Recent progress in multimodal large language models has led to strong performance on reasoning tasks, but these improvements largely rely on high-quality annotated data or teacher-model distillation, both of which are costly and difficult to scale. To address this, we propose an unsupervised self-evolution training framework for multimodal reasoning that achieves stable performance improvements without using human-annotated answers or external reward models. For each input, we sample multiple reasoning trajectories and jointly model their within group structure. We use the Actor's self-consistency signal as a training prior, and introduce a bounded Judge based modulation to continuously reweight trajectories of different quality. We further model the modulated scores as a group level distribution and convert absolute scores into relative advantages within each group, enabling more robust policy updates. Trained with Group Relative Policy Optimization (GRPO) on unlabeled data, our method consistently improves reasoning performance and generalization on five mathematical reasoning benchmarks, offering a scalable path toward self-evolving multimodal models. The code are available at https://github.com/OPPO-Mente-Lab/LLM-Self-Judge.
Figures & tables
Figure 1: Limitation of majority voting in unsupervised self-evolution.Right: An example where the most frequent answer is incorrect. Majority voting reinforces this dominant error, while our method favors higher-quality reasoning paths through Judge modulation.Left: Results on MathVision Wang et al. (2024) and DynaMath Zou et al. (2024) show that our approach consistently outperforms majority-voting-based self-training.
Figure 2: Overview of the proposed unsupervised self-evolution framework. The Actor generates multiple reasoning trajectories for the same input, while a frozen Judge provides bounded score modulation. The final rewards are optimized in a group-wise, distributional manner to enable stable policy updates without external supervision.
Training Data
Method
MathVision
MathVerse
WeMath
LogicVista
DynaMath
Avg.
Performance on Qwen2.5-VL-7B
—
Qwen2.5-VL-7B
25.0
44.2
37.1
46.3
20.3
34.6
Supervised Training & Teacher Model Distillation
Mixed Data
R1-Onevision-7B Yang et al. (2025b)
29.9
46.4
35.8
46.5
21.8
36.1
OpenVLThinker-8B Deng et al. (2025)
25.9
50.3
36.5
46.3
21.2
36.0
Vision-R1 Huang et al. (2025b)
29.4
52.4
35.4
49.7
25.2
38.4
Table 1: Main results on multimodal mathematical reasoning benchmarks. We report accuracy (%) on five math benchmarks. MajorVote corresponds to the MM-UPT method. denotes supervised training.
Method
MathVision
DynaMath
Avg.
Qwen2.5-VL-7B
25.0
20.3
22.65
+ Major Vote
27.5
21.4
24.45 +1.8
+ Self-Consistency
25.2
20.5
22.85 +0.2
+ Judge Scoring
27.3
21.1
24.20 +1.6
+ MV + JS
28.4
22.7
25.55 +2.9
+ SC + JS
30.1
23.7
26.90 +4.3
Table 2: Ablation experiments on different modules.
Model / Method
MathVision
DynaMath
Model / Method
MathVision
DynaMath
Qwen2-VL-2B
12.8
6.8
Qwen3-VL-8B
53.0
48.2
w/ major vote
9.6
4.2
w/ major vote
51.7
46.8
w/ ours
16.3
11.4
w/ ours
53.5
50.3
Qwen2.5-VL-3B
19.5
18.2
GLM-4.1V-9B
47.8
38.6
w/ major vote
21.3
19.1
w/ major vote
48.2
37.2
w/ ours
24.8
21.3
w/ ours
50.4
40.8
Table 3: Self-evolution performance comparison across different backbone models.
Figure 3: Training dynamics on MMR1 Leng et al. (2025) . The figure compares majority voting, supervised reinforcement learning, and our method during training, in terms of validation accuracy on MathVision, actor entropy, and average response length.
Figure 4: Ablation training dynamics on MMR1 Leng et al. (2025) . We compare Self-Consistency, Judge-only, and the full method in terms of validation accuracy on MathVision, actor entropy, and average response length during training.
Method
MathVision
DynaMath
Avg.
Qwen2.5-VL-7B
0.66
0.48
0.57
GRPO (w. label)
0.63
0.43
0.53 -0.04
Major Vote
0.58
0.37
0.48 -0.09
Ours
0.64
0.43
0.54 -0.03
Table 4: Comparison of pass@10 across benchmarks.
Model / Method
MathVision
LogicVista
DynaMath
Vision-R1-7B
29.4
49.7
25.2
w/ major vote
30.0
49.4
24.6
w/ ours
32.6
51.5
26.3
Table 5: Self-evolution results on a strong baseline that has already been trained with teacher distillation.
Method
Relative Time
Accuracy
Supervised GRPO
1.0 ×
29.1
MM-UPT (Major Vote)
1.0 ×
27.5
VisionZero
2.8 ×
27.6
EvoLMM
2.2 ×
25.8
Ours
1.4 ×
30.9
Table 6: Comparison of relative training cost and MathVision accuracy across different methods.
Training Setting
Method
ChartQA
MMVP
Base model
—
85.7
77.2
Geo3K
w/ MM-UPT
84.8
76.4
w/ ours
85.4
77.6
GeoQA
w/ MM-UPT
82.6
77.4
w/ ours
86.3
77.9
MMR1
w/ MM-UPT
85.4
74.6
Table 7: Generalization to chart understanding (ChartQA) and general visual reasoning (MMVP).
Appendix figures & tables10 assets
Supplementary material from the paper’s appendix.
Appendix
Category
Hyperparameter (Value)
Data Configuration
Train Batch Size
512
Max Prompt Length
1024
Max Response Length
2048
Filter Overlong Prompts
True
Truncation Strategy
error
Appendix
Table 8: Training hyperparameters.
Figure 5: A case study on Geo3K Lu et al. (2021)
Figure 6: A case study on Geo3K Lu et al. (2021)
Figure 7: A qualitative failure case analysis on the Geo3K dataset Lu et al. (2021) .
Method
MathVision
DynaMath
Self-Consistency
25.2
20.5
w. distribution
25.9
20.7
Judge
27.3
21.1
w. distribution
27.8
21.5
Ours w.o. distribution
30.1
23.7
Ours w. distribution
30.9
24.2
Appendix
Table 9: Effect of group-wise distributional modeling.
Method
Agree@1
SC-winner
J-winner
Qwen2.5-VL-7B
41.2
36.3
40.2
Ours
73.8
48.6
50.3
Appendix
Table 10: Relationship between self-consistency and Judge preferences.
Method
Overall
Algebra
Analytic Geo.
Arithmetic
Comb. Geo.
Qwen2.5-VL-7B
25.0
15.8
26.3
36.8
15.8
Ours
30.9
15.8
42.1
36.8
21.1
Method
Combinatorics
Counting
Descriptive Geo.
Graph Theory
Logic
Qwen2.5-VL-7B
10.5
21.1
26.3
15.8
15.8
Ours
21.1
21.1
21.1
10.5
21.1
Method
Metric (Angle)
Metric (Area)
Metric (Length)
Solid Geo.
Statistics
Appendix
Table 11: Category-wise overall accuracy (%) on MathVision (trained on Geo3K).
Method
Text Dominant
Vision Only
Vision Dominant
Vision Intensive
Text Lite
Qwen2.5-VL-7B
53.6
41.0
40.9
40.9
44.9
Ours
56.6
42.5
42.6
44.8
47.7
Appendix
Table 12: Category-wise overall accuracy (%) on MathVerse (trained on Geo3K).
Method
Overall
Inductive
Deductive
Numerical
Spatial
Mechanical
Qwen2.5-VL-7B
46.3
36.4
64.5
55.8
19.2
54.1
Ours
49.0
29.0
65.6
65.3
30.8
55.4
Appendix
Table 13: Category-wise overall accuracy (%) on LogicVista(trained on Geo3K).
Category
Qwen2.5-VL-7B
Ours
Δ
Two-step (S2)
55.28
58.61
+3.33
Understanding of Plane Figures
60.22
64.45
+4.23
Calculation of Solid Figures
77.26
79.03
+1.77
Direction
82.86
90.00
+7.14
Route Map
55.49
62.64
+7.15
Appendix
Table 14: Category-wise overall accuracy (%) on Wemath (trained on Geo3K).
Post-training via Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) is crucial for enhancing reasoning in Multimodal Large Language Models (MLLMs), yet existing paradigms often reach a performance bottleneck due to the limitations of static data. While current methods leverage self-reflection or self-evolution to push these boundaries, they still suffer from cognitive drift and hallucinated reasoning paths caused by low-quality synthetic data. To address these challenges, we propose Anchor Evolution (AnE), a new paradigm that integrates truth-anchored data curation and model evolution, achieving faithful and steady performance gains at the reasoning frontier. Specifically, we propose Truth Anchor Expansion, which pinpoints the model failing frontier via trajectory rollouts and leverages ground-truth databases to retrieve high-fidelity anchors for faithful data curation. Subsequently, we introduce the Scaffold-Stripping Mechanism to internalize reasoning capabilities. This mechanism first anchors reasoning paths via scaffold-augmented supervision to mitigate the learning complexity and distribution drift of direct SFT on raw data, then leverages RL to strip the scaffold template, thereby effectively transitioning the reasoning paths into intrinsic model capabilities. Experimental results on multimodal reasoning benchmarks show that our method substantially advances the model performance frontier, improving the base model by 10.3% across eight multimodal benchmarks and achieving state-of-the-art results. The code will be made publicly available.
Zehao Wang, Yihan Zeng, Zidong Gong +5
Harbin Institute of Technology · Huawei Noah’s Ark Lab · Independent Researcher
Reinforcement learning (RL) has emerged as a powerful approach for improving reasoning in language and vision-language models, yet its strongest successes still depend heavily on ground-truth supervision (e.g., verifiable reward). Such annotations are costly to obtain and become increasingly scarce as reasoning capabilities advance beyond what humans can reliably evaluate. Self-rewarding RL reduces this dependence by enabling models to derive reward signals from their own completions. However, training solely on self-generated feedback can reinforce existing biases and suboptimal behaviors, reduce response diversity, and ultimately lead to homogenized responses and training collapse. In this work, we show that unsupervised reasoning can emerge through cooperative multi-agent training. We introduce Co-RL, a framework in which multiple decoupled models, sharing no parameters, are simultaneously optimized through RL using rewards derived from their peers. We further show that increasing cohort diversity, through heterogeneous model families, sizes, and rephrased training samples, reduces the correlated errors that drive self-reinforcing feedback loops. This diversity consistently improves reasoning performance, maintains behavioral diversity, and mitigates training collapse. Across text-only and multimodal domains, Co-RL consistently outperforms the base models and prior label-free approaches, while matching or surpassing supervised methods, without access to any ground-truth labels. Concretely, Co-RL yields average gains of 3.0-8.6% across seven text-only benchmarks for LLMs and 2.3-7.2% across four multimodal benchmarks for VLMs. Code is available at https://github.com/DrStranded/Co-RL.
Yunhao Yang, Yuexin Bian, Yunjie Tian +6
Johns Hopkins University · UC San Diego · Independent Researcher +1
Can a language model improve reasoning by learning from its own imperfect responses, without rewards or teacher-provided solutions? We present Self-evolving Post-Training (SePT), a simple method that alternates temperature-controlled self-generation with next-token likelihood training. Each round uses the updated model to generate new training responses, with one response per prompt by default and no correctness filtering. Across six mathematical benchmarks, SePT improves a temperature-selected no-training baseline by 11.4 and 6.7 AVG points on Qwen2.5-Math-7B and Qwen2.5-7B, respectively, where AVG averages Pass@1, Pass@8 and Pass@32 across benchmarks. We analyze how sampling temperature shapes the learning signal and investigate the value of the resulting responses. Responses from a SePT-trained model improve a student initialized from the original weights, while their reasoning prefixes help an unchanged model complete solutions, even when matched in length to prefixes from a colder initial model. Comparing next-token predictions at identical contexts also reveals changes in token rankings that decoding-temperature adjustment cannot reproduce. Further evaluations across nine starting models, general reasoning and code generation examine broader applicability. Together, these results show that reward-free self-training can improve both a model's predictions and the supervision it provides. Our code is available at https://github.com/ElementQi/SePT.
Mengqi Li, Lei Zhao, Anthony Man-Cho So +2
The Chinese University of Hong Kong, Shenzhen · Shanghai Jiao Tong University · The Chinese University of Hong Kong