# Jigsaw-R1: A Study of Rule-based Visual Reinforcement Learning with Jigsaw Puzzles

arXiv: https://arxiv.org/abs/2505.23590 · HTML: https://mlsanity.com/paper/2505.23590/

## Key facts

- Cited by 36 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 87 of its 110 references that are in the map.
- First posted on arXiv 29 May 2025.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)

## Builds on (most cited first, 30 of 87)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Qwen2.5 Technical Report](https://mlsanity.com/paper/2412.15115/) (2024)
- [Qwen2-VL: Enhancing Vision-Language Model's Perception of the World at Any Resolution](https://mlsanity.com/paper/2409.12191/) (2024)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [ALBERT: A Lite BERT for Self-supervised Learning of Language Representations](https://mlsanity.com/paper/1909.11942/) (2019)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [Expanding Performance Boundaries of Open-Source Multimodal Models with Model, Data, and Test-Time Scaling](https://mlsanity.com/paper/2412.05271/) (2024)
- [Unsupervised Representation Learning by Predicting Image Rotations](https://mlsanity.com/paper/1803.07728/) (2018)
- [Unsupervised Learning of Visual Representations by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1603.09246/) (2016)
- [Understanding R1-Zero-Like Training: A Critical Perspective](https://mlsanity.com/paper/2503.20783/) (2025)
- [Scaling Laws for Reward Model Overoptimization](https://mlsanity.com/paper/2210.10760/) (2022)
- [Unsupervised Visual Representation Learning by Context Prediction](https://mlsanity.com/paper/1505.05192/) (2015)
- [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023)
- [Cambrian-1: A Fully Open, Vision-Centric Exploration of Multimodal LLMs](https://mlsanity.com/paper/2406.16860/) (2024)
- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [Show-o: One Single Transformer to Unify Multimodal Understanding and Generation](https://mlsanity.com/paper/2408.12528/) (2024)
- [Eyes Wide Shut? Exploring the Visual Shortcomings of Multimodal LLMs](https://mlsanity.com/paper/2401.06209/) (2024)
- [SeeClick: Harnessing GUI Grounding for Advanced Visual GUI Agents](https://mlsanity.com/paper/2401.10935/) (2024)
- [VLM-R1: A Stable and Generalizable R1-style Large Vision-Language Model](https://mlsanity.com/paper/2504.07615/) (2025)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (2025)
- [Janus: Decoupling Visual Encoding for Unified Multimodal Understanding and Generation](https://mlsanity.com/paper/2410.13848/) (2024)
- [Domain Generalization by Solving Jigsaw Puzzles](https://mlsanity.com/paper/1903.06864/) (2019)
- [Reasoning Models Don't Always Say What They Think](https://mlsanity.com/paper/2505.05410/) (2025)

## Built on by (most cited first, 30 of 36)

- [Thinking with Images for Multimodal Reasoning: Foundations, Methods, and Future Frontiers](https://mlsanity.com/paper/2506.23918/) (2025)
- [Uni-cot: Towards Unified Chain-of-Thought Reasoning Across Text and Vision](https://mlsanity.com/paper/2508.05606/) (2025)
- [ThinkMorph: Emergent Properties in Multimodal Interleaved Chain-of-Thought Reasoning](https://mlsanity.com/paper/2510.27492/) (2025)
- [Look-Back: Implicit Visual Re-focusing in MLLM Reasoning](https://mlsanity.com/paper/2507.03019/) (2025)
- [Spatial-SSRL: Enhancing Spatial Understanding via Self-Supervised Reinforcement Learning](https://mlsanity.com/paper/2510.27606/) (2025)
- [Beyond Seeing: Evaluating Multimodal LLMs on Tool-Enabled Image Perception, Transformation, and Reasoning](https://mlsanity.com/paper/2510.12712/) (2025)
- [When Visualizing is the First Step to Reasoning: MIRA, a Benchmark for Visual Chain-of-Thought](https://mlsanity.com/paper/2511.02779/) (2025)
- [DiffThinker: Towards Generative Multimodal Reasoning with Diffusion Models](https://mlsanity.com/paper/2512.24165/) (2025)
- [Why Reinforcement Fine-Tuning Enables MLLMs Preserve Prior Knowledge Better: A Data Perspective](https://mlsanity.com/paper/2506.23508/) (2025)
- [VR-Thinker: Boosting Video Reward Models through Thinking-with-Image Reasoning](https://mlsanity.com/paper/2510.10518/) (2025)
- [Agentic Jigsaw Interaction Learning for Enhancing Visual Perception and Reasoning in Vision-Language Models](https://mlsanity.com/paper/2510.01304/) (2025)
- [VisGym: Diverse, Customizable, Scalable Environments for Multimodal Agents](https://mlsanity.com/paper/2601.16973/) (2026)
- [Reinforcement Learning for Large Model: A Survey](https://mlsanity.com/paper/2508.08189/) (2025)
- [Revisiting the Necessity of Lengthy Chain-of-Thought in Vision-centric Reasoning Generalization](https://mlsanity.com/paper/2511.22586/) (2025)
- [SSL4RL: Revisiting Self-supervised Learning as Intrinsic Reward for Visual-Language Reasoning](https://mlsanity.com/paper/2510.16416/) (2025)
- [ViSS-R1: Self-Supervised Reinforcement Video Reasoning](https://mlsanity.com/paper/2511.13054/) (2025)
- [Retrieve, Integrate, and Synthesize: Spatial-Semantic Grounded Latent Visual Reasoning](https://mlsanity.com/paper/2605.07106/) (2026)
- [Reassessing the Role of Supervised Fine-Tuning: An Empirical Study in VLM Reasoning](https://mlsanity.com/paper/2512.12690/) (2025)
- [Bridging Interleaved Multi-Modal Reasoning as a Unified Decision Process](https://mlsanity.com/paper/2607.03748/) (2026)
- [PuzLM: Solving Jigsaw Puzzles with Sequence-to-Sequence Language Models](https://mlsanity.com/paper/2511.06315/) (2025)
- [PuzzleCraft: Exploration-Aware Curriculum Learning for Puzzle-Based RLVR in VLMs](https://mlsanity.com/paper/2512.14944/) (2025)
- [Improving Vision-language Models with Perception-centric Process Reward Models](https://mlsanity.com/paper/2604.24583/) (2026)
- [DiG: Differential Grounding for Enhancing Fine-Grained Perception in Multimodal Large Language Model](https://mlsanity.com/paper/2512.12633/) (2025)
- [SPHINX: A Synthetic Environment for Visual Perception and Reasoning](https://mlsanity.com/paper/2511.20814/) (2025)
- [Med-Scout: Curing MLLMs' Geometric Blindness in Medical Perception via Geometry-Aware RL Post-Training](https://mlsanity.com/paper/2601.23220/) (2026)
- [TPRU: Advancing Temporal and Procedural Understanding in Large Multimodal Models](https://mlsanity.com/paper/2602.18884/) (2026)
- [Learning Transferable Temporal Primitives for Video Reasoning via Synthetic Videos](https://mlsanity.com/paper/2603.17693/) (2026)
- [SSL-R1: Self-Supervised Visual Reinforcement Post-Training for Multimodal Large Language Models](https://mlsanity.com/paper/2604.20705/) (2026)
- [Boosting Visual Instruction Tuning with Self-Supervised Guidance](https://mlsanity.com/paper/2604.12966/) (2026)
- [Trace: A Taxonomy-Guided Environment for Multidomain Visual Reasoning](https://mlsanity.com/paper/2607.19790/) (2026)

## Abstract (arXiv)

The application of rule-based reinforcement learning (RL) to multimodal large language models (MLLMs) introduces unique challenges and potential deviations from findings in text-only domains, particularly for perception-heavy tasks. This paper provides a comprehensive study of rule-based visual RL, using jigsaw puzzles as a structured experimental framework. Jigsaw puzzles offer inherent ground truth, adjustable difficulty, and demand complex decision-making, making them ideal for this study. Our research reveals several key findings: textitFirstly, we find that MLLMs, initially performing near to random guessing on the simplest jigsaw puzzles, achieve near-perfect accuracy and generalize to complex, unseen configurations through fine-tuning. textitSecondly, training on jigsaw puzzles can induce generalization to other visual tasks, with effectiveness tied to specific task configurations. textitThirdly, MLLMs can learn and generalize with or without explicit reasoning, though open-source models often favor direct answering. Consequently, even when trained for step-by-step reasoning, they can ignore the thinking process in deriving the final answer. textitFourthly, we observe that complex reasoning patterns appear to be pre-existing rather than emergent, with their frequency increasing alongside training and task difficulty. textitFinally, our results demonstrate that RL exhibits more effective generalization than Supervised Fine-Tuning (SFT), and an initial SFT cold start phase can hinder subsequent RL optimization. Although these observations are based on jigsaw puzzles and may vary across other visual tasks, this research contributes a valuable piece of jigsaw to the larger puzzle of collective understanding rule-based visual RL and its potential in multimodal learning. The code is available at: https://github.com/zifuwanggg/Jigsaw-R1