# Faithful GRPO: Improving Visual Spatial Reasoning in Multimodal Language Models via Constrained Policy Optimization

arXiv: https://arxiv.org/abs/2604.08476 · HTML: https://mlsanity.com/paper/2604.08476/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 9 Apr 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-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, 29 of 29)

- [Microsoft COCO: Common Objects in Context](https://mlsanity.com/paper/1405.0312/) (2014)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [DAPO: An Open-Source LLM Reinforcement Learning System at Scale](https://mlsanity.com/paper/2503.14476/) (2025)
- [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)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [Constrained Policy Optimization](https://mlsanity.com/paper/1705.10528/) (2017)
- [Vision-R1: Incentivizing Reasoning Capability in Multimodal Large Language Models](https://mlsanity.com/paper/2503.06749/) (2025)
- [Safe RLHF: Safe Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2310.12773/) (2023)
- [LESS: Selecting Influential Data for Targeted Instruction Tuning](https://mlsanity.com/paper/2402.04333/) (2024)
- [Distance-IoU Loss: Faster and Better Learning for Bounding Box Regression](https://mlsanity.com/paper/1911.08287/) (2019)
- [Reward Constrained Policy Optimization](https://mlsanity.com/paper/1805.11074/) (2018)
- [R1-Onevision: Advancing Generalized Multimodal Reasoning through Cross-Modal Formalization](https://mlsanity.com/paper/2503.10615/) (2025)
- [VL-Rethinker: Incentivizing Self-Reflection of Vision-Language Models with Reinforcement Learning](https://mlsanity.com/paper/2504.08837/) (2025)
- [Reinforcement Learning with Verifiable Rewards Implicitly Incentivizes Correct Reasoning in Base LLMs](https://mlsanity.com/paper/2506.14245/) (2025)
- [GDPO: Group reward-Decoupled Normalization Policy Optimization for Multi-reward RL Optimization](https://mlsanity.com/paper/2601.05242/) (2026)
- [OmniSpatial: Towards Comprehensive Spatial Reasoning Benchmark for Vision Language Models](https://mlsanity.com/paper/2506.03135/) (2025)
- [MindCube: Spatial Mental Modeling from Limited Views](https://mlsanity.com/paper/2506.21458/) (2025)
- [Grounded Reinforcement Learning for Visual Reasoning](https://mlsanity.com/paper/2505.23678/) (2025)
- [VGR: Visual Grounded Reasoning](https://mlsanity.com/paper/2506.11991/) (2025)
- [SafeVLA: Towards Safety Alignment of Vision-Language-Action Model via Constrained Learning](https://mlsanity.com/paper/2503.03480/) (2025)
- [Traceable Evidence Enhanced Visual Grounded Reasoning: Evaluation and Methodology](https://mlsanity.com/paper/2507.07999/) (2025)
- [Make Every Move Count: LLM-based High-Quality RTL Code Generation Using MCTS](https://mlsanity.com/paper/2402.03289/) (2024)
- [MO-GRPO: Mitigating Reward Hacking of Group Relative Policy Optimization on Multi-Objective Problems](https://mlsanity.com/paper/2509.22047/) (2025)

## Built on by (most cited first, 6 of 6)

- [Self-Evolving Spatial Reasoning in Vision Language Models via Geometric Logic Consistency](https://mlsanity.com/paper/2605.18162/) (2026)
- [SER: Learning to Ground Video Reasoning with Semantic Evidence Rewards](https://mlsanity.com/paper/2606.24726/) (2026)
- [Be Faithful When Response: Returning Fluent and Grounded Answers for Vision-Language Models Reinforcement Learning](https://mlsanity.com/paper/2606.29984/) (2026)
- [SpatialCORE: Confidence-Aware Grounded Spatial Reasoning in Large Vision--Language Models](https://mlsanity.com/paper/2609.38716/) (2026)
- [Soft Spatial Reasoning](https://mlsanity.com/paper/2609.38717/) (2026)
- [A Low Grounding Score Is Not an Ungrounded Judge: Identifying the Perceptibility Confound in Multimodal Oversight](https://mlsanity.com/paper/2610.00111/) (2026)

## Abstract (arXiv)

Multimodal reasoning models (MRMs) trained with reinforcement learning with verifiable rewards (RLVR) show improved accuracy on visual reasoning benchmarks. However, we observe that accuracy gains often come at the cost of reasoning quality: generated Chain-of-Thought (CoT) traces are frequently inconsistent with the final answer and poorly grounded in the visual evidence. We systematically study this phenomenon across seven challenging real-world spatial reasoning benchmarks and find that it affects contemporary MRMs such as ViGoRL-Spatial, TreeVGR as well as our own models trained with standard Group Relative Policy Optimization (GRPO). We characterize CoT reasoning quality along two complementary axes: "logical consistency" (does the CoT entail the final answer?) and "visual grounding" (does each reasoning step accurately describe objects, attributes, and spatial relationships in the image?). To address this, we propose Faithful GRPO (FGRPO), a variant of GRPO that enforces consistency and grounding as constraints via Lagrangian dual ascent. FGRPO incorporates batch-level consistency and grounding constraints into the advantage computation within a group, adaptively adjusting the relative importance of constraints during optimization. We evaluate FGRPO on Qwen2.5-VL-7B and 3B backbones across seven spatial datasets. Our results show that FGRPO substantially improves reasoning quality, reducing the inconsistency rate from 24.5% to 1.7% and improving visual grounding scores by +13%. It also improves final answer accuracy over simple GRPO, demonstrating that faithful reasoning enables better answers.