GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning

Jiayin Sun; Caixia Sun; Boyu Yang; Hailin Li; Xiao Chen; Yi Zhang; Errui Ding; Liang Li

cs.CVMar 24, 2026

GeoTikzBridge: Advancing Multimodal Code Generation for Geometric Perception and Reasoning

Authors: Jiayin Sun, Caixia Sun, Boyu Yang, Hailin Li, Xiao Chen, Yi Zhang, Errui Ding, Liang Li,

Organizations: JIUTIAN Research

Abstract

Multimodal Large Language Models (MLLMs) have recently demonstrated remarkable perceptual and reasoning abilities. However, they struggle to perceive fine-grained geometric structures, constraining their ability of geometric understanding and visual reasoning. To address this, we propose GeoTikzBridge, a framework that enhances local geometric perception and visual reasoning through tikz-based code generation. Within this framework, we build two models supported by two complementary datasets. The GeoTikzBridge-Base model is trained on GeoTikz-Base dataset, the largest image-to-tikz dataset to date with 2.5M pairs (16 $\times$ larger than existing open-sourced datasets). This process is achieved via iterative data expansion and a localized geometric transformation strategy. Subsequently, GeoTikzBridge-Instruct is fine-tuned on GeoTikz-Instruct dataset which is the first instruction-augmented tikz dataset supporting visual reasoning. Extensive experimental results demonstrate that our models achieve state-of-the-art performance among open-sourced MLLMs. Furthermore, GeoTikzBridge models can serve as plug-and-play reasoning modules for any MLLM(LLM), enhancing reasoning performance in geometric problem-solving. Datasets and codes are publicly available at: https://github.com/sjy-1995/GeoTikzBridge.

Figures & tables

Figure 1: GeoTikzBridge demonstrates advantages in geometric perception and mathematical reasoning. (1) GeoTikzBridge-Base achieves the most accurate reconstruction of local geometric structures compared to existing approaches. (2) The generated tikz representations enhance MLLMs’ mathematical and visual geometric reasoning.

Figure 2: Framework of the proposed iterative self-refinement for GeoTikz-Base dataset and GeoTikzBridge-Base model. It iteratively conducts three steps: dataset construction and sample generation, localized geometric transformation, and model optimization.

Figure 3: Distribution of the 2.5M GeoTikz-Base dataset.

Method	DaTikZ			MathVista-GPS			GAOKAO-MM-Math			EDUBenchmark
	CLIP-S $\uparrow$	FID $\downarrow$	CSR $\uparrow$	CLIP-S $\uparrow$	FID $\downarrow$	CSR $\uparrow$	CLIP-S $\uparrow$	FID $\downarrow$	CSR $\uparrow$	CLIP-S $\uparrow$	FID $\downarrow$	CSR $\uparrow$
Open-sourced VLMs
Qwen2.5-VL-32B [ 4 ]	0.788	77.2	80.6%	0.832	61.0	97.6%	0.808	92.2	94.4%	0.748	87.0	81.2%
Qwen2.5-VL-72B [ 4 ]	0.795	49.8	81.5%	0.858	46.9	98.1%	0.854	61.3	90.1%	0.781	60.5	81.8%
Qwen3-VL-30B-A3B [ 40 ]	0.672	174.4	89.1%	0.802	65.7	81.0%	0.826	107.9	95.2%	0.748	95.9	80.2%
InternVL3-78B [ 57 ]	0.747	62.7	78.8%	0.860	47.9	92.3%	0.871	55.4	93.7%	0.801	58.3	81.5%

Table 1: Performance comparison of image-to-tikz methods across four datasets. The best and second-best results are marked with bold and underlines, respectively.

Method	MathVista	GAOKAO-MM	RBench-M	RBench-V	RBench-V
	(GPS)	(Math)	(en)	(Math)	(Overall)
Closed-sourced VLMs
GPT-4V [ 29 ]	0.505	0.450	-	-	-
GPT-4-turbo [ 1 ]	0.583	0.500	-	-	-
GPT-4o [ 19 ]	0.647	-	0.334	0.244	0.141
Claude3.5-Sonnet [ 3 ]	0.644	-	0.397	-	-

Table 2: Performance comparison of downstream mathematical reasoning across five benchmarks. The best and second-best results are marked with bold and underlines, respectively.

Method	MSE $\downarrow$	SSIM $\uparrow$	PSNR $\uparrow$	CLIP Score $\uparrow$	FID $\downarrow$	CSR $\uparrow$
FigCodifier [ 42 ]	1435.9	0.135	17.6dB	0.936	9.798	88.0%
GeoTikzBridge-Base-8B	692.6	0.549	23.1dB	0.967	5.476	95.4%
GeoTikzBridge-Instruct	211.7	0.844	89.6dB	0.992	1.158	96.7%

Table 3: Performance comparison of instructed code generation in the downstream auxiliary line generation task. The best results are marked with bold.

Exp ID	I	II	III	IV
Problem Text	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$
Raw Geometric Image	$\checkmark$	$\checkmark$	$\checkmark$	$\checkmark$
Tikz Code With Aux. Line Added	$\times$	$\times$	$\checkmark$	$\checkmark$
Image With Aux. Line Added	$\times$	$\checkmark$	$\times$	$\checkmark$
Answer Accuracy	0.688	0.697	0.707	0.736

Table 4: Performance comparison of four different visual reasoning formats on the MathVista-GPS benchmark. The baseline model is InternVL3.5-38B.

Figure 4: Ablation study of geometric representation on the MathVista-GPS benchmark. The baseline model is Qwen3-VL-30B-A3B.

Figure 5: Ablation study of localized geometric transformation strategies for GeoTikzBridge-Base-8B, evaluated on the MathVista-GPS benchmark.

Figure 6: Visualization results of tikz codes generated by GeoTikzBridge-Base compared with GPT-5.0 [ 30 ] , each figure shows the input image (either geometric or non-geometric) and the corresponding image rendered from our predicted tikz code.

Figure 7: Visualization results of instruction-driven auxiliary line generation compared with GPT-5.0 [ 30 ] , each figure shows the input geometric image, the natural language instruction for auxiliary line addition, and the rendered image from the generated tikz code.

Figure S1 : Prompt input to Doubao for filtering unreliable instruction annotations in the GeoTikz-Instruct dataset construction.

Figure S2 : Ablation study of different values of self-refinement $K$ for GeoTikzBridge-Base-8B, evaluated on the MathVista-GPS benchmark.

Figure S3 : Ablation study of different values of CLIP score based filtering threshold $\tau$ for GeoTikzBridge-Base-8B, evaluated on the MathVista-GPS benchmark.

Figure S4 : FID, SigLip/DINO scores of Base-8B model (up) and Instruct-8B model (bottom) across different geometric structures.

Figure S5 : Average failure rate distributions of InternVL3.5-38B+GeoTikzBridge-Base-8B across different geometric structures (up) and mathematical domains (bottom).

Figure S6 : Failure cases of InternVL3.5-38B with tikz code input.

Method	CLIP	SigLip	DINO
FigCodifier	0.936	0.940	0.957
ours-Base-8B	0.967	0.970	0.978
ours-Instruct-8B	0.992	0.992	0.995

Table S5 : Performance comparison of instructed code generation methods across CLIP, SigLip, and DINO model metrics.

Method	DaTikZ			MathVista-GPS
	ClIP	SigLip	DINO	ClIP	SigLip	DINO
Qwen2.5-VL-72B	0.795	0.803	0.832	0.858	0.880	0.911
Qwen3-VL-30B	0.672	0.696	0.758	0.802	0.839	0.893
InternVL3.5-38B	0.733	0.752	0.786	0.786	0.793	0.855
GLM4.5V-106B	0.806	0.812	0.834	0.769	0.773	0.838
FigCodifier	0.785	0.791	0.819	0.884	0.906	0.922

Table S6 : Performance comparison of image-to-tikz methods across CLIP, SigLip, and DINO model metrics.

Method	FID $\downarrow$	CSR $\uparrow$	CLIP $\uparrow$	SigLip $\uparrow$	DINO $\uparrow$
GPT-5.0	44.8	96.9%	0.880	0.903	0.921
ours-Base-8B	36.0	97.1%	0.895	0.919	0.937

Table S7 : Performance comparison of image-to-tikz methods with GPT-5.0 on the MathVista-GPS benchmark across five metrics.

Method	Accuracy (Base/+Ours)
GPT-5.0	0.891/ 0.937
Claude-4.5-Sonnect	0.774/ 0.846
Gemini-3-Pro	0.779/ 0.923

Table S8 : Mathematical reasoning performance of latest closed-source models on the MathVista-GPS benchmark. Scores are reported as original model / model + GeoTikzBridge-Base-8B.

Figure S7 : Visualization results of tikz codes generated by GeoTikzBridge-Base, consisting of input images (either geometric or non-geometric) and the corresponding figures rendered from our predicted tikz codes.

Figure S8 : Visualization results of instruction-driven auxiliary line generation, including the input geometric images, the natural language instructions for auxiliary line addition, and the rendered figures from the generated tikz codes.

Figure S9 : Example I: Angle calculation problem solving comparison with and without tikz code. Tikz clarifies geometric relationships to avoid perceptual errors in angle reasoning.

Figure S10 : Example II: Segment length problem solving comparison with and without tikz code. Tikz facilitates accurate proportion and theorem application for length reasoning.

Figure S11 : Example III (1/2): Auxiliary line instruction (connecting circle center and tangent points) and tikz code generation. The line manifests radius-tangent perpendicularity.

Figure S12 : Example III (2/2): Problem solving comparison under different forms, with incorrect analysis/answers highlighted in red and key correct ones in green. Both auxiliary line image and its tikz combination enable correct reasoning via explicit perpendicularity recognition.

Figure S13 : Example IV (1/2): Auxiliary line instruction (extending midpoint connection) and tikz code generation. The line constructs a key right triangle by forming intersection $Q$ .

Figure S14 : Example IV (2/2): Problem solving comparison under different forms, with incorrect analysis/answers highlighted in red and key correct ones in green. The auxiliary line image provides a visual foundation for constructing the right triangle $\triangle$ NPQ. Its combination with tikz code achieves correct reasoning, since tikz explicitly encodes the spatial structure of the constructed right triangle.

Multimodal Large Language Models

Multimodal large language models combine language models with image, video, audio, and other inputs for grounded understanding and generation.

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Large Multimodal Models (LMMs) often struggle with geometric reasoning due to visual hallucinations and a lack of mathematically precise Chain-of-Thought (CoT) data. To address this, we propose the GeoSym Engine, an automated and scalable neuro-symbolic framework. By leveraging a type-conditional grammar and an analytic SymGT Solver, it derives exact symbolic ground truths and seamlessly integrates with a robust rendering pipeline to produce high-precision geometric diagrams. Using this engine, we construct GeoSym127K, a difficulty-stratified dataset featuring 51K high-resolution images, 127K questions with symbolic ground truths, and 55K answer-verified CoT QA pairs. We also introduce GeoSym-Bench, an expert-curated suite of 511 complex samples for rigorous evaluation. Through extensive supervised fine-tuning (SFT), we demonstrate that GeoSym drives concentrated improvements specifically on diagram-dependent and multi-step geometry tasks. Our Qwen3-VL-8B model gains an absolute +22.21% on the MathVerse Vision-Only subset and reaches 61.52% (+6.19% improvement) on WeMath, mitigating long-horizon logic fragmentation and outperforming advanced closed-source models like Doubao-1.8. Furthermore, applying Reinforcement Learning with Verifiable Rewards (RLVR) via GRPO reveals that initializing from structural SFT checkpoints substantially elevates the performance ceiling over zero-shot RL. Driven by deterministic exact-match signals, this showcases the robust scaling potential of our verifiable reasoning synthesis. Datasets and code are available at https://huggingface.co/datasets/Tomie0506/GeoSym127K and https://github.com/Tomie56/GeoSym127K.

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