Coarse-to-Fine Process Reward Modeling for Mathematical Reasoning

Jinman Zhao; Sheng Ouyang; Yong Liu; Yulan Hu

REVIEW 3 major objections 5 minor 1 cited by

Coarse-to-Fine Process Reward Modeling for Mathematical Reasoning

T0 review · 3 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

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

Pith's one-line read The paper claims that merging adjacent reasoning steps into coarse windows before training—then shrinking the window—improves process reward models for mathematical reasoning across every backbone, loss, and dataset tested.

desk verdict A simple data-augmentation trick for PRM training that looks useful at C=2, but the reported gains aren't cleanly attributable to the coarse-to-fine mechanism without an equal-data control. read the letter →

arxiv 2501.13622 v4 pith:7XWJES47 submitted 2025-01-23 cs.AI

Yulan Hu , Sheng Ouyang , Jinman Zhao , Yong Liu This is my paper · ORCID

classification cs.AI

keywords processrewardmodelmathematicalreasoningcoarse-to-finelearningstepmergingredundantstepsbest-of-nevaluationslidingwindowPRMtraining

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 argues that the step-level labels used to train process reward models are imprecise because LLM-generated reasoning steps often repeat or restate earlier information instead of adding new content. It proposes CFPRM, a coarse-to-fine strategy: merge C consecutive steps into a single coarse step, label that merged step by the label of its final step, then shrink C down to 1 so the training corpus contains the original fine steps alongside coarser ones. Tested on GSM-Plus and MATH500, with two backbone language models and three losses (MSE, BCE, Q-ranking), the added coarse samples improve average best-of-n accuracy for every baseline method when C=2, with gains of up to 3.4 points. If the claim holds, CFPRM is a plug-in data-augmentation method that improves PRM accuracy without changing the model architecture or loss function.

What carries the argument

The operative mechanism is a sliding-window merging-and-relabeling loop. For a trajectory $s_1,\dots,s_N$, a window size $C$ turns each block $s_{i:i+C-1}$ into one merged step whose label is the label of the last step $s_{i+C-1}$; the window slides over the whole trajectory, and the process repeats for every $C$ from $C_{\max}$ down to 1. The merged samples are combined with the original fine-grained steps into one corpus, which is traversed coarse-to-fine during training. This is the component that carries the reported gains: it supplies multi-granularity supervision without needing a redundant-step detector.

What would settle it

Hold the backbone, loss, and C fixed at the paper's best setting (C=2, MSE on the MATH backbone), and add a third training corpus matched in sample count but built by duplicating individual steps instead of merging windows. If best-of-n accuracy matches CFPRM, the coarse-to-fine relabeling is not the active ingredient; if it is clearly lower, the merging mechanism is confirmed.

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Extended reading notes

Core claim

The central discovery is that deliberately coarsening the granularity of process supervision—rather than detecting redundancy—is enough to make process reward models better. CFPRM slides a window of size C over a reasoning trajectory, merges each window into one holistic step, assigns it the label of its last individual step, and then repeats with C decreasing to 1. This produces a training set in which the model sees the same reasoning at several granularities; with C=2, all three tested PRM methods improve average best-of-n accuracy on both GSM-Plus and MATH500 under their native losses, and the MSE-trained baseline gains 1.3 and 3.4 points on the two benchmarks respectively.

Load-bearing premise

The whole method depends on treating the last step of a merged window as the truth of the entire window; if a correct earlier part followed by a wrong conclusion is too coarsely labeled, the relabeling could erase partial-progress signal instead of removing redundancy.

Editorial extensions

If this is right

CFPRM is a plug-in: it can be layered onto any existing PRM training pipeline without altering the loss objective, the backbone, or the sampling procedure.
At window size C=2, every base method improves average best-of-n accuracy on both GSM-Plus and MATH500, under both backbone models.
The optimal window size depends on the loss: Q-ranking, which evaluates transitions between adjacent steps, is more sensitive to large C, and at C=4 it can fall below the raw baseline.
Because the corpus is traversed from coarse to fine, the model first absorbs merged holistic steps and then the original fine steps, preserving fine-grained supervision.
CFPRM requires no explicit detection of redundant steps; it simply adds merged samples at multiple granularities to the existing training corpus.

Reading between the lines

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

Inference: the same coarse-to-fine relabeling could help PRMs in other multi-step domains, such as code repair or tool-use traces, where self-corrections and repeated statements are common, though the paper only tests mathematical reasoning.
Inference: the last-step labeling rule is a design choice rather than a necessity; majority voting over the window, or a mixed label, might handle windows that contain both a correct prefix and an incorrect conclusion, and comparing rules would separate the merging effect from the relabeling effect.
Inference: the reported gains could also be read as a data-augmentation effect rather than redundancy mitigation, because CFPRM adds extra training samples; a sample-matched control would test the stated mechanism.
Inference: the authors' own limitation notes point to adaptive window-size selection, and a loss-aware schedule for C could remove the C=4 regression seen with Q-ranking.

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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

Quick take: CFPRM is a simple, honest, plug-in data-formatting trick for process reward modeling. The contribution is real but small; the measured gains (0.5–3.4 points BoN) are plausible. The main thing to know: the paper's central claim—"consistent improvements irrespective of backbone or loss"—is supported only in the weak sense that adding merged coarse samples to the original fine-grained data helps. There is no control that adds the same number of extra training samples without the merging/relabeling. So we don't learn whether the mechanism is coarse-to-fine granularity or just more supervised data.

What's new and good: sliding-window merging of consecutive steps and relabeling by the last step is not in the cited baselines ShepHerd, ReSTMCTS*, or PQM. The idea is clearly presented, easy to reproduce (if code ships), and applied uniformly across three loss objectives. The Limitations section is refreshingly direct: it admits no redundant-step detection and no adaptive C. The paper doesn't oversell.

Soft spots, in order of importance:

1. The equal-data confound. Algorithm 1 adds all merged windows to the original data. Every CFPRM run trains on a strictly larger corpus than its baseline. Gains of 1–3 points could easily come from seeing more samples. A control that trains on the original data plus duplicated original steps, or on randomly paired windows with the same last-step labeling, would settle this. This is the biggest gap.

2. No variance or significance. They say five runs but report only means. With small effects (0.5–2 points on some cells), the consistent-improvement claim needs error bars, especially for the smaller gains.

3. C is chosen on the test sets. Figure 3 sweeps C=2,3,4 on GSM-Plus/MATH500, and Table 2 uses C=2. No validation split. If C were chosen on a held-out set, the result would be cleaner.

4. The last-step labeling rule is an assumption, not a mechanism. They label a merged window by its final step. If that rule corrupts training signal, the gains wouldn't come from the stated redundancy-reduction story. The paper doesn't test this directly.

None of these are fatal to the practical usefulness of the trick. If the code ships and the equal-data control confirms the effect, this is a decent minor contribution for PRM practitioners. But as it stands, the causal claim outruns the evidence.

Who should read it: people training PRMs or doing data-centric reasoning work. It's not a theory paper and doesn't need deep math; the value is empirical.

Recommendation: send it to review, but the referee should ask for the equal-data control, error bars, and a validation split for C. It's a legitimate short-paper contribution, not a desk reject.

Referee Report

3 major / 5 minor

Summary. The paper proposes CFPRM, a coarse-to-fine process reward model (PRM) training strategy. Reasoning traces are augmented by merging adjacent steps with a sliding window of size C, labeling each merged window by the label of its last step, and adding these merged samples to the original fine-grained data. The window size is gradually reduced from Cmax to 1, producing training data at multiple granularities. The authors evaluate CFPRM on GSM-Plus and MATH500 using two Qwen2.5-7B backbones and three loss objectives (BCE, MSE, Q-ranking) under best-of-n selection. The main results in Table 2 report consistent improvements when C=2; Figure 3 examines C=2, 3, 4 and finds mixed results, including a negative effect for C=4 with Q-ranking on MATH500.

Significance. If the central claim holds, CFPRM is a simple, plug-and-play data augmentation method that improves PRM accuracy without changing the architecture or loss function. The paper addresses a real issue—redundant steps in process supervision—and evaluates on external benchmarks with multiple backbones and loss criteria. The design is easy to reproduce, and the authors explicitly note that the method is applicable to arbitrary loss criteria. However, the significance is moderated by the absence of an equal-data control, which leaves open the possibility that the gains are a data-volume effect rather than a coarse-to-fine effect, and by the lack of statistical significance testing despite five repetitions.

major comments (3)

[§2.2 and §3.2 (Algorithm 1, Table 2)] The experimental protocol compares each baseline trained on the original fine-grained data with the same baseline trained on the original data plus all merged coarse samples. The CFPRM training corpus is therefore strictly larger than the baseline's. Reported improvements in best-of-n accuracy could be a trivial data-volume effect, independent of the proposed coarse-to-fine merging or the last-step labeling rule. The paper provides no ablation that trains a baseline on an equally sized augmented corpus (e.g., duplicated original steps, or randomly paired windows with a different labeling rule). Without such an equal-data control, the gains in Table 2 do not uniquely support the claim that merging and relabeling steps at multiple granularities is what helps. I request an additional experiment that isolates the data-volume factor.
[§3.2 and Figure 3] The main results fix C=2 and claim consistent improvements across all configurations. However, Figure 3 shows that C=2 is not uniformly best and that C=4 can hurt performance (e.g., Q-ranking on MATH500 drops below the raw baseline). The paper does not describe how C is selected; it appears to be chosen based on test-set performance. This undermines the generalizability claim and the statement that CFPRM 'consistently brings performance improvements.' Please report results for a C selected on a held-out validation split, or show that the main conclusions are robust to reasonable choices of C. In addition, the paper states that each experiment is repeated five times to report the mean, but no variance or significance test is given; with small effect sizes (0.5–1.8 points), error bars or a paired test are necessary to assess reliability.
[§2.2 'Merged steps labeling'] The label of a merged window is set to the label of its last step. This is a strong assumption: a correct step merged with a later wrong step is labeled entirely negative, and a wrong step followed by a correct step is labeled positive. The paper provides no justification or ablation for this relabeling rule, even though the entire data pipeline depends on it. I request an ablation comparing the last-step labeling rule against alternatives such as majority label, OR-label (any positive), or using the label of the final step in the window. This would clarify whether the proposed labeling contributes to the observed gains or merely preserves the original trajectory's outcome signal.

minor comments (5)

[Table 2] The 'Avg.' column is described as the average across four sampling conditions, but it is not clear whether this is the mean of @8/@16/@32/@64 or some other aggregate. Please make the definition explicit in the table caption.
[Abstract and §1] The abstract states 'Extensive experiments on two reasoning datasets across three loss criteria validate the CFPRM's effectiveness and versatility.' Given the mixed results for C=4 in Figure 3, the term 'extensive' is acceptable but 'validate' is too strong; consider softening to 'support' or 'demonstrate'.
[Figure 2] The label annotation in Figure 2 is confusing ('+ -Label + + - + +'). It would help to explicitly show which merged window receives which label and how the label is derived from the last step.
[§5 Limitations] The Limitations section mentions redundant-step detection and adaptive C, but does not acknowledge the increased training-data volume or the last-step labeling assumption as potential confounds. Adding these would give a more complete picture of the method's scope.
[§3.1] The paper says 'Our code will be released in the future.' For a methods paper, releasing code or at least providing detailed hyperparameters and data-processing scripts is important for reproducibility. Please clarify the release timeline or include a pseudo-code supplement beyond Algorithm 1.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reasoning; the method is an empirical data-augmentation strategy evaluated on external benchmarks, with no derivation equivalent to its inputs.

full rationale

The paper contains no derivation chain in which an output is defined from the input. CFPRM is a data-collection and relabeling procedure (Algorithm 1): it merges consecutive reasoning steps, assigns each merged window the label of its last step, and trains a PRM on the original fine-grained corpus plus the merged coarse samples. The evaluation uses external benchmarks GSM-Plus and MATH500, and the training data come from PRM800K; neither the benchmark labels nor the best-of-n accuracy are used to define the merged labels or to derive the method's predictions. The reported improvements in Table 2 are empirical measurements, not consequences of the method's definitions. The main methodological concerns raised by the skeptical reader are experimental-control issues rather than circularity: (i) the CFPRM training corpus is strictly larger than the baseline's, so the gains may partly reflect added training data rather than the coarse-to-fine mechanism; and (ii) C=2 is selected after the sensitivity study in Figure 3, and Figure 3 shows that some C values (notably C=4 for Q-ranking) do not improve over the baseline, so the 'consistent improvements across all configurations' claim is stronger than the full C sweep supports. The Limitations section itself acknowledges that 'the optimal C should be designed adaptively with respect to different loss criteria.' These are legitimate concerns about experimental design and generalization, but they do not make the central result equivalent to its inputs by construction. There are no load-bearing self-citations, no renamed known results presented as new theory, and no fitted parameter being relabeled as a prediction. The core empirical claim is therefore self-contained and not circular.

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

The central improvement rests on three domain assumptions and one hand-chosen parameter. The only numerical free parameter is the window size C, and the paper gives no validation-based selection procedure. Cmax and the exact multi-granularity composition are underspecified, and the relabeling rule is an unvalidated modeling choice. No new physical or mathematical entities are posited.

free parameters (2)

Window size C = 2 in main results; 3 and 4 explored
Chosen by hand with no validation split described. Section 3.2 sets C=2, and Section 3.3 varies C over the same test benchmarks, so the main choice is effectively tuned on test data.
Maximum window size Cmax = unspecified
Algorithm 1 requires a Cmax, but the main experiments report only C=2. The relationship between Cmax and the reported C is unclear, so the augmentation recipe cannot be exactly reconstructed.

assumptions (3)

domain assumption LLM reasoning steps often contain redundancy with no incremental information, and this redundancy hinders PRM training.
Stated in Section 1 and used to motivate CFPRM, but no quantitative evidence is given that the redundant steps in Figure 1 actually hurt trained PRMs.
domain assumption The merged window label can be taken from the last individual step.
Assumed in Section 2.2 under 'Merged steps labeling'. No experiment validates whether the last step's label is a good proxy for the merged chunk.
domain assumption Training sequentially from coarse to fine is beneficial.
The method combines all granularities and traverses from Cmax to 1, per Section 2.2 and Algorithm 1. No ablation isolates the contribution of this ordering versus simply adding all merged samples.

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Cite this review

Pith. "Pith review of Coarse-to-Fine Process Reward Modeling for Mathematical Reasoning." pith.science (2026). https://pith.science/paper/7XWJES47

@misc{pith2026250113622,
  author       = {Pith},
  title        = {Pith review of: Coarse-to-Fine Process Reward Modeling for Mathematical Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7XWJES47}},
  note         = {Machine review of arXiv:2501.13622}
}

read the original abstract

The Process Reward Model (PRM) plays a crucial role in mathematical reasoning tasks, requiring high-quality supervised process data. However, we observe that reasoning steps generated by Large Language Models (LLMs) often fail to exhibit strictly incremental information, leading to redundancy that can hinder effective reasoning. To address this issue, we propose CFPRM, a simple yet effective coarse-to-fine strategy. Instead of focusing on the detection of redundant steps, our approach first establishes a coarse-grained window to merge adjacent reasoning steps into unified, holistic steps. The window size is then progressively reduced to extract fine-grained reasoning steps, enabling data collection at multiple granularities for training. By leveraging this hierarchical refinement process, CFPRM mitigates redundancy while preserving essential fine-grained knowledge. Extensive experiments on two reasoning datasets across three loss criteria validate the CFPRM's effectiveness and versatility.

Figures

Figures reproduced from arXiv: 2501.13622 by the authors.

**Figure 1.** Redundant steps merging. proach involves constructing automatic labeling methods, either by defining the probability of each intermediate step as the potential to deduce the final correct answer (Wang et al., 2024), or by using a tree-based structure to iteratively refine the logits of each intermediate trajectory (Zhang et al., 2024). Despite the preliminary success of these methods, they primarily focus on accur… view at source ↗

**Figure 2.** Coarse-to-fine process data collection. Steps merging. Consider the problem in [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

**Figure 3.** The BoN accuracy change under different values of C. 3.2 Main Results For CFPRM, we set C to 2 to merge the adjacent two steps, showing the performance in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

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Reference graph

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Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.

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URL: " 'urlintro :=

ENTRY address author booktitle chapter edition editor howpublished institution journal key month note number organization pages publisher school series title type volume year eprint doi pubmed url lastchecked label extra.label sort.label short.list INTEGERS output.state before.all mid.sentence after.sentence after.block STRINGS urlintro eprinturl eprintpr...

[2] [2]

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 global.max substring 't := if while FUNCTION word.in bbl.in capitalize " " * FUNCT...

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Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 2023. Gpt-4 technical report. arXiv preprint arXiv:2303.08774

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Karl Cobbe, Vineet Kosaraju, Mohammad Bavarian, Mark Chen, Heewoo Jun, Lukasz Kaiser, Matthias Plappert, Jerry Tworek, Jacob Hilton, Reiichiro Nakano, et al. 2021. Training verifiers to solve math word problems. arXiv preprint arXiv:2110.14168

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Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al-Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Amy Yang, Angela Fan, et al. 2024. The llama 3 herd of models. arXiv preprint arXiv:2407.21783

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Dan Hendrycks, Collin Burns, Saurav Kadavath, Akul Arora, Steven Basart, Eric Tang, Dawn Song, and Jacob Steinhardt. 2021. Measuring mathematical problem solving with the math dataset. arXiv preprint arXiv:2103.03874

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Jie Huang, Xinyun Chen, Swaroop Mishra, Huaixiu Steven Zheng, Adams Wei Yu, Xinying Song, and Denny Zhou. 2023. Large language models cannot self-correct reasoning yet. arXiv preprint arXiv:2310.01798

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Jean Kaddour, Joshua Harris, Maximilian Mozes, Herbie Bradley, Roberta Raileanu, and Robert McHardy. 2023. Challenges and applications of large language models. arXiv preprint arXiv:2307.10169

arXiv 2023