# MMR1: Enhancing Multimodal Reasoning with Variance-Aware Sampling and Open Resources

arXiv: https://arxiv.org/abs/2509.21268 · HTML: https://mlsanity.com/paper/2509.21268/

## Key facts

- Cited by 39 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 41 of its 93 references that are in the map.
- First posted on arXiv 25 Sep 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)

## Builds on (most cited first, 30 of 41)

- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [LLaVA-OneVision: Easy Visual Task Transfer](https://mlsanity.com/paper/2408.03326/) (2024)
- [InternVL3: Exploring Advanced Training and Test-Time Recipes for Open-Source Multimodal Models](https://mlsanity.com/paper/2504.10479/) (2025)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Kimi k1.5: Scaling Reinforcement Learning with LLMs](https://mlsanity.com/paper/2501.12599/) (2025)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Model](https://mlsanity.com/paper/2504.07615/) (2025)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [Dynamic Prompt Learning via Policy Gradient for Semi-structured Mathematical Reasoning](https://mlsanity.com/paper/2209.14610/) (2022)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [From System 1 to System 2: A Survey of Reasoning Large Language Models](https://mlsanity.com/paper/2502.17419/) (2025)
- [OpenThoughts: Data Recipes for Reasoning Models](https://mlsanity.com/paper/2506.04178/) (2025)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [VAPO: Efficient and Reliable Reinforcement Learning for Advanced Reasoning Tasks](https://mlsanity.com/paper/2504.05118/) (2025)
- [LMM-R1: Empowering 3B LMMs with Strong Reasoning Abilities Through Two-Stage Rule-Based RL](https://mlsanity.com/paper/2503.07536/) (2025)
- [LogicVista: Multimodal LLM Logical Reasoning Benchmark in Visual Contexts](https://mlsanity.com/paper/2407.04973/) (2024)
- [REINFORCE++: Stabilizing Critic-Free Policy Optimization with Global Advantage Normalization](https://mlsanity.com/paper/2501.03262/) (2025)
- [VisualMRC: Machine Reading Comprehension on Document Images](https://mlsanity.com/paper/2101.11272/) (2021)
- [SoTA with Less: MCTS-Guided Sample Selection for Data-Efficient Visual Reasoning Self-Improvement](https://mlsanity.com/paper/2504.07934/) (2025)
- [LIMR: Less is More for RL Scaling](https://mlsanity.com/paper/2502.11886/) (2025)
- [OpenVLThinker: Complex Vision-Language Reasoning via Iterative SFT-RL Cycles](https://mlsanity.com/paper/2503.17352/) (2025)
- [CLEVR-Math: A Dataset for Compositional Language, Visual and Mathematical Reasoning](https://mlsanity.com/paper/2208.05358/) (2022)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [Reason-RFT: Reinforcement Fine-Tuning for Visual Reasoning of Vision Language Models](https://mlsanity.com/paper/2503.20752/) (2025)
- [What Makes a Reward Model a Good Teacher? An Optimization Perspective](https://mlsanity.com/paper/2503.15477/) (2025)

## Built on by (most cited first, 30 of 39)

- [LongVT: Incentivizing "Thinking with Long Videos" via Native Tool Calling](https://mlsanity.com/paper/2511.20785/) (2025)
- [OpenMMReasoner: Pushing the Frontiers for Multimodal Reasoning with an Open and General Recipe](https://mlsanity.com/paper/2511.16334/) (2025)
- [MMFineReason: Closing the Multimodal Reasoning Gap via Open Data-Centric Methods](https://mlsanity.com/paper/2601.21821/) (2026)
- [Scaling Language-Centric Omnimodal Representation Learning](https://mlsanity.com/paper/2510.11693/) (2025)
- [Thinking in Uncertainty: Mitigating Hallucinations in MLRMs with Latent Entropy-Aware Decoding](https://mlsanity.com/paper/2603.13366/) (2026)
- [VADE: Variance-Aware Dynamic Sampling via Online Sample-Level Difficulty Estimation for Multimodal RL](https://mlsanity.com/paper/2511.18902/) (2025)
- [Video-KTR: Reinforcing Video Reasoning via Key Token Attribution](https://mlsanity.com/paper/2601.19686/) (2026)
- [Seeing with You: Perception-Reasoning Coevolution for Multimodal Reasoning](https://mlsanity.com/paper/2603.28618/) (2026)
- [Revisiting the Necessity of Lengthy Chain-of-Thought in Vision-centric Reasoning Generalization](https://mlsanity.com/paper/2511.22586/) (2025)
- [Beyond SFT-to-RL: Pre-alignment via Black-Box On-Policy Distillation for Multimodal RL](https://mlsanity.com/paper/2604.28123/) (2026)
- [From Seeing to Thinking: Decoupling Perception and Reasoning Improves Post-Training of Vision-Language Models](https://mlsanity.com/paper/2605.20177/) (2026)
- [Boosting Reasoning in Large Multimodal Models via Activation Replay](https://mlsanity.com/paper/2511.19972/) (2025)
- [Learning When to Look: A Disentangled Curriculum for Strategic Perception in Multimodal Reasoning](https://mlsanity.com/paper/2512.17227/) (2025)
- [Seeing Through the Chain: Mitigate Hallucination in Multimodal Reasoning Models via CoT Compression and Contrastive Preference Optimization](https://mlsanity.com/paper/2602.03380/) (2026)
- [When Models Judge Themselves: Unsupervised Self-Evolution for Multimodal Reasoning](https://mlsanity.com/paper/2603.21289/) (2026)
- [What does RL improve for Visual Reasoning? A Frankenstein-Style Analysis](https://mlsanity.com/paper/2602.12395/) (2026)
- [Building a Precise Video Language with Human-AI Oversight](https://mlsanity.com/paper/2604.21718/) (2026)
- [TRON: Targeted Rule-Verifiable Online Environments for Visual Reasoning RL](https://mlsanity.com/paper/2606.01599/) (2026)
- [Zone of Proximal Policy Optimization: Teacher in Prompts, Not Gradients](https://mlsanity.com/paper/2606.18216/) (2026)
- [Latent Visual States for Efficient Multimodal Reasoning](https://mlsanity.com/paper/2606.24233/) (2026)
- [Reasoning Matters: Mitigate Hallucination in Multimodal Large Reasoning Models via Reasoning-Conditioned Preference Optimization](https://mlsanity.com/paper/2605.27906/) (2026)
- [Are Reasoning Vision-Language Models Robust to Semantic Visual Distractions?](https://mlsanity.com/paper/2606.08894/) (2026)
- [AnE: Pushing the Reasoning Frontier of Multimodal LLMs via Anchor Evolution](https://mlsanity.com/paper/2605.25571/) (2026)
- [LASER: A Corrective Lens for LVLMs via Visual Attention Preservation and Sink Suppression](https://mlsanity.com/paper/2607.01707/) (2026)
- [Co-RL: Unsupervised Reasoning Emerges from Diverse Cohort in Multi-agent RL](https://mlsanity.com/paper/2608.17253/) (2026)
- [MMVistaReason: Toward Open-Data and Post-Training Recipes for Multimodal Reasoning](https://mlsanity.com/paper/2610.01352/) (2026)
- [CityRiSE: Reasoning Urban Socio-Economic Status in Large Vision-Language Models via Reinforcement Learning](https://mlsanity.com/paper/2510.22282/) (2025)
- [R1-SyntheticVL: Is Synthetic Data from Generative Models Ready for Multimodal Large Language Model?](https://mlsanity.com/paper/2602.03300/) (2026)
- [Guided Verifier: Collaborative Multimodal Reasoning via Dynamic Process Supervision](https://mlsanity.com/paper/2602.04290/) (2026)
- [LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning](https://mlsanity.com/paper/2603.12166/) (2026)

## Abstract (arXiv)

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 https://github.com/LengSicong/MMR1.