R1-ShareVL: Incentivizing Reasoning Capabilities of Multimodal Large Language Models via Share-GRPO

Dear reviewer MP3K,

Thank you for your professional and valuable feedback. We appreciate your recognition that our paper clearly identifies the drawbacks of GRPO and addresses these important issues. We are also encouraged by your positive assessment of our proposed method’s effectiveness and its significant improvements over other GRPO-based approaches. Below, we address your concerns and questions individually:

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W1: Analysis of model improvements on certain benchmark, e.g., MMMU and AI2D

Thank you for your comments. Our training data, as well as other open-sourced R1-related datasets, are primarily focused on the mathematics domain. To further evaluate the generalization ability of R1-Share, we considered challenging out-of-domain (OOD) benchmarks like MMMU and AI2D. Specifically, MMMU covers multiple disciplines, and AI2D focuses on science diagrams. Both benchmarks differ significantly from the training data. We compared R1-Share with MM-Eureka, since our training data is a subset of that used for MM-Eureka. On MMMU, existing reasoning methods like MM-Eureka achieve an accuracy of 55.3%, whereas R1-Share achieves 58.1%, marking a 2.8-point improvement. For AI2D, R1-Share also achieves state-of-the-art performance, with R1-Share-32B reaching 86.2% accuracy. These results demonstrate that R1-Share offers superior OOD generalization capabilities compared to GRPO.

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W2: Apply ShareGRPO in NLP domain

This is a question well worth exploring. We conducted a preliminary exploration by applying ShareGRPO to LLM, and observed consistent performance improvements in this setting as well. We trained the Qwen2.5-7B-Instruct model using both ShareGRPO (w/o multi-modal transformations) and GRPO methods, with 5K samples from the Light-R1 dataset. The results show that ShareGRPO can also be applied to the NLP domain and achieves better performance than GRPO.

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W3: Comparison between GRPO and DPO

Thank you for your comment. SeVa [1] is an insightful and relevant work which uses designed augmentation to the image input to generate negative data for DPO training, and we will cite it in the revised manuscript. GRPO is designed to incentivize long-chain reasoning capabilities without pre-generated reasoning annotations, while DPO training requires reasoning data to be generated in advance, making the training results highly dependent on the quality of the dataset.

To delve deeper into this question, we include a comparison to further examine the reasoning capabilities incentivized by each method, by constructing DPO data based on the same underlying dataset. Using our 52K dataset, we use Qwen2.5-VL-72B generates long-chain steps to serve as the chosen data for DPO. And we prompt GPT-4o to generate reject responses using the method from SeVa [1] and STE [2]. The results show that GRPO is more effective at incentivizing the model’s reasoning ability.

[1] Self-Supervised Visual Preference Alignment

[2] Self-Taught Evaluators

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Thank you again for your review and for recognizing our work. We are encouraged by your feedback and will do our best to further refine this manuscript. If you feel your questions have been addressed, we would be grateful if you could kindly consider raising your score. Thank you!

Dear reviewer EzA1,

We appreciate your valuable comments and suggestions. We are glad to hear that you find our experimental results promising and our method straightforward and easy to implement. Below, we are going to address your concerns one by one to the best of our ability.

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W1: Clarification on our motivation and contribution

Many thanks for raising this concern.

The major weakness is the limited novelty. In essence, it is a data augmentation technique. Both the "offline textual SCT" and "online multimodal SCT" could be performed in a purely offline manner; one could simply apply the online transformations prior to training to generate a large number of questions.

We would like to kindly clarify that the key innovation of ShareGRPO is not simply the use of data transformation. We only use transformations to generate semantically consistent question variants and create shared responses for subsequent joint optimization. The core idea lies in leveraging shared and diverse responses for both self-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j = k$) and cross-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j \neq k$), each based on their respective conditional probabilities.

In addition, we also conducted experiments to compare the results of data augmentation and ShareGRPO. The results indicate that the performance gains of ShareGRPO are not due to data augmentation, but rather to the mitigation of advantage vanishing through shared responses.

The shared advantage computation is a straightforward combination resulting from two different group definitions and is closer to an engineering detail than a separate algorithm justifying a new name.

We respectfully clarify that the global shared advantage is also an innovation of this paper, specifically designed to facilitate shared advantage updates. It further enhances both the direction and magnitude of credit assignment to $\pi_{\theta}(o_i^{Q_j} \mid Q_k)$. Unlike GRPO, which computes the advantage within the set of responses generated for each individual question, ShareGRPO extends this to a hierarchical advantage calculation that incorporates both global and local advantages. The local advantage calculation differs from that in standard GRPO, while the global advantage refers to computing the advantage across all responses generated from all question variants. This specialized advantage calculation in ShareGRPO leads to improved performance, as shown in the table below.

Lastly, we summarize the contributions of this work as follows to highlight its uniqueness: We propose Share-GRPO, the first method to introduce information sharing into MLLM reinforcement learning. It shares diverse reasoning trajectories across an expanded question space to alleviate sparse reward and advantage vanishing issues. We further design a hierarchical advantage estimation mechanism that shares reward information both across and within question variants, enabling more accurate and robust estimation. Finally, extensive experiments on six MLLM reasoning benchmarks validate the effectiveness of our approach.

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W2: Refine Equations (5), (6), and (7)

Thank you for taking the time to carefully review our work and point out these issues! We agree that the notation could be clearer and more rigorous. We originally added the index $k$ in Equations (5) and (6) because, in Equation (8), we need to distinguish the calculations of $A$ for different policies $\pi_{\theta}(\cdot \mid Q_k)$. Below, we adopt a different formulation of the equations and provide a detailed explanation of the formulas.

The indices $k$ and $j$ are primarily used in Equation (8) for the conditional probability $\pi_{\theta}(o_i^{Q_j} \mid Q_k)$. Their purpose is to distinguish between the response $o_i$ generated from $Q_j$ and the question variant $Q_k$ on which the conditional probability is evaluated. This allows us to differentiate between self-updating (when $j = k$) and cross-updating (when $j \neq k$) scenarios in the computation.

For $\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, when $k = j$, all responses $o_i$ are generated from $Q_j$ and are used to update the same question $Q_k$. In this case, we apply both global and local advantage estimation, as these responses are directly associated with their original variant.

$$A_{i, j}^{\text{hier}} = A_{i, j}^{\text{global}} + A_{i, j}^{\text{local}}$$

For $\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, when $k \neq j$, the response $o_i$ is generated from $Q_j$ but used to update a different variant $Q_k$. Here, we adopt only the global advantage estimation, since the response is being shared across variants.

$$A_{i, j}^{\text{hier}} = A_{i, j}^{\text{global}}$$

For global advantage computation, we estimate the advantage from a global perspective, where the relative advantage is computed using the rewards obtained from all question variants.

$$A_{i, j}^{\text{global}} = \frac{R_i^{Q_j} -\text{mean}\left(\{{[\{r_{1}^{Q_1}, ..., r_{n}^{Q_1}}\}], ..., [\{r_{1}^{Q_m}, ..., r_{n}^{Q_m}\}\}]\right)}{\text{std}\left(\{[\{r_{1}^{Q_1}, ..., r_{n}^{Q_1}\}], ..., [\{r_{1}^{Q_m}, ..., r_{n}^{Q_m}\}\}]\right)}.$$

For local advantage computation, we also estimate the advantage at a local level, where the relative advantage is computed within the responses generated from each individual question variant Qj ∈ Q. Specifically, for each question variant Qj, the local advantage is estimated as follows:

$$A_{i, j}^{\text{local}} = \frac{ R_i^{Q_j} - \mathrm{mean}\left(\{ r_1^{Q_j}, ..., r_n^{Q_j} \}\right) }{ \mathrm{std}\left(\{ r_1^{Q_j}, ..., r_n^{Q_j} \}\right) }$$

Thank you for you suggestions. We have revised and clarified these expressions in the updated manuscript.

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Q1: The results without global shared advantage and the clarification of advantage computation Thank you for your question.

I would be interested to know the performance without the global shared advantage and with only the local shared advantage (but with the same data augmentation).

We provide results without the global shared advantage, which show a slight decrease in performance. This is because the global shared advantage offers higher confidence in credit assignment.

In such a case, the method would revert to the normal GRPO, where the advantage is only normalized across the same question (specifically, the same variant of the same question).

We believe that there may be some misunderstanding. ShareGRPO, even when using only local shared advantage and without the global shared advantage, does not revert to normal GRPO. We would like to kindly highlight that the essential innovation of ShareGRPO is not simply the introduction of transformation or the use of a global shared advantage. The core idea lies in leveraging shared and diverse responses for both self-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j = k$) and cross-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j \neq k$), each based on their respective conditional probabilities. The semantically consistent transformation is primarily a means to create a shared and diverse response pool, while the global shared advantage further enhances both the direction and magnitude of credit assignment to $\pi_{\theta}(o_i^{Q_j} \mid Q_k)$.

I suspect that simply increasing the number of samples per question variant would be sufficient for enhancing credit assignment

We agree that simply increasing the number of samples per question would enhance credit assignment. However, as shown in Table 5, simply increasing the number of rollouts leads to more homogeneous responses and quickly reaches a performance ceiling. For example, when the GRPO rollout number increases from 12 to 24, the accuracy on MathVista improves by only 0.2%, while significantly increasing computational burden. Therefore, it is more effective and efficient to increase the number of question variants and adopt shared response updating as used in ShareGRPO.

Q2: Inclusion of learning curve

Thank you for your suggestion! We agree that providing learning curves is valuable for analyzing optimization and convergence. Accordingly, we have included learning curves in Figure 1(b) of the main paper. While we would like to provide additional learning curves in the rebuttal, technical restrictions from NeurIPS prevent us from submitting figures at this stage. We will include more learning curves in the revised version, such as reward curve, and response length curve.

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Thank you again for your insightful and professional comment, which made our work more complete and solid! If there are any further questions, please let us know. If you feel all questions have been addressed, we would be grateful if you could kindly consider re-rating our work. Looking forward to hearing back from you!

Thank you for your response!

we believe your understanding is correct! We apologize for any confusion caused. The 20% increase we mentioned refers specifically to the case where the number of questions is 2 and the number of rollouts is 6. We will clarify this point in the revised paper. In fact, our default setting throughout the paper is with two questions, as we found this configuration already yields strong results (if you are interested in more details for this part, please refer to our responses to Reviewer Amky’s W1 and Reviewer v7hu’s W5(b)). This setting also strikes a good balance between performance and training efficiency.

For the detailed computation time analysis, we used the EasyR1 framework for training and monitored the process using wandb. The table below presents the computation time for each component within a single RL step, arranged in the order of execution, with the total time per step shown at the end. As shown, ShareGRPO only increases the computation time per step by 20%.

This phenomenon can be explained by the fact that, in each training phase, parallel computation (which is increased by methods such as ShareGRPO) only accounts for part of the total time per component. Other substantial fixed or distributed overheads—such as parameter synchronization, communication latency, buffer initialization, and scheduling—remain largely unchanged and unavoidable. As a result, the overall increase in computation time is much less than the theoretical complexity might suggest.

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Thank you again for your valuable and professional comments! We hope that our response has addressed your concerns. If so, we would greatly appreciate it if you could kindly consider re-rating our work. If you have any further questions or suggestions, please feel free to comment here.

Dear Reviewer EzA1,

We hope this message finds you well. As the discussion period in nearing its end with less than 8 hours remaining, we are writing to kindly check whether we have addressed all your concerns satisfactorily. If there are any additional points or feedback you'd like us to consider, please let us know. Your insights are invaluable to us, and we will incorporate your suggestions into the revised version. Lastly, we will remain actively engaged in the discussion until the end of the rebuttal period to address any remaining issues.

Thank you very much for your review!

Dear reviewer v7hu,

Many thanks for your valuable comments and questions, which help us a lot to improve our work. We are glad that you find ShareGRPO’s richer reward signals convincing, and that you consider our experiments comprehensive and the paper well-structured. We are going to try our best to address your questions one by one as follows.

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W1: Data quality concerns regarding GPT-4o-based problem augmentation

Thank you for raising this concern. We have taken several measures to ensure the quality of the augmented problems, as detailed below, and we will include these in the revised paper:

1. We experimented with various prompts to ensure stable and high-quality outputs.
2. We developed rule-based scripts to automatically filter out incomplete generations, ensuring that the retained sentences are complete and that the options remain consistent with the original questions.
3. We manually reviewed a large number of cases to further ensure the quality and correctness of the outputs.
4. We also conducted GRPO training using only one newly generated question variant. The training process was stable and achieved a slight performance improvement as shown below, which empirically demonstrates the quality of the generated questions.

We will include these discussion in the revision.

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W2: Discussion about Figure.1(b) and advantage vanishing issue

Thank you for raising this concern. We would like to kindly clarify that there are many factors that lead to the advantage vanishing problem. For example, (1) Memorization and reward hacking: MLLMs may memorize the final answer due to data leakage and can produce the correct final answer even when intermediate reasoning steps are incorrect. Please refer to our response to the reviewer Amky's W1 for further details about memorization issues; (2) Trapped in low quality questions: For certain low-quality questions, the MLLM is unable to produce correct answers, leading to all rollouts being incorrect; and (3) Genuine reasoning ability: The model may have truly learned to solve the problem through reasoning, leading to consistently correct answers.

ShareGRPO is primarily designed to address issues (1) and (2) by generating shared and diverse responses through semantically consistent transformations. These responses are then used for both self-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j = k$) and cross-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j \neq k$), based on their respective conditional probabilities.

As training progresses, the reasoning ability of MLLMs steadily improves, enabling them to genuinely solve problems, even when presented with semantically varied questions, and to develop true reasoning skills. This inevitably leads to more cases where the model answers all variants correctly, thus resulting in training convergence and a decrease in the valid advantage ratio. To address issue (3), dynamic sampling from DAPO [1] is specifically designed for such scenarios. As shown in Table 3, our results demonstrate the complementarity and compatibility of ShareGRPO with dynamic sampling.

[1] DAPO: An Open-Source LLM Reinforcement Learning System at Scale

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W3: Average performance in Tab.4 and Tab.5

This is a good question! We have provided the average performance results below. We believe including these results makes our findings more convincing. Thank you!

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W4: Clarification on the notation in Eq.5 and Eq.6

Thank you for pointing out the confusion regarding the subscript "k" in Eq. (5) and (6). We acknowledge that the notation could be more clearly defined, and we will revise the equations and provide additional explanations in the revised version to ensure clarity. Due to character limitations, we have provided a detailed explanation in our response to Reviewer EzA1’s W2. Please kindly refer to that section for further details.

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W5 (a): Clarification on the reproducibility of ShareGRPO

Thank you for raising this concern. We fixed the random seed during training and conducted five independent runs. The results show that the performance fluctuation is minor. We believe this level of variation is acceptable, as similar fluctuations are also observed in GRPO, due to the inherent randomness in reinforcement learning.

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W5 (b): Explanations on the Performance Gains with Increasing the Number of Question variants $m$

Thank you for raising this concern! Based on Table 3 and Table 4, we observe that increasing the number of question variants from $m=1$ to $m=2$ leads to a significant performance improvement (72.8% → 75.4% on MathVista). This improvement is primarily due to our use of semantically consistent transformations and shared response optimizations, which effectively address the advantage vanishing issue. However, the gain is smaller when increasing $m$ from 2 to 4. This is because, with two variants, the MLLM is already able to generate both positive and negative rollouts, which sufficiently addresses the sparse reward issue. As a result, further increasing $m$ provides diminishing returns. Therefore, to balance efficiency and performance, we use two question variants as the default setting.

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Q1: Explanation of Eq.7

Thank you for your comment! We first clarify the meaning of $\pi_{\theta}(\cdot \mid Q)$ in GRPO. In GRPO, for a given question $Q$, we first roll out $n$ responses and, for each response, compute both its advantage $A$ and the conditional probability $\pi_{\theta}(\cdot \mid Q)$ for each token in the response. Here, $\pi_{\theta}(\cdot \mid Q)$ denotes the parameterized policy (with parameters $\theta$) that outputs a probability distribution over possible tokens conditioned on $Q$. If the advantage is positive, the probability of the corresponding tokens is increased; if the advantage is negative, the probability of these tokens is suppressed.

In Equation.(7), what does $\pi_{\theta}({o_i^{Q_j}} \mid {Q_k})$ mean?

In ShareGRPO, we extend this framework by introducing multiple question variants [$\{Q_1, Q_2, \dots, Q_m\}$]. For each variant $Q_j$, we generate a set of responses $\mathbf{O}=[[\{\{o_{1}^{Q_1}, ..., o_{n}^{Q_1}\}], ..., [\{o_{1}^{Q_m}, ... o_{n}^{Q_m}\}\}]]$. Each response $o_i^{Q_j}$, where j belongs to m, is thus explicitly generated by the policy model conditioned on $Q_j$.

The notation $\pi_{\theta}(o_i^{Q_j} \mid Q_k)$ in Eq. (7) represents the probability (under the current policy) of generating the entire response $o_i^{Q_j}$, but conditioned on a possibly different question variant $Q_k$.

1. When $j = k$, this is the “self-updating” case, where we update the parameters using the response under its own generating context.

2. When $j \neq k$, this is the “cross-updating” case, where we reuse a response generated from one question variant and update its probability under a different variant.

This design allows ShareGRPO to perform cross-variant updates, promoting information sharing and robustness across semantically consistent but syntactically different variants.

We appreciate your feedback and will further clarify this notation in the revised manuscript.

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Q2: Apply ShareGRPO to text-only LLM

Thank you! This is certainly worth exploring further. We didn't conduct experiments with text-only LLMs before, as Share-GRPO was originally designed for MLLMs, incorporating features such as multi-modal image transformations. However, we agree that extending Share-GRPO to text-only reasoning tasks is a promising direction for future work. Hence, we conducted a preliminary exploration by applying ShareGRPO to pure text tasks, and observed consistent performance improvements in this setting as well. We trained the Qwen2.5-7B-Instruct model using both ShareGRPO (w/o multi-modal transformations) and GRPO methods, with 5K samples from the Light-R1 dataset. The results show that ShareGRPO achieves better results than GRPO.

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Lastly, thank you very much for your constructive feedback and suggestions. We will incorporate these points into the revised paper. If you have any further questions, please feel free to let us know. We will be available throughout the rebuttal period.

Thank you for your comment! We are glad to engage with you during the discussion phase.

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W2: Are there any methods to quantify the proportion of these three factors? Providing their relative proportions and tracking their trends throughout the training process would strengthen the argument.

This is a good suggestion! We collected 50 samples from our training data, and manually categorized them into the four types: (1) Questions with memorization and reward hacking issues, (2) Low-quality questions, (3) Under-Learned questions, (4) Well-learned questions. Among these, factors (1), (2), and (4) lead to advantage vanishing, while factor (3) represents samples the model is learning, which do not exhibit advantage vanishing.

The definitions of these three categories are as follows:

1. Questions with memorization and reward hacking issues: The questions produce all correct final answers during rollouts, while its reasoning process contains clear intermediate errors, resulting in advantage vanishing.
2. Low-quality questions: The questions include minor issues such as typos or mixed-language usage. While these flaws do not hinder comprehension, the base model fails to answer them correctly in all rollouts, resulting in advantage vanishing.
3. Under-Learned questions: The questions produce both positive and negative samples during rollout.
4. Well-learned questions: The questions produce all-correct reasoning and final answer, resulting in advantage vanishing, where we believe this should be fine as the model can well solve these questions.

We measure how the proportion of each category changes along the training to reveal that how ShareGRPO mitigates advantage vanishing issues. Specifically, to analyze the proportions and trends of advantage vanishing caused by these factors (i.e., (1), (2) and (4)) during training, we evaluated intermediate checkpoint models at training steps 25, 50, 75, and 100. Each model was tested on the same set of questions, and we manually reviewed the responses at each stage. This allowed us to track how the impact of each factor evolved over the training. The table below presents the proportion of advantage vanishing for each factor at different training stages.

During training, the proportion of (1) memorization and (2) low-quality input cases steadily declined, while the proportion of (4) well-learned questions improved, demonstrating the effectiveness of our ShareGRPO and reinforcing our argument. Compared to GRPO, ShareGRPO more effectively mitigates the advantage degradation caused by issues (1) memorization and (2) low quality questions, ultimately leading to a higher proportion of correct reasoning and final answers and better accuracy.

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W5(a): My question primarily concerns whether different random augmentations lead to significantly different final performance. Therefore, I think the experiments in the rebuttal should use varying random seeds, rather than a fixed one, to reflect this robustness.

Thank you very much for this question! We conducted three runs with different random seeds. The experimental results show that our method is reproducible and robust. As training progresses, the models consistently converge to similar performance levels, demonstrating stable behavior across different random augmentations.

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We will include these discussions in the revised version. Thank you again for your constructive response!

Dear reviewer Amky,

We appreciate the reviewer's professional, detailed, and valuable comments and suggestions. We sincerely thank you for recognizing our contributions regarding the clarity and readability of the manuscript, the conceptual simplicity and practical impact of our approach, and the effectiveness of Share-GRPO over GRPO. Below, we are going to respond to your concerns one by one.

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W1: Analysis of the transformation’s effect on reasoning

For textual transformations, the overall difficulty of the problem does not change significantly. However, it is important to highlight that, based on our experiments and supported by previous studies [1,2], current MLLMs have data leakage and memorization issues. Specifically, MLLMs may memorize the correct answers, which allows them to produce the correct final answer even when their intermediate reasoning steps are incorrect, leading to reward hacking issues in GRPO (i.e., cases where models answer all correctly in rollout without genuine reasoning). Therefore, by applying textual transformations to introduce new question variants, ShareGRPO can alleviate the sparse reward issue caused by memorization, as responses are generated for the questions the model has not memorized. This enables MLLMs to better learn to reason during the ShareGRPO training.

Additionally, MLLMs are sensitive to prompts [3,4]. Even semantically equivalent questions with different formulations can elicit different responses from the model. We leverage this property by generating semantically consistent question variants, which encourages more diverse reasoning responses. These diverse responses are then shared and used to update all question variants. This diversity (which is more likely to include both positive and negative samples) helps to address the advantage vanishing problem. At the same time, training with ShareGRPO enhances the model’s robustness to prompt variations.

For multi-modal image transformation, we believe that adding noise or rotating the image increases the difficulty of the problem. This helps reduce the proportion of all-correct cases during training and enhances the model’s robustness to visual variations.

Table 4 shows nearly identical scores for 2–4 question variants, further calling into question the diversity effect.

Based on Table 3 and Table 4, we observe that increasing the number of questions from 1 to 2 raises the accuracy from 72.8% to 75.4%, demonstrating the effectiveness of ShareGRPO compared to GRPO. The improvement is limited when increasing from 2 to 4 questions, as with two variants, the MLLM is already able to generate both positive and negative rollouts, effectively mitigating the sparse reward issue. As a result, further gains are less pronounced. Therefore, to balance efficiency and performance, we use two question variants as the default setting. In summary, the significant performance improvement when increasing the number of question variants from 1 to 2 demonstrates that our method effectively mitigates the advantage vanishing problem, highlighting the effectiveness of ShareGRPO.

[1] Reasoning or Memorization? Unreliable Results of Reinforcement Learning Due to Data Contamination

[2] MMReason: An Open-Ended Multi-Modal Multi-Step Reasoning Benchmark for MLLMs Toward AGI

[3] How Susceptible are LLMs to Influence in Prompts?

[4] Large Language Models Sensitivity to The Order of Options in Multiple-Choice Questions

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Q1: Qualitative error cases about transformations

This is a good question. We agree that providing deeper analyses of how question transformations affect reward signals and model reasoning would strengthen the claim. We would like to kindly clarify that we provide some qualitative cases in Appendix E. Due to the technical restrictions from NeurIPS, we used existing images rather than new ones to provide qualitative explanations. For Rollout Case No.1-1 in Appendix E, it can be observed that the original question is answered incorrectly. If MLLMs consistently fails on this question, the advantages in GRPO vanish, preventing effective learning. However, through semantic-consistent transformations in ShareGRPO, new variants such as No.1-2 and No.1-3 yield correct reasoning paths. These successful trajectories can then be shared back with the original question, allowing the model to recover meaningful optimization signals. For Rollout Case No.2-1, it can be observed that the original question is answered correctly. Assuming all responses to its rewritten variants are also correct, GRPO will encounter only successful trajectories, leading to sparse rewards and advantage vanishing. By introducing input transformations through ShareGRPO, variants of Case No.2-1 (i.e., No.2-2 and No.2-3) result in incorrect answers. This facilitates learning from both correct and incorrect reasoning trajectories, enhancing the model’s generalization and robustness to question shifts.

We hope these analyses and explanations could address your concerns. We will include them in the revised manuscript. Thank you!

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W2: Expansion-technique details and validation of transformations

Since paraphrasing relies on GPT-4o prompts, a validation step is needed to guarantee semantic equivalence;

Thank you for raising this important concern. In fact, we conducted extensive experiments to validate the quality of the generated questions.

1. We experimented with various prompts to ensure stable and high-quality outputs.
2. We developed rule-based scripts to automatically filter out incomplete generations, ensuring that the retained sentences are complete and that the options remain consistent with the original questions.
3. We manually reviewed a large number of cases to further ensure the quality and correctness of the outputs.
4. We also conducted GRPO training using only one newly generated question variant per sample. The training process was stable and achieved a slight performance improvement as shown below, which empirically demonstrates the quality of the generated questions.

Please justify each operation (e.g., rotation, noise)

we carefully select transformations (e.g., rotation, noise injection) that preserve critical visual cues necessary for reasoning, and avoid transformations (e.g., cropping, color distortion) that may disrupt key information. First, we intentionally avoided transformations that could affect critical information in the images. For example, cropping might remove a key edge in a math problem, and color transformations could impact questions that rely on color-related information. Next, we selected transformations such as rotation and noise injection, which preserve the critical visual cues necessary for reasoning. Together with our transformation-specific prompts, these changes do not affect the correctness of the problem’s answer.

discuss how it differs from standard data-augmentation baselines.

I believe there is some misunderstanding here. The innovation of this paper does not lie in introducing data augmentation. The main contribution is using carefully designed semantic transformations to generate shared and diverse responses, and then self/cross-updating the question variants with these shared responses. Specifically, GRPO calculates the conditional probability of each generated response with respect to the original question and updates the token probabilities accordingly, i.e., $\pi_{\theta}(o_i^{Q} \mid Q)$. The GRPO + data augmentation approach works similarly, except it replaces the original question with the augmented one. In contrast, ShareGRPO generates a set of shared responses for the original question and its semantically consistent variants. These responses are then used for both self-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j = k$) and cross-updating ($\pi_{\theta}(o_i^{Q_j} \mid Q_k)$, where $j \neq k$), based on their respective conditional probabilities.

Additionally, we compare the results of ShareGRPO and GRPO with data augmentation, as shown below. The results indicate that the performance gains of ShareGRPO are not due to data augmentation, but rather from mitigating advantage vanishing through shared responses.

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W3 & Q2: Compare ShareGRPO with full experiment results with Qwen 2.5-VL + GRPO

Thank you for your suggestion. We have now provided the full experimental results comparing Qwen 2.5-VL + GRPO and Qwen 2.5-VL + ShareGRPO across all benchmarks. The results, shown in Table below, demonstrate that ShareGRPO achieves consistent improvements over GRPO, with an average performance gain of 1.9% across all benchmarks.

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Many thanks for your professional, detailed, and valuable reviews! We have done our best to address each of your concerns and hope our response can resolve them. Please let us know if you have any other questions. If you feel all questions have been addressed, we would greatly appreciate it if you could kindly consider re-rating our work. We are looking forward to hearing from you!

Thank you again for your thorough and professional review, which has greatly improved the quality and clarity of our paper.

We will include the complete baseline of all experimental results, the results obtained from training on only one new question, as well as other points discussed in the review, in the revised paper. Please feel free to contact us if you have any further questions or suggestions. Thank you!