Large multimodal reasoning models have achieved rapid progress, but their advancement is constrained by two major limitations: the absence of open, large-scale, high-quality long chain-of-thought (CoT) data, and the instability of reinforcement learning (RL) algorithms in post-training. Group Relative Policy Optimization (GRPO), the standard framework for RL fine-tuning, is prone to gradient vanishing when reward variance is low, which weakens optimization signals and impairs convergence. This work makes three contributions: (1) We propose Variance-Aware Sampling (VAS), a data selection strategy guided by Variance Promotion Score (VPS) that combines outcome variance and trajectory diversity to promote reward variance and stabilize policy optimization. (2) We release large-scale, carefully curated resources containing ~1.6M long CoT cold-start data and ~15k RL QA pairs, designed to ensure quality, difficulty, and diversity, along with a fully reproducible end-to-end training codebase. (3) We open-source a family of multimodal reasoning models in multiple scales, establishing standardized baselines for the community. Experiments across mathematical reasoning benchmarks demonstrate the effectiveness of both the curated data and the proposed VAS. Comprehensive ablation studies and analyses provide further insight into the contributions of each component. In addition, we theoretically establish that reward variance lower-bounds the expected policy gradient magnitude, with VAS serving as a practical mechanism to realize this guarantee. Our code, data, and checkpoints are available at this https URL .
Introduction
Introduction
This repo introduces our work on enhancing multimodal reasoning models. Current progress is limited by:
❌ Lack of open, large-scale, high-quality long chain-of-thought (CoT) data
❌ Instability of RL fine-tuning, where standard GRPO often suffers from gradient vanishing under low reward variance
🔑 Our Contributions
Variance-Aware Sampling (VAS):
A new data selection strategy guided by the Variance Promotion Score (VPS). VAS combines outcome variance and trajectory diversity to promote reward variance, stabilize policy optimization, and improve convergence.
Large-scale curated resources:
~1.6M long CoT cold-start trajectories with verified short answer
~15k RL QA pairs
Designed for quality, difficulty, and diversity
Open-source codebase & models:
Fully reproducible end-to-end training pipeline
Released models at multiple scales as standardized baselines for multimodal reasoning
Please refer to our TRAIN.md for detailed instructions on training with VAS.
Methodology Overview
Our method introduces Variance-Aware Sampling (VAS) to address the gradient vanishing problem in reinforcement learning with Group Relative Policy Optimization (GRPO).
Overview of the VAS framework
🔹 Framework
As illustrated in Figure 1, training begins with a pool of prompts from the dataset:
A random sampler provides uniform coverage of data.
A weighted sampler, guided by Variance Promotion Score (VPS), prioritizes prompts with higher reward variance and trajectory diversity.
These two sources are combined to form training batches, balancing exploration and coverage.
The policy model generates rollouts, which are evaluated with rewards and used to update the policy. VPS scores are periodically re-estimated as the model improves, ensuring dynamic adaptation.
This design ensures that training consistently focuses on prompts that provide strong learning signals, while still maintaining sufficient randomness for coverage.
algo
🔹 Algorithm
Algorithm 1 provides a step-by-step description of VAS within the GRPO framework:
Initialization: For each prompt, multiple rollouts are sampled to estimate pass rate, outcome variance (OVS), trajectory diversity (TDS), and VPS.
Periodic VPS update: At specified intervals, these statistics are refreshed to reflect the evolving policy.
Batch construction: A mixture of prompts is drawn—some uniformly at random, others proportionally to VPS—controlled by the mixture ratio λ.
Policy optimization: Rollouts are generated for the selected prompts, GRPO loss is computed, and the policy parameters are updated accordingly.
By adaptively steering training toward prompts with higher reward variance, VAS effectively stabilizes optimization and amplifies gradient signals, enabling more efficient and robust learning.
Open Resources
We release the following resources for the community:
MMR1-SFT (~16M): Supervised fine-tuning dataset with 16M long CoT cold-start trajectories (Gemini2.5 Pro/Flash) with verified short answer (GPT-4o)
MMR1-RL (15k): RL dataset with 15k question-answer pairs (GPT-4o)
MMR1-7B-RL: 7B checkpoint trained with MMR1-SFT and MMR1-RL
MMR1-32B-SFT: 32B checkpoint trained with MMR1-SFT
MMR1-32B-RL: 32B checkpoint trained with MMR1-SFT and MMR1-RL (On the way!)
data
The dataset spans diverse domains—including mathematics, science, charts/figures, document tables, and general understanding—covering ~1.6M math samples and an additional ~37K samples across other domains. It integrates existing public resources (e.g., MathVerse, ScienceQA, ChartQA, DocVQA, GQA) together with newly curated and self-collected data, ensuring quality, difficulty, and diversity. This collection establishes one of the most comprehensive open resources for multimodal reasoning models.
We hope these resources can serve as a benchmark for the community and facilitate the research of multimodal reasoning.
Evaluation Results
We evaluate our models on a suite of mathematics-related multimodal reasoning benchmarks (MathVerse, MathVista, MathVision, LogicVista, and ChartQA).
result
MMR1-7B-RL achieves an average score of 58.4, establishing new state-of-the-art performance among 7B-scale reasoning models.
MMR1-3B-RL performs competitively with 52.7, showing strong reasoning ability even at smaller scale.
Our models consistently outperform or match larger baselines, demonstrating the effectiveness of Variance-Aware Sampling (VAS) and our curated long CoT training data.
Analysis of VAS Training Dynamics
We further analyze the effectiveness of Variance-Aware Sampling (VAS) through training efficiency and the evolution of Variance Promotion Score (VPS).
anal1
Training Efficiency (Fig. 2).
Gradient norm: VAS substantially amplifies gradient magnitudes compared to the vanilla baseline, mitigating the gradient vanishing issue. This indicates that VAS consistently provides stronger optimization signals.
Clip fraction: Higher clipping fractions in VAS runs suggest that policy updates are closer to the trust-region boundary, enabling more effective utilization of the learning signal without destabilizing training.
Validation accuracy: Both full VAS (λ = 1.0) and mixed VAS–random sampling (λ = 0.5) converge faster and achieve higher final accuracy than the baseline, demonstrating that VAS improves both efficiency and performance. Notably, the mixed strategy achieves competitive results while maintaining broader data coverage.
anal2
VPS Dynamics (Fig. 3).
Score distribution: VPS distributions evolve from relatively uniform at the beginning of training to more concentrated in the middle bins, suggesting convergence in identifying consistently informative prompts.
Weight transitions: Transition matrices show that many prompts shift across bins over time, with both upward and downward movements, reflecting the dynamic nature of reward variance as the policy evolves. Early transitions are more widespread, while later updates become more stable, consistent with convergence.
Interpretation: This dynamic reweighting ensures that the model continually prioritizes prompts with higher variance while still allowing redistribution as learning progresses, preventing overfitting to a static subset of data.
👉 Together, these analyses highlight how VAS effectively mitigates gradient vanishing, improves sample efficiency, and adapts dynamically to the evolving training landscape.
Qualitative Demo
To illustrate the reasoning capability of our models, we provide qualitative examples from MathVerse.
The demo showcases how the model carefully analyzes the problem, plans a structured solution, executes step-by-step reasoning, verifies results, and even provides alternative solution paths.
demo
This demonstrates the model’s ability to maintain logical consistency, perform reflective verification, and present human-readable reasoning traces.
Citation
If you find MMR1 useful for your research and applications, please cite using this BibTeX:
bibtex
1@misc{leng2025mmr1,
2 title={MMR1: Enhancing Multimodal Reasoning with Variance-Aware Sampling and Open Resources},
3 author={Sicong Leng and Jing Wang and Jiaxi Li and Hao Zhang and Zhiqiang Hu and Boqiang Zhang and Yuming Jiang and Hang Zhang and Xin Li and Lidong Bing and Deli Zhao and Wei Lu and Yu Rong and Aixin Sun and Shijian Lu},
4 year={2025},
5 eprint={2509.21268},
6 archivePrefix={arXiv},
7 primaryClass={cs.CV},
8 url={https://arxiv.org/abs/2509.21268},
9}
License
This project is released under the Apache 2.0 license as found in the LICENSE file.
The service is a research preview intended for non-commercial use ONLY, subject to the model Licenses of Qwen, Terms of Use of the data generated by OpenAI and Gemini, and Privacy Practices of ShareGPT. Please get in touch with us if you find any potential violations.
