# StainFlow: Entity-Stain Tracking and Evidence Linking for Process Rewards in GUI Agents arXiv: https://arxiv.org/abs/2606.07027 ยท HTML: https://mlsanity.com/paper/2606.07027/ ## Key facts - Cited by 2 papers in the map (data through 14 Oct 2026). - Placed in GUI and mobile agents, one of 16 directions in LLM agents and tool use. - Builds on 40 of its 47 references that are in the map. - First posted on arXiv 5 Jun 2026. ## Placed in - LLM agents and tool use / [GUI and mobile agents](https://mlsanity.com/agents/gui-and-mobile-agents/) - LLM alignment / RLHF / preference optimisation / [Process reward models for reasoning](https://mlsanity.com/alignment/process-reward-models-for-reasoning/) ## Builds on (most cited first, 30 of 40) - [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024) - [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025) - [Qwen3-VL Technical Report](https://mlsanity.com/paper/2511.21631/) (2025) - [WebArena: A Realistic Web Environment for Building Autonomous Agents](https://mlsanity.com/paper/2307.13854/) (2023) - [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024) - [OpenAI GPT-5 System Card](https://mlsanity.com/paper/2601.03267/) (2025) - [Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotations](https://mlsanity.com/paper/2312.08935/) (2023) - [CogAgent: A Visual Language Model for GUI Agents](https://mlsanity.com/paper/2312.08914/) (2023) - [SeeClick: Harnessing GUI Grounding for Advanced Visual GUI Agents](https://mlsanity.com/paper/2401.10935/) (2024) - [Group-in-Group Policy Optimization for LLM Agent Training](https://mlsanity.com/paper/2505.10978/) (2025) - [AndroidWorld: A Dynamic Benchmarking Environment for Autonomous Agents](https://mlsanity.com/paper/2405.14573/) (2024) - [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024) - [GUI-R1 : A Generalist R1-Style Vision-Language Action Model For GUI Agents](https://mlsanity.com/paper/2504.10458/) (2025) - [UI-TARS-2 Technical Report: Advancing GUI Agent with Multi-Turn Reinforcement Learning](https://mlsanity.com/paper/2509.02544/) (2025) - [DigiRL: Training In-The-Wild Device-Control Agents with Autonomous Reinforcement Learning](https://mlsanity.com/paper/2406.11896/) (2024) - [Qwen3.5-Omni Technical Report](https://mlsanity.com/paper/2604.15804/) (2026) - [OpenCUA: Open Foundations for Computer-Use Agents](https://mlsanity.com/paper/2508.09123/) (2025) - [GUI Agents with Foundation Models: A Comprehensive Survey](https://mlsanity.com/paper/2411.04890/) (2024) - [AgentRewardBench: Evaluating Automatic Evaluations of Web Agent Trajectories](https://mlsanity.com/paper/2504.08942/) (2025) - [UI-Venus Technical Report: Building High-performance UI Agents with RFT](https://mlsanity.com/paper/2508.10833/) (2025) - [MAI-UI Technical Report: Real-World Centric Foundation GUI Agents](https://mlsanity.com/paper/2512.22047/) (2025) - [Process Reward Models for LLM Agents: Practical Framework and Directions](https://mlsanity.com/paper/2502.10325/) (2025) - [Mobile-Agent-v3.5: Multi-platform Fundamental GUI Agents](https://mlsanity.com/paper/2602.16855/) (2026) - [ARPO:End-to-End Policy Optimization for GUI Agents with Experience Replay](https://mlsanity.com/paper/2505.16282/) (2025) - [AgentPRM: Process Reward Models for LLM Agents via Step-Wise Promise and Progress](https://mlsanity.com/paper/2511.08325/) (2025) - [DistRL: An Asynchronous Distributed Reinforcement Learning Framework for On-Device Control Agents](https://mlsanity.com/paper/2410.14803/) (2024) - [EvoCUA: Evolving Computer Use Agents via Learning from Scalable Synthetic Experience](https://mlsanity.com/paper/2601.15876/) (2026) - [MobileGUI-RL: Advancing Mobile GUI Agent through Reinforcement Learning in Online Environment](https://mlsanity.com/paper/2507.05720/) (2025) - [Agentic Reward Modeling: Integrating Human Preferences with Verifiable Correctness Signals for Reliable Reward Systems](https://mlsanity.com/paper/2502.19328/) (2025) - [ZeroGUI: Automating Online GUI Learning at Zero Human Cost](https://mlsanity.com/paper/2505.23762/) (2025) ## Built on by (most cited first, 2 of 2) - [SeekJudge: A Practical Reward Framework for Reinforcement Learning in Computer-Use Agents](https://mlsanity.com/paper/2607.23263/) (2026) - [Adaptive-Group Process Rewards for GUI Agents](https://mlsanity.com/paper/2610.17710/) (2026) ## Abstract (arXiv) Reinforcement Learning (RL) has become a promising approach for improving GUI Agents in long-horizon, stochastic digital environments, but trajectory-level success feedback is too sparse to provide reliable credit assignment for intermediate exploration steps. To mitigate this issue, recent studies introduce Process Reward Models (PRMs), which provide finer-grained training feedback through global milestone verification or local step-level evaluation. However, these methods still suffer from two level-specific limitations: global milestone decomposition is subjective and singular, making it difficult to accommodate the multiple valid execution paths in real GUI tasks, while fixed local judging windows may miss long-range key evidence or dilute the decision signal with irrelevant frames. Inspired by stain-tracing mechanisms in network flow analysis, we propose StainFlow, an entity-stain-flow process reward model for GUI Agents. To reduce the subjectivity of global partitioning, we introduce the Global Entity Stain Tracking module, which extracts visually verifiable task entities and tracks how their stain concentrations and states evolve along the trajectory, allowing task phases to be objectively separated by changes in the entity evidence flow. To improve the accuracy of local verification, we introduce the Local Stain Evidence Linking module. Centered on the triggering entities of each candidate key node, it retrieves relevant steps based on their stain concentrations and state changes, and dynamically constructs high-density evidence windows for verifying true key nodes. Extensive experiments on AndroidWorld and OGRBench show that StainFlow relatively improves online RL success by 3.2% and trajectory completion judgment accuracy by 1.8%.