Reinforcing Step-level Reasoning for Effective Self-Correction in LLMs

Cong-Duy Nguyen; Do Xuan Long; Luu Anh Tuan; Nhat M. Hoang; Ponhvoan Srey; Vu Duc Anh

REVIEW 3 major objections 5 minor 12 references

Reinforcing Step-level Reasoning for Effective Self-Correction in LLMs

T0 review · 3 major / 5 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Training LLMs to detect and repair their own erroneous reasoning steps, in two reinforcement-learning stages, produces larger and more robust accuracy gains on math benchmarks than step-level preference learning alone.

desk verdict A novel two-stage self-correction recipe whose headline comparison against Step-DPO is confounded by extra data and compute, yet the idea is worth sending to a serious referee. read the letter →

arxiv 2608.11573 v1 pith:H2XEQASH submitted 2026-08-12 cs.CL cs.AI

Vu Duc Anh , Nhat M. Hoang , Do Xuan Long , Cong-Duy Nguyen , Ponhvoan Srey , Luu Anh Tuan This is my paper · ORCID

classification cs.CLcs.AI

keywords self-correctionstep-levelreasoningpreferenceoptimizationdirectmathematicallargelanguagemodelsreinforcementlearningerrordetection

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

This paper claims that a language model becomes a more reliable mathematical reasoner when it is explicitly trained to detect and repair its own erroneous reasoning steps, rather than only to prefer better next steps. The proposed two-stage framework first applies step-level preference optimization to strengthen step-wise reasoning, then trains the model to prefer a continuation that flags and fixes an incorrect step over a continuation that leaves the error in place. A teacher-assisted variant adds a rationale explaining each detected error, and the reported evaluations on seven 7B-14B LLMs across four math benchmarks show consistent gains over step-preference and self-correction baselines, including out-of-domain problems. The paper's behavioral analysis argues that what matters is not how often a model corrects itself but how selectively and accurately it does so.

What carries the argument

The load-bearing object is the step-wise self-correction preference pair. Formally, for a trajectory prefix ending at an incorrect step $s_k^-$, the chosen continuation $c_k^+$ is built as an error-detection signal $d_{k-1}$ followed by the corrected step $s_k^+$ (plus, in SFS-DPO-R, a teacher rationale $r_{k-1}$); the rejected continuation is $s_{k+1}^-$, the step the model would produce if the error were left unaddressed. A direct preference optimization (DPO) loss $L_{\mathrm{SC}}$ pushes the policy toward the corrected continuation and away from the error-continuing continuation, while the first-stage loss $L_{\mathrm{Pre}}$ aligns next-step preferences on correct prefixes. The mechanism converts a coarse answer-level signal into a localized repair-level signal, and the paper argues that selectivity, or knowing when not to correct, is part of what the objective teaches.

What would settle it

Run the trained models on a held-out set where every transition phrase from the training list is paraphrased or replaced, and ask human annotators to mark whether the flagged step truly contains an error and whether its position matches the actual first error; if self-correction rate and Error Recall fall to near-chance when the memorized phrases are unavailable, the paper's selective-correction claim is contradicted.

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Extended reading notes

Core claim

On the paper's own terms, the central discovery is that step-level self-correction should be trained as an explicit preference: given an incorrect step $s_k^-$ following a correct prefix, the model is taught to prefer the continuation $c_k^+ = \{d_{k-1}, s_k^+\}$ that first emits an error-detection signal and then a corrected step, over the continuation $s_{k+1}^-$ that would follow if the error were ignored. This objective is applied after an initialization stage of step-level preference optimization, which the experiments show is necessary: removing it, or training correction jointly with reasoning, degrades performance on MATH and GSM8K. With the rationale-augmented variant, each correction is preceded by a teacher-generated explanation of why the previous step is wrong. The paper reports that this recipe outperforms the step-preference baseline in 11/14 settings (SFS-DPO) and 12/14 settings (SFS-DPO-R), yields consistent out-of-domain gains, and produces fewer but more effective self-corrections than SFT-based self-correction baselines.

Load-bearing premise

The load-bearing premise is that a model emitting one of the training signal phrases (such as 'The previous step is incorrect') has genuinely detected and localized an error; if the model only memorizes the phrases without finding real mistakes, the paper's self-correction metrics would overstate its correction ability.

Editorial extensions

If this is right

If the central claim holds, step-level self-correction training is a more direct route to accuracy gains than step-level preference learning alone: the proposed methods beat the step-preference baseline in 11/14 and 12/14 in-domain settings, with average MATH gains of 1.11% and 1.36% over seven backbones.
The gains transfer out of domain: on GK2023 and OCW, the methods maintain or improve accuracy on every backbone, with Qwen2.5-Math-7B-Instruct improving by 10.9 points on GK2023 and 8.8 points on OCW.
Initialization order matters: removing the step-level RL initialization, training correction jointly with reasoning, or replacing it with standard RL initialization all degrade MATH and GSM8K performance, so the sequential two-stage design is load-bearing.
More self-correction is not better: despite lower self-correction rates and lower Error Recall than prior SFT-based self-correction baselines, the proposed models reach higher accuracy, implying selective correction rather than frequent correction is the operative mechanism.
Explanatory rationales add value: the teacher-assisted variant's error explanations consistently improve over the teacher-free variant, particularly on in-domain accuracy, suggesting that the 'why' behind an error is useful supervision.

Reading between the lines

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

My inference, beyond the paper: because the detection signal and the evaluation metric share the same transition phrase list, the paper's self-correction rate and Error Recall likely overstate genuine error localization; a paraphrase-invariant probe would separate phrase recall from real detection.
My inference, beyond the paper: the two-stage structure, step-preference first and repair-preference second, is a transferable recipe for any domain where errors localize to discrete steps, such as code debugging or multi-hop fact-checking; the paper only tests mathematics.
My inference, beyond the paper: since teacher rationales appear only in training data, the teacher-assisted variant is a form of rationale distillation; a natural extension is to test whether students that generate their own explanations at inference time retain the gains without teacher dependence.

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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

Dear colleague,

Two things to know about arXiv:2608.11573. First, the proposed SFS-DPO / SFS-DPO-R recipe is genuinely new: a Step-DPO initialization followed by a preference objective that contrasts a self-corrected continuation against an unaddressed erroneous continuation, with a teacher-rationale variant. That specific construction is not in the cited prior work. Second, the paper's central comparison is confounded: SFS-DPO gets 8,416 extra training pairs and four extra epochs in Stage 2, while the Step-DPO baseline appears to get only the 10K initialization set. The paper never runs a control on the same 8,416 samples without the self-correction signal, so the observed gains over Step-DPO can't be attributed cleanly to the self-correction formulation.

What the paper does well: the experiments are broad (seven backbones, in-domain plus OOD), the ablations in Table 4 suggest the two-stage design matters, and the authors are transparent about using the same transition phrases for training and evaluation. They also report McNemar's tests on the main benchmarks and explain why OOD tests are underpowered. The qualitative examples are helpful, even though a couple show SFS-DPO-R still going wrong.

Soft spots, in order of severity. The data/compute confound is the big one; it needs a same-data control before the central claim is credible. The behavioral metrics (self-correction rate, Error Recall) are partly circular, since the model is trained to emit the same phrases that later count as self-correction. The effect sizes are small—often under one point—and many differences are not statistically significant. And there's no code or data release, which makes reproducibility a real question.

The paper is not a waste of time. If you work on self-correction or step-level preference optimization, the idea is worth engaging with. My recommendation: send it to peer review, but tell the authors to add a control that trains on the same 8,416 samples with a standard step-preference objective, and to either de-couple the behavioral metrics from the training phrases or present them as what they are—proxy measures. That would turn a conditional paper into a solid one.

Referee Report

3 major / 5 minor

Summary. The paper proposes SFS-DPO, a two-stage reinforcement learning framework for step-level self-correction in LLM math reasoning. Stage 1 applies step-level preference optimization (Step-DPO-style) to strengthen step-wise reasoning; Stage 2 trains the model to prefer a self-corrected continuation that explicitly detects and fixes an erroneous step over a continuation that leaves the error unaddressed. A teacher-assisted variant, SFS-DPO-R, augments the correction with GPT-4o-generated rationales. The paper evaluates on MATH, GSM8K, GK2023, and OCW across seven 7B-14B backbones, reports gains over Step-DPO and over SFT-based self-correction baselines, and analyzes self-correction frequency, error recall, and qualitative behavior. The central claim is that explicitly modeling step-level self-correction yields stronger gains than prior step-wise preference learning.

Significance. If the central comparison were clean, the paper would make a useful contribution: it connects step-level preference learning with explicit self-correction training, uses substantially less data than several prior self-correction methods, and evaluates across a broad set of modern open-weight LLMs. The loss formulation is a standard DPO variant, which makes the method easy to implement, and the multi-backbone evaluation is a genuine strength. However, the headline comparison against Step-DPO is confounded by additional training data and epochs, and the behavioral metrics are partly circular because the same transition phrases used to construct training targets are used to detect self-correction in evaluation. The core accuracy results are not invalidated, but the evidence for the self-correction mechanism as the cause of the gains is not yet established.

major comments (3)

[Section 4.1 and Table 2] The headline comparison against Step-DPO is confounded by training data and compute. Step-DPO is trained only on the 10K step-preference set, while SFS-DPO and SFS-DPO-R receive the same 10K set plus 8,416 self-correction preference pairs and four additional epochs in the second stage. Table 4 varies the initialization strategy but keeps the second stage fixed, so it does not provide the necessary control: a model trained on the same 8,416 derived pairs with an ordinary next-step preference objective (or with the same epochs) but without the self-correction formulation. Without this control, the observed gains in Table 2 could be due to more preference optimization on question-derived pairs rather than to explicit step-level self-correction. Please add this matched-data control or explicitly re-scope the claim as a systems comparison.
[Section 4.1 and Figure 6] The behavioral metrics are partly circular. The training data for Stage 2 are built by appending one of the transition phrases in Figure 6 to the correct step to form the chosen continuation, and the same phrase list is then used to automatically identify self-correction in generated responses. Thus higher self-correction rate and Error Recall may partly reflect imitation of the training template rather than genuine error localization. This affects the interpretation of Section 5.3 and Table 3, where lower self-correction rates are interpreted as 'selective' correction. Please either use a held-out set of detection signals or validate the behavioral metrics against human annotations of true error detection.
[Section 4.3 and Appendix A] The out-of-domain claims are made without uncertainty quantification. Appendix A states that significance tests are omitted for GK2023 and OCW due to small sample sizes, but Section 4.3 asserts 'consistent improvements' and substantial OOD gains. With 385 and 272 test items, differences of a few percentage points correspond to small counts; please provide confidence intervals, exact McNemar p-values (even if underpowered), or a clear statement that OOD differences are within noise. This is needed to support the generalization claim.

minor comments (5)

[Section 4.3, Table 2] The claim that SFS-DPO and SFS-DPO-R 'consistently maintain or improve accuracy across all backbones and datasets' is not literally true for Qwen2-7B-SFT on GK2023, where SFS-DPO scores 46.0 versus a 46.2 baseline.
[Section 5.3, Figure 2] The text asserts a positive correlation between self-correction rate and task accuracy, but no correlation coefficient or statistical test is reported; please quantify the relationship.
[Table 5] The SFS-DPO-R qualitative trace contains conflicting reasoning, including a statement that '20 hours' is the correct total work time and then a correction that the total should be 40 hours; the example should be edited or replaced to clearly support the claim of targeted correction.
[Section 4.1] Error Recall is defined only as 'the fraction of incorrect reasoning steps that the model flags via a self-correction signal'; the manuscript should specify how incorrect steps are annotated in evaluation and whether the annotation is step-level gold data or automatically derived.
[Appendix A] The one-sided McNemar's tests are applied per setting without multiple-comparison correction across the 14 in-domain settings in Table 2; at minimum, report raw p-values and the number of comparisons.

Circularity Check

1 steps flagged · score 4.0 of 10

Behavioral self-correction metrics are partly circular because the transition phrases used to detect self-correction at evaluation are the same phrases used to construct the Stage-2 training targets; benchmark accuracy remains externally grounded.

self definitional [Section 4.1 (Dataset Construction & Training Setup), Figures 6-7; metrics defined in Section 4.1]
"Following Pan et al. (2025), to construct the chosen step, we concatenate the correct reasoning step with a self-correction signal. The same set of signal phrases, listed in Figure 6, is then used to automatically identify self-correction behavior in generated responses."

In Stage 2, the preferred continuation is defined as c+_k = {d_{k-1}, s+_k}, where d_{k-1} is an error-detection signal drawn from the Figure 6 transition phrases, and L_SC trains the model to prefer that continuation. The evaluation then counts any generation containing those same phrases as 'self-correction' for the self-correction rate and Error Recall metrics. Thus the behavioral evidence for 'the model detects and corrects its own errors' is largely a re-measurement of the training target itself: a model can score higher on these metrics by memorizing the signal phrases rather than by localizing actual reasoning errors.

full rationale

The central benchmark results are evaluated against external test sets (MATH, GSM8K, GK2023, and OCW), so the main claim of accuracy improvement is not circular. The only identified circularity is in the behavioral analysis: self-correction rate and Error Recall are defined using the same Figure 6 transition phrases that were inserted into the chosen continuations during Stage-2 training, making the measured behavior partly coincide with the training objective by construction. The skeptical concern that SFS-DPO receives extra preference pairs and epochs relative to Step-DPO is a comparison confound, not a definitional or self-citation circularity, and is therefore noted but not counted as a circular step. No load-bearing self-citation or imported uniqueness claim was found.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central claim rests on the Step-DPO dataset labels, the DPO objective, and the assumption that the transition phrases mark genuine self-correction. The SFS-DPO-R variant additionally depends on GPT-4o rationales. No invented entities are introduced; the method is a training objective applied to existing models.

free parameters (1)

beta (preference regularization coefficient) = not reported
Appears in both loss objectives (L_Pre and L_SC) but its value is never given in the paper, leaving the exact training objective under-specified.

assumptions (4)

domain assumption Step-level correctness labels in the Step-DPO dataset are accurate.
Both training stages rely on the 10K step-level preference dataset from Lai et al. (2024); the paper does not audit label quality.
standard math The DPO loss is a valid surrogate for the desired preference ordering at the step level.
The method inherits the DPO framework (Rafailov et al., 2023) and Step-DPO (Lai et al., 2024) without re-deriving its assumptions.
domain assumption The transition signal phrases from Pan et al. (2025) reliably mark genuine self-correction.
These phrases are used both to construct the chosen training continuations and to detect self-correction in generated responses, so the behavioral metrics assume they indicate real error detection.
domain assumption GPT-4o-generated rationales in SFS-DPO-R are correct and beneficial.
The teacher variant assumes the rationales are high-quality; the paper does not measure rationale accuracy separately.

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Cite this review

Pith. "Pith review of Reinforcing Step-level Reasoning for Effective Self-Correction in LLMs." pith.science (2026). https://pith.science/paper/H2XEQASH

@misc{pith2026260811573,
  author       = {Pith},
  title        = {Pith review of: Reinforcing Step-level Reasoning for Effective Self-Correction in LLMs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/H2XEQASH}},
  note         = {Machine review of arXiv:2608.11573}
}

read the original abstract

Achieving effective self-correction, where models verify and correct their own mistakes, remains a fundamental challenge for large language models (LLMs). In this work, we propose Self-Fix Step-DPO (SFS-DPO), a reinforcement learning based, two-stage framework for step-level self-verification and self-correction. The first stage strengthens step-level reasoning via step-level preference optimization, while the second stage explicitly trains models to self-verify and self-correct. We further introduce a teacher-assisted variant, SFS-DPO-R, which incorporates explanatory rationales for error verification to provide stronger corrective signals. Comprehensive in-domain and out-of-domain evaluations across multiple LLMs demonstrate that SFS-DPO and SFS-DPO-R consistently outperform prior step-level training baselines. Our analysis further reveals improvements in self-correction frequency and effectiveness, highlighting the importance of strengthening step-level reasoning for robust performance.

Figures

Figures reproduced from arXiv: 2608.11573 by the authors.

**Figure 1.** Initialization Stage (Stage 1) learns local step preferences by favoring correct continuations over incorrect ones, without revising errors. Step-wise SelfCorrection (Stage 2) complements this by training explicit self-corrections: revising incorrect steps toward preferred continuations before proceeding, converting step-wise preferences into targeted multi-step reasoning improvements. has inspired a parallel line… view at source ↗

**Figure 2.** Self-correction rate of SFS-DPO-R under five Instruct LLMs. Self-correction rate shows a positive [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Distribution of numbers of self-correction [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 5.** Figure 5: Self-correction rate of SFS-DPO-R under two [PITH_FULL_IMAGE:figures/full_fig_p011_5.png]

**Figure 6.** Figure 6: Dataset construction for SFSDPO with the set of transition phrases fetched from [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]

**Figure 7.** Figure 7: Illustration of the process for constructing the SFS-DPO-R dataset. Incorrect intermediate reasoning steps [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

12 extracted references · 7 canonical work pages

[5]

The previous step is incorrect

Direct preference optimization: Your language model is secretly a reward model.Advances in neural information processing systems, 36:53728–53741. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language mode...

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[8]

Step 3: We also know that cos(90◦−x) is equal to the sine of the angle x

This means that statement B is true. Step 3: We also know that cos(90◦−x) is equal to the sine of the angle x. So, cos(90◦−x) = sinx . And we know that sinx= 42

work page
[9]

Step 4: However, statement D says that sin(90◦−x)−cos = 0

This means that statement C is true. Step 4: However, statement D says that sin(90◦−x)−cos = 0 . But we just found out that sin(90◦−x) = cosx and cosx= 42

work page
[10]

This means that statement D is also true

So, sin(90◦−x)−cos = 42 59− 42 59 = 0. This means that statement D is also true. « Repeated block » « Repeated block » « Repeated block » « Repeated block » No answer SFS-DPO-R Step 1: We know that in a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, sinx= 42 59...

work page
[11]

This means statement D is true

So, sin(90◦−x)−cos= cosx−cosx= 0 . This means statement D is true. So, all the statements A, B, C, and D are true. But the question asks for the statement that is NOT true. So, there must be a mistake in our reasoning. Let’s retrace our steps. Upon closer inspection, we realize that in step 4, we assumed thatsin(90◦−x) = cosx . But this is not correct. Th...

work page
[12]

A",A,N); label(

With this correction, we can see that statement B is not true. So, the statement that is NOT true is B. The answer is: B Table 10: Qualitative comparison on the Gaokao2023 dataset between the base Qwen2-7B-SFT model and Qwen2- 7B-SFT-SFS-DPO-R. While the base model produces a seemingly coherent but incomplete reasoning trajectory, SFS-DPO-R explicitly ide...

work page
[13]

Self-Fix Step-DPO

We include one comparison with LEMMA and S2R, where these methods exhibit self-correction behavior but still produce excessive or insuffi- ciently targeted revisions. The remaining exam- ples focus on the base model and Step-DPO. The base model often propagates earlier errors with- out explicit repair, while Step-DPO can improve local step preference but ...

work page 2025
[59]

Step 2: We also know that sin(90◦−x) is equal to the cosine of the angle x

This means that statement A is true. Step 2: We also know that sin(90◦−x) is equal to the cosine of the angle x. So, sin(90◦−x) = cosx . And we know that cosx= 42

work page

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Training verifiers to solve math word prob- lems.Preprint, arXiv:2110.14168. Aaron Grattafiori, Abhimanyu Dubey, Abhinav Jauhri, Abhinav Pandey, Abhishek Kadian, Ahmad Al- Dahle, Aiesha Letman, Akhil Mathur, Alan Schelten, Alex Vaughan, et al. 2024. The llama 3 herd of mod- el...

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InThe Twelfth Inter- national Conference on Learning Representations

Let’s verify step by step. InThe Twelfth Inter- national Conference on Learning Representations. Haoxiong Liu, Yifan Zhang, Yifan Luo, and Andrew C Yao. 2025. Augmenting math word problems via 9 iterative question composing. InProceedings of the AAAI Conference on Artificial I...

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Step-level value preference optimization for mathematical reasoning. InFindings of the Associ- ation for Computational Linguistics: EMNLP 2024, pages 7889–7903, Miami, Florida, USA. Association for Computational Linguistics. Qiguang Chen, Libo Qin, Jinhao Liu, Dengyun Peng, Ji...

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.

[1] [5]

The previous step is incorrect

Direct preference optimization: Your language model is secretly a reward model.Advances in neural information processing systems, 36:53728–53741. Zhihong Shao, Peiyi Wang, Qihao Zhu, Runxin Xu, Junxiao Song, Xiao Bi, Haowei Zhang, Mingchuan Zhang, YK Li, Yang Wu, et al. 2024. Deepseekmath: Pushing the limits of mathematical reasoning in open language mode...

arXiv 2025

[2] [8]

Step 3: We also know that cos(90◦−x) is equal to the sine of the angle x

This means that statement B is true. Step 3: We also know that cos(90◦−x) is equal to the sine of the angle x. So, cos(90◦−x) = sinx . And we know that sinx= 42

work page

[3] [9]

Step 4: However, statement D says that sin(90◦−x)−cos = 0

This means that statement C is true. Step 4: However, statement D says that sin(90◦−x)−cos = 0 . But we just found out that sin(90◦−x) = cosx and cosx= 42

work page

[4] [10]

This means that statement D is also true

So, sin(90◦−x)−cos = 42 59− 42 59 = 0. This means that statement D is also true. « Repeated block » « Repeated block » « Repeated block » « Repeated block » No answer SFS-DPO-R Step 1: We know that in a right triangle, the sine of an angle is defined as the ratio of the length of the side opposite the angle to the length of the hypotenuse. So, sinx= 42 59...

work page

[5] [11]

This means statement D is true

So, sin(90◦−x)−cos= cosx−cosx= 0 . This means statement D is true. So, all the statements A, B, C, and D are true. But the question asks for the statement that is NOT true. So, there must be a mistake in our reasoning. Let’s retrace our steps. Upon closer inspection, we realize that in step 4, we assumed thatsin(90◦−x) = cosx . But this is not correct. Th...

work page

[6] [12]

A",A,N); label(

With this correction, we can see that statement B is not true. So, the statement that is NOT true is B. The answer is: B Table 10: Qualitative comparison on the Gaokao2023 dataset between the base Qwen2-7B-SFT model and Qwen2- 7B-SFT-SFS-DPO-R. While the base model produces a seemingly coherent but incomplete reasoning trajectory, SFS-DPO-R explicitly ide...

work page

[7] [13]

Self-Fix Step-DPO

We include one comparison with LEMMA and S2R, where these methods exhibit self-correction behavior but still produce excessive or insuffi- ciently targeted revisions. The remaining exam- ples focus on the base model and Step-DPO. The base model often propagates earlier errors with- out explicit repair, while Step-DPO can improve local step preference but ...

work page 2025

[8] [59]

Step 2: We also know that sin(90◦−x) is equal to the cosine of the angle x

This means that statement A is true. Step 2: We also know that sin(90◦−x) is equal to the cosine of the angle x. So, sin(90◦−x) = cosx . And we know that cosx= 42

work page