Although visual reasoning is crucial for solving complex geometry tasks, existing vision-language models rely heavily on text-only reasoning. Some recent methods introduce intermediate visual states to facilitate reasoning, but they are often hindered by inaccurate geometric representations and low rendering fidelity, ultimately leading to unreliable outputs. To address these limitations, we propose MetaReason, a framework for multimodal reasoning in plane geometry that leverages structured meta-information to enable accurate auxiliary-line construction. The framework first parses geometric images into meta-information, performs controllable edits with predefined tools to synthesize high-fidelity visual states, and then conducts reasoning based on these augmented views. To support this framework, we construct TutorGeo, a comprehensive dataset containing 17k image-to-meta conversion samples, 60k text-only reasoning traces, and 60k interleaved multimodal reasoning traces. Using this dataset, we combine supervised fine-tuning and reinforcement learning to develop robust multimodal reasoning capabilities. We also introduce ExamGeo, a benchmark derived from real-world examination problems that enables systematic evaluation across varying difficulty levels. Experimental results demonstrate that MetaReason significantly outperforms existing open-source models and achieves competitive performance against proprietary models.
Figures & tables
Figure 1: Comparison of auxiliary-line construction quality. Existing methods often suffer from low rendering fidelity or violate geometric constraints, while MetaReason preserves geometric relations and generate accurate diagrams.
Figure 2: Overview of the MetaReason Framework. The geometric question is first converted to meta-information by MetaConverter, followed by rationality verification via MetaJudge. If reasonable, MetaReasoner implements interleaved multimodal reasoning with a pre-defined toolbox. Otherwise, it falls back to text-only reasoning.
Figure 3: The TutorGeo Data Processing Pipeline. Raw geometric QA samples are transformed into interleaved multimodal trajectories via a four-step pipeline: (1) Meta-Information Extraction and Verification, (2) Trajectory Rewriting, (3) Tool Call Injection, and (4) Visual State Generation.
Models
#Params.
MM
ExamGeo
GeoLaux-mini
GeoQA
L1
L2
L3
L4
Avg.
Accuracy
Angle
Area
Length
Other
Avg.
Closed-source Models
GPT-5.2 ( OpenAI 2025a )
-
✗
67.0
61.5
44.8
36.5
48.7
76.9
88.3
88.9
93.8
88.4
90.4
Claude-Sonnet-4.6 ( Anthropic 2026 )
-
✗
64.0
55.0
45.0
40.5
48.0
56.1
93.8
91.0
97.0
85.5
94.7
Gemini-3.1-Pro ( Google DeepMind 2026 )
-
✗
80.0
53.5
28.0
16.5
36.0
67.9
96.7
95.1
98.3
91.3
97.1
Open-source Models
Table 1: Comparison of model performance on ExamGeo, GeoLaux-mini ( Fu et al. 2025 ) and GeoQA ( Chen et al. 2021 ) benchmarks. The abbreviation MM denotes the multimodal reasoning paradigm. ExamGeo consists of four difficulty levels from “L1” to “L4”, with higher numbers indicating greater difficulty. The best and second-best results are indicated in bold and underlined text, respectively. All results are reported as percentages (%).
Figure 4: Case Study of Geometric Reasoning. Compared to methods that exhibit hallucinations due to the absence of auxiliary lines (Qwen3-VL-8B-Instruct) or inaccurate visual support (CodePlot-CoT and BAGEL-Canvas), our MetaReason framework generates deterministic visual states via tool-augmented meta-editing and derives the correct conclusion. For clarity, only the reasoning for the first statement is shown; the reported predictions cover all four statements.
Models
Training
MM
ExamGeo
GeoLaux_mini
GeoQA
L1
L2
L3
L4
Avg.
Accuracy
Angle
Area
Length
Other
Avg.
MetaReason-RL
✔
✔
72.0
70.0
51.6
45.5
56.1
80.1
88.8
79.6
87.6
68.1
87.5
w/o MetaReason
✔
✗
73.0
59.5
44.6
33.0
48.1
75.6
78.8
64.4
77.1
68.1
77.1
w/o TutorGeo training
✗
✔
37.0
27.5
22.2
19.0
24.1
46.6
68.4
72.1
81.1
81.2
73.6
Qwen3VL-8B-Instruct
✗
✗
12.0
14.0
13.4
12.0
13.1
28.5
57.3
64.7
69.3
79.7
62.5
Table 2: Ablation study of the two-stage training pipeline utilizing TutorGeo and the MetaReason framework across ExamGeo, GeoLaux_mini ( Fu et al. 2025 ) , and GeoQA ( Chen et al. 2021 ) . The abbreviation MM denotes the multimodal reasoning paradigm, while Training represents the two-stage training pipeline incorporating the proposed TutorGeo. The best and second-best results are highlighted in bold and underlined text, respectively. All results are reported as percentages (%).
Appendix figures & tables8 assets
Supplementary material from the paper’s appendix.
Appendix
Element
Description
Required Fields
Example
point
A named point with coordinates, used to construct geometric objects such as segments, lines, and circles.
• name: [coord_x, coord_y]
"A": [10.5, 20.0]
segment
A line segment connecting two named points in the point set.
Table 3: Definition of meta-information. This table provides detailed specifications for geometric elements, including point , segment , line , and circle . Each element is defined by a set of predefined fields, such as coordinates , points , and radius .
Figure 5: An Example of Meta-Information and the Corresponding Rendered Image.
Figure 6: Usage frequency of tools in the extended tool set across the training trajectories.
Benchmark
ExamGeo
GeoLaux-mini
GeoQA
Consistency
52.5%
71.2%
82.0%
Appendix
Table 4: Strict diagram-level consistency of MetaConverter on different benchmarks.
Benchmark
ExamGeo
GeoLaux-mini
GeoQA
Acceptance Precision
98.0%
90.9%
94.5%
Inconsistent Rejection
98.5%
93.9%
94.0%
Appendix
Table 5: Performance of MetaJudge on different benchmarks.
Figure 7: Case study of Geometric Reasoning on ExamGeo.
Figure 8: Case study of Geometric Reasoning on GeoQA
Figure 9: Case study of Geometric Reasoning on GeoLaux-mini. The aspect ratio of this figure is consistent with the original image provided in the GeoLaux-mini dataset. No scaling or post-processing has been applied, despite the visible vertical compression.
College of Computer Science and Artificial Intelligence, Fudan University · School of ECE, Peking University · School of Software and Microelectronics, Peking University +1