefined difficulty metrics. Second, we develop "Guided Prompting," which dynamically reduces sample difficulty through strategic hints, enabling effective utilization of challenging samples that would otherwise degrade performance. Comprehensive experiments on supervised fine-tuning and reinforcement learning demonstrate that CCL significantly outperforms uniform training approaches across five mathematical reasoning benchmarks, confirming its effectiveness across both paradigms in enhancing sample utilization and model performance.

Figures

Figures reproduced from arXiv: 2506.04065 by the authors.

Figure 1
Figure 1. Overall pipeline of our method. Step 1: For each question in the training set, the model generates multiple responses and calculates the accuracy on that sample. Based on these accuracy scores, samples are ranked and organized into curriculum datasets. Step 2: Transforming difficult samples to reduce the answering difficulty for the model, bringing samples within the model’s solvable range. Step 3: The model undergo… view at source ↗
Figure 2
Figure 2. Performance of multiple models on MATH dataset subsets with predefined difficulty levels. As predefined difficulty increases from Level 1 to Level 5, model accuracy does not consistently decline but instead exhibits significant fluctuations, demonstrating that predefined difficulty standards may not correctly adapt to all models. defining difficulty using a uniform standard proves inadequate. Samples that are extrem… view at source ↗
Figure 4
Figure 4. Comparison of model performance after train [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figures from the paper (4 more)
Figure 5
Figure 5. Figure 5: Decomposition of reference answers into step-by-step solution. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]
Figure 6
Figure 6. Figure 6: Prompt Used in GRPO [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Prompt Used in SFT. Stage 1 Stage 2 Stage 3 19.5 20.0 20.5 21.0 21.5 22.0 22.5 Accuracy Qwen2.5-Math-1.5B - SFT Stage 1 Stage 2 Stage 3 26 27 28 29 30 Accuracy Qwen2.5-Math-7B - SFT Stage 1 Stage 2 Stage 3 34 35 36 37 38 Accuracy Qwen2.5-Math-1.5B - GRPO Stage 1 Stage …
Figure 8
Figure 8. Figure 8: Performance Across Training Stages Using CCL. [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]

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Forward citations

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    online" 'onlinestring :=

    ENTRY address archivePrefix author booktitle chapter edition editor eid eprint eprinttype howpublished institution journal key month note number organization pages publisher school series title type volume year doi pubmed url lastchecked label extra.label sort.label short.list...

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    write newline

    " write newline "" before.all 'output.state := FUNCTION n.dashify 't := "" t empty not t #1 #1 substring "-" = t #1 #2 substring "--" = not "--" * t #2 global.max substring 't := t #1 #1 substring "-" = "-" * t #2 global.max substring 't := while if t #1 #1 substring * t #2 gl...

Pith tools

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