# H-GRPO: Permutation-Invariant Reinforcement Learning for Grounded Visual Reasoning

arXiv: https://arxiv.org/abs/2606.29915 · HTML: https://mlsanity.com/paper/2606.29915/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Multimodal reasoning, one of 17 directions in LLM reasoning.
- Builds on 44 of its 54 references that are in the map.
- First posted on arXiv 29 Jun 2026.

## Placed in

- LLM reasoning / [Multimodal reasoning](https://mlsanity.com/lr/multimodal-reasoning/)
- Multimodal LLMs / vision-language models / [VLM benchmarks and visual reasoning](https://mlsanity.com/mllm/vlm-benchmarks-and-visual-reasoning/)

## Builds on (most cited first, 30 of 44)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Sentence-BERT: Sentence Embeddings using Siamese BERT-Networks](https://mlsanity.com/paper/1908.10084/) (2019)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [GPT-4o System Card](https://mlsanity.com/paper/2410.21276/) (2024)
- [Visual Genome: Connecting Language and Vision Using Crowdsourced Dense Image Annotations](https://mlsanity.com/paper/1602.07332/) (2016)
- [VQA: Visual Question Answering](https://mlsanity.com/paper/1505.00468/) (2015)
- [MMMU: A Massive Multi-discipline Multimodal Understanding and Reasoning Benchmark for Expert AGI](https://mlsanity.com/paper/2311.16502/) (2023)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [CLEVR: A Diagnostic Dataset for Compositional Language and Elementary Visual Reasoning](https://mlsanity.com/paper/1612.06890/) (2016)
- [OK-VQA: A Visual Question Answering Benchmark Requiring External Knowledge](https://mlsanity.com/paper/1906.00067/) (2019)
- [Kosmos-2: Grounding Multimodal Large Language Models to the World](https://mlsanity.com/paper/2306.14824/) (2023)
- [Are We on the Right Way for Evaluating Large Vision-Language Models?](https://mlsanity.com/paper/2403.20330/) (2024)
- [SAM 3: Segment Anything with Concepts](https://mlsanity.com/paper/2511.16719/) (2025)
- [Multimodal Chain-of-Thought Reasoning in Language Models](https://mlsanity.com/paper/2302.00923/) (2023)
- [NExT-QA:Next Phase of Question-Answering to Explaining Temporal Actions](https://mlsanity.com/paper/2105.08276/) (2021)
- [Aligning Large Multimodal Models with Factually Augmented RLHF](https://mlsanity.com/paper/2309.14525/) (2023)
- [A-OKVQA: A Benchmark for Visual Question Answering using World Knowledge](https://mlsanity.com/paper/2206.01718/) (2022)
- [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)
- [Visual-RFT: Visual Reinforcement Fine-Tuning](https://mlsanity.com/paper/2503.01785/) (2025)
- [RLHF-V: Towards Trustworthy MLLMs via Behavior Alignment from Fine-grained Correctional Human Feedback](https://mlsanity.com/paper/2312.00849/) (2023)
- [Neural Module Networks](https://mlsanity.com/paper/1511.02799/) (2015)
- [A simple neural network module for relational reasoning](https://mlsanity.com/paper/1706.01427/) (2017)
- [Don't Just Assume; Look and Answer: Overcoming Priors for Visual Question Answering](https://mlsanity.com/paper/1712.00377/) (2017)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [Visual7W: Grounded Question Answering in Images](https://mlsanity.com/paper/1511.03416/) (2015)
- [Neural-Symbolic VQA: Disentangling Reasoning from Vision and Language Understanding](https://mlsanity.com/paper/1810.02338/) (2018)
- [R1-VL: Learning to Reason with Multimodal Large Language Models via Step-wise Group Relative Policy Optimization](https://mlsanity.com/paper/2503.12937/) (2025)
- [Visual CoT: Advancing Multi-Modal Language Models with a Comprehensive Dataset and Benchmark for Chain-of-Thought Reasoning](https://mlsanity.com/paper/2403.16999/) (2024)

## Built on by (most cited first, 1 of 1)

- [AgroGround: Multi-Granularity Grounded Recognition in Agriculture](https://mlsanity.com/paper/2610.04425/) (2026)

## Abstract (arXiv)

Vision-Language Models (VLMs) often achieve high performance on benchmarks while remaining "black boxes", yet they remain prone to hallucination or rely on superficial shortcuts. In this work, we propose a framework designed to enhance both performance and interpretability through De-compositional Evidence Grounding. Unlike monolithic inference approaches, our approach forces the model to decompose a global query into a sequence of atomic sub-questions, each requiring an explicit sub-answer and critically a localized evidence bounding box. By grounding intermediate logical steps (e.g. identifying a container, analyzing liquid properties, and assessing environmental context) in specific visual regions, we construct a structured reasoning path that mirrors human-like deduction. This allows the final answer to emerge as a logical consequence of verified visual facts rather than a statistical guess.