# How Many Pixels Is a Digit Worth? Place-Aware Coordinate Entropy for GUI Agent Confidence Estimation

arXiv: https://arxiv.org/abs/2609.24277 · HTML: https://mlsanity.com/paper/2609.24277/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in GUI and mobile agents, one of 16 directions in LLM agents and tool use.
- Builds on 19 of its 26 references that are in the map.
- First posted on arXiv 21 Sep 2026.

## Placed in

- LLM agents and tool use / [GUI and mobile agents](https://mlsanity.com/agents/gui-and-mobile-agents/)

## Builds on (most cited first, 19 of 19)

- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [OSWorld: Benchmarking Multimodal Agents for Open-Ended Tasks in Real Computer Environments](https://mlsanity.com/paper/2404.07972/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Selective Classification for Deep Neural Networks](https://mlsanity.com/paper/1705.08500/) (2017)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (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)
- [GPT-4V(ision) is a Generalist Web Agent, if Grounded](https://mlsanity.com/paper/2401.01614/) (2024)
- [AndroidWorld: A Dynamic Benchmarking Environment for Autonomous Agents](https://mlsanity.com/paper/2405.14573/) (2024)
- [Aguvis: Unified Pure Vision Agents for Autonomous GUI Interaction](https://mlsanity.com/paper/2412.04454/) (2024)
- [ScreenSpot-Pro: GUI Grounding for Professional High-Resolution Computer Use](https://mlsanity.com/paper/2504.07981/) (2025)
- [ShowUI: One Vision-Language-Action Model for GUI Visual Agent](https://mlsanity.com/paper/2411.17465/) (2024)
- [MAI-UI Technical Report: Real-World Centric Foundation GUI Agents](https://mlsanity.com/paper/2512.22047/) (2025)
- [EvoCUA: Evolving Computer Use Agents via Learning from Scalable Synthetic Experience](https://mlsanity.com/paper/2601.15876/) (2026)
- [Towards Trustworthy GUI Agents: A Survey](https://mlsanity.com/paper/2503.23434/) (2025)
- [Understanding GUI Agent Localization Biases through Logit Sharpness](https://mlsanity.com/paper/2506.15425/) (2025)
- [SafeGround: Know When to Trust GUI Grounding Models via Uncertainty Calibration](https://mlsanity.com/paper/2602.02419/) (2026)

## Abstract (arXiv)

GUI agents predict click coordinates as digit-token sequences, but standard text-LLM confidence estimation methods rank correct clicks from wrong ones only weakly. GUI-specific alternatives use K samples or new supervision, but still leave room for improvement. We trace part of this to place-value asymmetry: bounding-box correctness often makes higher-place digits more important than lower-place digits, so uniform aggregation weakens the signal that determines correctness. The fix is to weight each digit's Shannon entropy by its place value. We call this Place-Aware Coordinate Entropy (PACE). Across fixed-scale agents on ScreenSpot-Pro and ScreenSpot-v2, PACE wins both AUROC and selective accuracy on all primary comparisons in a single forward pass, matching or outperforming K-sample baselines at a fraction of the cost. PACE provides a per-click confidence estimate that turns coordinate-token internals into a practical confidence signal for GUI agent deployment.