Dataset
Point-Level Accuracy
Success is measured by distance to a target point, not membership in a tolerant UI region.
Precision-Aware Geometric Reasoning
PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control
PAGER turns geometric reasoning into pixel-level GUI execution. PAGE Bench measures this precision-sensitive setting with verified GeoGebra trajectories, process supervision, and geometry-aware evaluation.
Jingxuan Wei1,*
Xi Bai1,*
Shan Liu3,*
Caijun Jia1,*
Zheng Sun1
Xinglong Xu1
Siyuan Li2
Linzhuang Sun1
Bihui Yu1
Conghui He2
Cheng Tan2
1 University of Chinese Academy of Sciences
2 Shanghai Artificial Intelligence Laboratory
3 China University of Petroleum-Beijing
4,906
geometry problems
224K
GUI actions
53,277
construction tasks
10
skill categories
62.20
step success
29.52
overall score
Motivation
When a correct action still lands in the wrong place
Conventional GUI tasks tolerate nearby clicks inside the same component. Geometric construction does not: a misplaced point changes every dependent line, circle, angle, intersection, label, and polygon.
Dependency Coupling
Early coordinate drift cascades through downstream geometric objects and relations.
Continuous Parameters
Drawing requires exact endpoints, radii, text anchors, object styles, and canvas coordinates.
Semantic-Execution Gap
Models can choose the right operation type while failing to execute a valid construction.
PAGER Framework
Plan dependencies, execute pixels, optimize precision
PAGER factorizes drawing into dependency-structured planning and state-conditioned GUI execution, then trains with pixel-grounded SFT and precision-aligned reinforcement learning.
1
Dependency Planning
Induces a construction graph and orders primitives so prerequisite objects are available before dependent operations.
2
Pixel Execution
Grounds each sub-task into click, paint, and type actions conditioned on the current canvas state and action history.
3
Precision Rewards
Combines action-type correctness, parameter accuracy, and rendered geometric validity to reduce rollout drift.
PAGE Bench
A closed execution loop for geometric GUI trajectories
PAGE Bench converts K-12 geometry problems into executable GeoGebra task sequences, replays them in a live GUI, records pixel-level process traces, and filters invalid constructions after verification.
4,443 / 463
train / test split
45.76
actions per problem
88.03%
click + paint actions
Key Statistics
Corpus scale and process scale from the PAGE Bench source table.
| Statistic | Count | Share | Process | Count |
|---|---|---|---|---|
| Total problems | 4,906 | 100.00% | Total tasks | 53,277 |
| Train / Test | 4,443 / 463 | 90.56 / 9.44 | Avg. tasks / problem | 10.86 |
| Open-ended | 2,857 | 58.23% | Total actions | 224,497 |
| Grade 8-10+ | 4,387 | 89.42% | Click + paint | 197,634 |
| Intermediate / Hard | 2,940 / 1,677 | 94.11% | Type actions | 26,863 |
Results
PAGER improves trajectory-level stability
Strong VLMs often achieve high action-type accuracy, but task success remains low. PAGER closes this gap by improving parameter control and preserving dependent geometric structure across the rollout.
Task Success vs. Overall Score
Representative models from the main-results table.
Semantic-Execution Gap
Claude-Sonnet-4.6 reaches 95.85 Action Accuracy, and Gemini-3.1-Pro reaches 66.66 Step Success, yet their complete Task Success remains 1.11 and 5.82. PAGER reaches 23.78 Task Success and 29.52 Overall, showing stronger stability across full construction trajectories.
4.1x
task success over Gemini-3.1-Pro
62.20
step success for point-precise control
Main Results on Precise Geometric Tasks
Full table from the paper. Metrics cover action semantics, parameter precision, step/task success, compositional process scores, visual/geometric final quality, and overall performance.
| Model | Action | Param | Step | Task | O-Comp. | S-Comp. | S-Vis. | S-Geo. | Middle | Final | Overall |
|---|---|---|---|---|---|---|---|---|---|---|---|
| Open-source VLMs | |||||||||||
| Qwen3-VL-8B | 52.03 | 9.48 | 9.38 | 0.25 | 3.09 | 3.83 | 3.69 | 3.05 | 8.18 | 3.42 | 5.80 |
| DeepSeek-VL2 | 26.33 | 1.75 | 1.53 | 0.00 | 18.25 | 8.46 | 3.70 | 12.40 | 3.11 | 11.23 | 7.17 |
| GLM-4.5V | 78.91 | 12.17 | 11.76 | 0.00 | 5.44 | 7.93 | 2.89 | 13.41 | 11.46 | 7.27 | 9.37 |
| InternVL2.5-8B | 40.34 | 1.48 | 1.33 | 0.00 | 9.23 | 7.19 | 1.72 | 10.85 | 4.45 | 7.44 | 5.94 |
| KimiVL-A3B | 46.60 | 0.59 | 0.57 | 0.00 | 1.70 | 7.12 | 1.24 | 14.05 | 4.83 | 5.70 | 5.27 |
| MiniCPM-V-2.6-8B | 45.87 | 1.06 | 0.71 | 0.00 | 16.01 | 4.81 | 1.17 | 8.18 | 4.84 | 8.12 | 6.48 |
| LLaVA-NeXT-8B | 45.77 | 1.69 | 1.59 | 0.00 | 8.04 | 5.13 | 1.74 | 8.75 | 5.06 | 6.05 | 5.56 |
| Closed-source VLMs | |||||||||||
| Claude-Sonnet-4.6 | 95.85 | 36.44 | 36.38 | 1.11 | 7.04 | 9.46 | 3.11 | 15.39 | 21.17 | 8.65 | 14.91 |
| GPT-5.4 | 88.04 | 31.71 | 31.41 | 0.56 | 10.99 | 9.59 | 3.53 | 15.39 | 18.59 | 9.96 | 14.28 |
| Qwen3.6-Plus | 90.95 | 51.60 | 51.07 | 4.90 | 18.19 | 11.04 | 4.23 | 10.52 | 27.41 | 11.72 | 19.56 |
| Gemini-3.1-Pro | 89.18 | 66.68 | 66.66 | 5.82 | 20.97 | 14.17 | 7.63 | 21.21 | 32.41 | 16.31 | 24.36 |
| Specialized GUI Agents | |||||||||||
| UI-TARS | 47.08 | 8.79 | 8.38 | 0.00 | 7.06 | 5.26 | 3.78 | 5.21 | 7.26 | 5.49 | 6.38 |
| OS-ATLAS | 51.24 | 9.19 | 8.80 | 0.29 | 14.56 | 6.65 | 4.32 | 6.36 | 7.98 | 8.50 | 8.24 |
| InfiGUI-R1-3B | 44.81 | 16.51 | 16.18 | 0.00 | 18.23 | 9.66 | 4.14 | 13.82 | 9.37 | 11.96 | 10.66 |
| OpenCUA-7B | 55.86 | 10.57 | 9.85 | 0.12 | 15.39 | 8.92 | 3.11 | 10.77 | 8.69 | 10.07 | 9.38 |
| GUI-Actor-7B | 47.26 | 5.31 | 5.02 | 0.00 | 18.66 | 6.04 | 1.42 | 7.58 | 6.26 | 9.21 | 7.74 |
| PAGER | 82.62 | 62.76 | 62.20 | 23.78 | 28.88 | 15.30 | 7.05 | 15.63 | 41.25 | 17.79 | 29.52 |
Detailed Analysis
Evaluation consistency and capability diagnostics
The main result table establishes the headline comparison. These supplementary views show whether the automated verifier agrees with expert judgment and where models fail across fine-grained geometric skills.
Automated Scores Align with Human Judgments
Human ratings track the automated evaluation closely, with a correlation of r=0.9397. Most existing MLLMs cluster in the lower-left region, while PAGER appears in the top-right corner, showing that higher verifier scores correspond to human-perceived geometric correctness.
Fine-Grained Capability Breakdown
The ten-skill heatmap separates easier tool-mapping and object-construction abilities from harder dependency-heavy cases. Baselines drop sharply on multi-step planning, structural constraints, auxiliary elements, and real-world geometric modeling, while PAGER remains consistently stronger.
Case Study
Coordinate drift becomes visible in the final construction
The rectangle example shows how early vertex errors distort diagonals, intersections, and downstream relations, while PAGER better preserves the intended geometric structure.
Error propagation
The rectangle construction requires accurate vertex placement before drawing diagonals and intersection relations. Small coordinate errors in early steps change the geometry that later operations depend on.
Constraint preservation
PAGER keeps the rectangular structure and central diagonal intersection more stable, while baseline models drift into distorted quadrilaterals, redundant elements, or missing construction steps.
Citation
Draft citation from the current paper source. Verify the final venue and identifier before publishing.
@misc{wei2026pager,
title={PAGER: Bridging the Semantic-Execution Gap in Point-Precise Geometric GUI Control},
author={Jingxuan Wei and Xi Bai and Shan Liu and Caijun Jia and Zheng Sun and Xinglong Xu and Siyuan Li and Linzhuang Sun and Bihui Yu and Conghui He and Cheng Tan},
year={2026},
url={}
}