arxiv: 2604.03647 · v2 · submitted 2026-04-04 · 💻 cs.CV · cs.AI

Recognition: 2 theorem links

· Lean Theorem

Stabilizing Unsupervised Self-Evolution of MLLMs via Continuous Softened Retracing reSampling

Yunyao Yu , Zhengxian Wu , Zhuohong Chen , Hangrui Xu , Zirui Liao , Xiangwen Deng , Zhifang Liu , Senyuan Shi

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Haoqian Wang

Authors on Pith no claims yet

Pith reviewed 2026-05-13 17:43 UTC · model grok-4.3

classification 💻 cs.CV cs.AI

keywords self-evolutioncsrsreasoningcontinuousmodelretracingsoftenedunsupervised

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The pith

CSRS improves MLLM self-evolution stability by using retracing mechanisms and softened continuous rewards instead of majority voting, reaching SOTA on geometric reasoning benchmarks like MathVision.

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

Multimodal large language models can try to improve themselves without human labels by generating their own training signals. The common approach picks the answer that appears most often across many tries, but this can just reinforce the model's existing mistakes or biases rather than finding correct reasoning. The new method adds a retracing step where the model goes back to key points and tries different paths again to explore less common but possibly better reasoning routes. It also uses a softened reward that gives partial credit based on how frequently an answer appears across samples instead of all-or-nothing. An extra visual perturbation step forces the model to focus on the actual math logic rather than surface image features. Experiments on a 7B model show better performance on math vision benchmarks and state-of-the-art results for geometric tasks.

Core claim

Experimental results demonstrate that CSRS significantly enhances the reasoning performance of Qwen2.5-VL-7B on benchmarks such as MathVision. We achieve state-of-the-art (SOTA) results in unsupervised self-evolution on geometric tasks.

Load-bearing premise

The assumption that frequency of answers across sampled reasoning paths (even after softening) reliably indicates objective correctness rather than shared model biases, combined with the claim that visual semantic perturbation successfully shifts focus to mathematical logic.

Figures

Figures reproduced from arXiv: 2604.03647 by Hangrui Xu, Haoqian Wang, Senyuan Shi, Xiangwen Deng, Yunyao Yu, Zhengxian Wu, Zhifang Liu, Zhuohong Chen, Zirui Liao.

**Figure 1.** Figure 1: Overview of our work. During unsupervised self-evolutionary reinforcement learning, traditional majority voting methods (left) for pseudo-labeling rely solely on the model’s inherent biases. This frequently leads to model collapse, where the model degenerates into a deterministic mapping and fails to explore the true solutions. To alleviate this phenomenon, our method introduces CSRS (right) to reduce the… view at source ↗

**Figure 2.** Figure 2: Pipeline of our method. (Round1) illustrate initially maternal trajectories and answers generated by MLLM. (Round2) shows three core components of CSRS and improvement to rewards. man solve a problem. These pivots are key steps that shape the following reasoning and determine whether the final answer is correct. 3.2.2 Algorithm Details To overcome the training instability and model collapse caused by the b… view at source ↗

**Figure 3.** Figure 3: Visualization of the accuracy and propotion of high-confidence samples during training. (a) Answer accuracy calculated within partitioned frequency intervals, where each sample is uniquely assigned based on its frequency. (b) The evolution of high-confidence (frequence ∈ [0.8 − 1.0]) samples proportions during training, which serves as a key indicator of model collapse [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗

**Figure 4.** Figure 4: The change of distribution of Maternal Answers Set and Re-inference Answers Set. The figure shows different distribution of samples in two sets at the step of 20,60,100. Blue dots represent the semantic space of vanilla responses, while orange dots denote the semantic space of responses generated by CSRS. prehensive evaluation ranging from formal geometric problems to complex mathematical reasoning situa… view at source ↗

**Figure 5.** Figure 5: Entropy Change during training We further compare the evolution of policy entropy between our proposed CSRS and the Majority Voting baseline (MM-UPT) throughout the training process, as illustrated in [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗

**Figure 6.** Figure 6: Case studies in geometric reasoning. 16 [PITH_FULL_IMAGE:figures/full_fig_p016_6.png] view at source ↗

read the original abstract

In the unsupervised self-evolution of Multimodal Large Language Models, the quality of feedback signals during post-training is pivotal for stable and effective learning. However, existing self-evolution methods predominantly rely on majority voting to select the most frequent output as the pseudo-golden answer, which may stem from the model's intrinsic biases rather than guaranteeing the objective correctness of the reasoning paths. To counteract the degradation, we propose Continuous Softened Retracing reSampling (CSRS) in MLLM self-evolution. Specifically, we introduce a Retracing Re-inference Mechanism (RRM) that the model re-inferences from anchor points to expand the exploration of long-tail reasoning paths. Simultaneously, we propose Softened Frequency Reward (SFR), which replaces binary rewards with continuous signals, calibrating reward based on the answers' frequency across sampled reasoning sets. Furthermore, incorporated with Visual Semantic Perturbation (VSP), CSRS ensures the model prioritizes mathematical logic over visual superficiality. Experimental results demonstrate that CSRS significantly enhances the reasoning performance of Qwen2.5-VL-7B on benchmarks such as MathVision. We achieve state-of-the-art (SOTA) results in unsupervised self-evolution on geometric tasks. Our code is avaible at https://github.com/yyy195/CSRS.

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

CSRS adds retracing, softened frequency rewards, and visual perturbation to majority-voting self-evolution, with reported gains on MathVision, but the evidence that it actually favors correctness over model biases is still missing.

read the letter

The main takeaway is that this paper gives a concrete recipe for stabilizing unsupervised self-evolution in MLLMs. It replaces plain majority voting with three pieces: retracing re-inference to pull in more long-tail paths, a continuous softened frequency reward instead of binary selection, and visual semantic perturbation to steer away from superficial image cues. They test on Qwen2.5-VL-7B and report clear lifts on MathVision plus a SOTA claim for unsupervised geometric reasoning, with code released on GitHub.

Referee Report

3 major / 2 minor

Summary. The paper proposes Continuous Softened Retracing reSampling (CSRS) to stabilize unsupervised self-evolution in multimodal LLMs. It introduces a Retracing Re-inference Mechanism (RRM) to expand exploration of long-tail reasoning paths, a Softened Frequency Reward (SFR) that replaces binary majority-voting rewards with continuous frequency-based signals, and Visual Semantic Perturbation (VSP) to reduce reliance on visual superficial cues in favor of mathematical logic. Experiments on Qwen2.5-VL-7B report significant gains on geometric reasoning benchmarks such as MathVision, reaching SOTA results for unsupervised self-evolution.

Significance. If the central empirical claims hold after proper controls, the work would offer a practical alternative to majority-voting self-training that mitigates model bias amplification. The combination of retracing sampling, continuous rewards, and targeted perturbation addresses a recognized weakness in current self-evolution pipelines for MLLMs on tasks requiring precise visual-mathematical alignment.

major comments (3)

[Experimental Results / Abstract] The central claim that SFR supplies a more reliable training signal than majority voting rests on the unverified assumption that softened answer frequencies correlate with objective correctness rather than shared model biases. The manuscript provides no quantitative validation (e.g., Pearson correlation between SFR scores and ground-truth accuracy on a labeled subset of MathVision, or accuracy lift when training on SFR-selected vs. majority-voted paths).
[Experimental Results] The paper asserts that VSP successfully shifts model focus from visual superficiality to mathematical logic, yet no ablation isolates the contribution of VSP (e.g., CSRS without VSP vs. full CSRS) or measures reduction in visual-error modes on geometric problems. Without these controls, the SOTA claim on MathVision cannot be attributed to the proposed mechanisms.
[Experimental Results] No information is given on experimental controls: number of independent runs, statistical significance of reported gains, hyper-parameter sensitivity of the softening temperature in SFR, or comparison against strong supervised baselines and recent self-evolution methods beyond majority voting.

minor comments (2)

[Abstract] Abstract contains a typo: 'avaible' should be 'available'.
[Method] Notation for RRM, SFR, and VSP is introduced without a clear summary table or diagram showing how the three components interact during a single training iteration.

Simulated Author's Rebuttal

3 responses · 0 unresolved

Thank you for the valuable feedback. We address each major comment below and will update the manuscript accordingly to strengthen the experimental validation.

read point-by-point responses

Referee: [Experimental Results / Abstract] The central claim that SFR supplies a more reliable training signal than majority voting rests on the unverified assumption that softened answer frequencies correlate with objective correctness rather than shared model biases. The manuscript provides no quantitative validation (e.g., Pearson correlation between SFR scores and ground-truth accuracy on a labeled subset of MathVision, or accuracy lift when training on SFR-selected vs. majority-voted paths).

Authors: We agree this validation is important. In the revised manuscript, we will add a quantitative analysis including the Pearson correlation between SFR scores and ground-truth accuracy on a labeled subset of MathVision, as well as performance comparison between SFR-selected and majority-voted paths to demonstrate the reliability of the softened reward signal. revision: yes
Referee: [Experimental Results] The paper asserts that VSP successfully shifts model focus from visual superficiality to mathematical logic, yet no ablation isolates the contribution of VSP (e.g., CSRS without VSP vs. full CSRS) or measures reduction in visual-error modes on geometric problems. Without these controls, the SOTA claim on MathVision cannot be attributed to the proposed mechanisms.

Authors: We will include an ablation study comparing CSRS with and without VSP in the revised version. We will also provide an analysis of error modes on geometric problems to quantify the reduction in reliance on visual superficial cues, thereby isolating VSP's contribution. revision: yes
Referee: [Experimental Results] No information is given on experimental controls: number of independent runs, statistical significance of reported gains, hyper-parameter sensitivity of the softening temperature in SFR, or comparison against strong supervised baselines and recent self-evolution methods beyond majority voting.

Authors: The revised manuscript will report the number of independent runs (with statistical significance via t-tests), include hyper-parameter sensitivity analysis for the SFR softening temperature, and add comparisons to additional self-evolution methods. For supervised baselines, we will include them where relevant to contextualize the unsupervised gains. revision: partial

Circularity Check

0 steps flagged

No circularity detected; derivation is self-contained

full rationale

The paper defines CSRS via three new mechanisms (RRM for re-inference from anchors, SFR for continuous frequency-based rewards, VSP for visual perturbation) without any equations or claims reducing to self-definition, fitted inputs renamed as predictions, or load-bearing self-citations. Frequency signals are external observations across samples, not internal to the model output by construction. Performance is validated on external benchmarks (MathVision), so the chain does not collapse to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the unstated premise that frequency-based continuous rewards plus retracing will systematically favor correct reasoning paths over biased ones, plus the assumption that visual perturbations isolate logical reasoning. No free parameters or invented entities are named in the abstract.

axioms (2)

domain assumption Frequency of sampled answers correlates with objective correctness after softening
This is the core replacement for majority voting and is invoked to justify the SFR component.
domain assumption Visual semantic perturbation successfully decouples reasoning from superficial image features
Invoked to ensure prioritization of mathematical logic.

pith-pipeline@v0.9.0 · 5564 in / 1467 out tokens · 29595 ms · 2026-05-13T17:43:41.842577+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes

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echoes
ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

Softened Frequency Reward (SFR)... Rf_final = (γ tanh(β (fr/fbase + ϵ - 1)) + 1) × Rbase ... GSR = exp(η(ρ - ϵ)) < GMV = exp(η)
IndisputableMonolith/Foundation/BranchSelection.lean branch_selection unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

Continuous Rewards as a Stabilizer Compared to 0-1 Rewards... exponential self-reinforcement process

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

11 extracted references · 11 canonical work pages · 2 internal anchors

[1]

Proximal Policy Optimization Algorithms

Direct preference optimization: Y our lan- guage model is secretly a reward model. Advances in neural information processing systems, 36:53728– 53741. 9 John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. 2017. Proximal policy optimization algorithms. arXiv preprint arXiv:1707.06347. SentenceTransformers. 2024. all-minilm-l6-v2....

work page internal anchor Pith review Pith/arXiv arXiv 2017
[2]

Anderson

The curse of recursion: Training on gen- erated data makes models forget. arXiv preprint arXiv:2305.17493. Gokul Swamy, Sanjiban Choudhury, Wen Sun, Zhi- wei Steven Wu, and J Andrew Bagnell. 2025. All roads lead to likelihood: The value of rein- forcement learning in ﬁne-tuning. arXiv preprint arXiv:2503.01067. Omkar Thawakar, Shravan V enkatraman, Ritesh...

work page arXiv 2025
[3]

arXiv preprint arXiv:2509.16456

Gpo: Learning from critical steps to improve llm reasoning. arXiv preprint arXiv:2509.16456. Jihun Y un, Juno Kim, Jongho Park, Junhyuck Kim, Jongha Jon Ryu, Jaewoong Cho, and Kwang-Sung Jun. 2025. Alignment as Distribution Learning: Y our Preference Model is Explicitly a Language Model. arXiv preprint. ArXiv:2506.01523 [cs]. Renrui Zhang, Dongzhi Jiang, ...

work page arXiv 2025
[4]

Absolute Zero: Reinforced Self-play Reasoning with Zero Data

Springer. Andrew Zhao, Yiran Wu, Y ang Y ue, Tong Wu, Quentin Xu, Y ang Y ue, Matthieu Lin, Shenzhi Wang, Qingyun Wu, Zilong Zheng, and Gao Huang. 2025. Absolute Zero: Reinforced Self-play Reasoning with Zero Data . arXiv preprint. ArXiv:2505.03335 [cs]. Y ujun Zhou, Zhenwen Liang, Haolin Liu, Wenhao Y u, Kishan Panaganti, Linfeng Song, Dian Y u, Xi- angl...

work page internal anchor Pith review arXiv 2025
[5]

Since AB ∥ DC , ∠BDA = ∠BDC

Maternal Rollouts for Problem Maternal Response 1 : To ﬁnd angle BDA, we note that the inscribed angle BDC intercepts arc CB (94◦), so ∠BDC = 47 ◦. Since AB ∥ DC , ∠BDA = ∠BDC . Therefore, ∠BDA = 47 ◦. Maternal Response 2 : Using cyclic quadrilateral properties, ∠BCA intercepts arc CB , so ∠BCA = 47◦. Opposite angles in a cyclic quadrilateral sum to 180◦,...

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[6]

The inscribed angle BDA subtends the same arc BA

Cut rollouts for Problem Re-inference Response 9 : The central angle BZA is given as 104◦. The inscribed angle BDA subtends the same arc BA. By the inscribed angle theorem, ∠BDA = 1 2 · ∠BZA = 52 ◦. The parallel lines con- dition is not needed for this calculation. Re-inference Response 15 : The reasoning is as fol- lows: The central angle BZA is 104◦. Si...

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[7]

output:

Maternal Rollout Example prompt:"system Y ou are a helpful assistant. user For the pair of similar ﬁgures, use the given areas to ﬁnd x. Y ou FIRST think about the reasoning process as an internal monologue and then provide the ﬁnal an- swer. The reasoning process MUST BE enclosed within <think> </think> tags. The ﬁnal answer MUST BE put in \\boxed.assist...

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[8]

Solving for k, we get k = \sqrt{\frac{50}{72}} = \sqrt{\frac{25}{36}} = \frac{5}{6} . 7. The side length x corresponds to the smaller ﬁgure, and the side length of the larger ﬁgure is 6 inches. 8. Therefore, x = 6 times \frac{5}{6} = 5 . So, the value of x is 5 inches.</think> \\boxed{5}"

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[9]

output:

Retracing Rollout Example prompt:"system Y ou are a helpful assistant. user Find x. Assume that segments that appear to be tangent are tangent. Y ou FIRST think about the reasoning process as an internal monologue and then provide the ﬁnal answer. The reasoning process MUST BE enclosed 14 within <think> </think> tags. The ﬁnal answer MUST BE put in \\boxe...

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[10]

Bad Cases Concatenated Prompt: Y ou are a helpful assistant. user. Find J L, if KP = 4 and P M = 7 . Y ou FIRST think about the reasoning process as an internal mono- logue and then provide the ﬁnal answer. The reasoning process MUST BE enclosed within <think> </think> tags. The ﬁnal answer MUST BE put in \boxed{}. In the diagram, we have a kite shape wit...

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[11]

22 Incorrect Response 4: Assuming symmetry incorrectly leads to J L = KP = 4, then the full diagonal length is doubled: J L = 2 × 4 = 8 . 8 15 Question:Quadrilateral $A B C D$ is inscribed in $\odot Z$ such that $m \angle B Z A=104, m \widehat{C B}=94,$ and $\overline{A B} \| \overline{D C} .$ Find $m \angle B D A$ Answer:52 Maternal Response 1: To find a...

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