Euclid30K: Multimodal Geometry Dataset

• Euclid30K is a multimodal dataset featuring 29,695 diagram-question-answer triples covering both planar and solid geometry for K–12 and Olympiad levels.
• The dataset employs rigorous automated annotation and quality control steps, including diagram de-duplication and LaTeX normalization, to ensure reliable content.
• Serving as a surrogate curriculum for vision–language models, Euclid30K enhances spatial perception, enabling significant zero-shot transfer gains on spatial reasoning benchmarks.

Euclid30K is a curated multimodal corpus purpose-built to serve as a surrogate curriculum for developing spatial perception and reasoning in vision–LLMs (VLMs). Comprising approximately 29,695 geometry problems paired with diagrams and expert-validated answers, Euclid30K covers both planar (2D) and solid (3D) geometry across the K–12 and Olympiad syllabus. The dataset underpins advances in spatial intelligence for Multimodal LLMs (MLLMs) by introducing geometric problem-solving as a transferable pretext task, enabling systematic study of spatial induction, grounding, and generalization in artificial agents (Lian et al., 29 Sep 2025).

1. Dataset Scope and Taxonomy

Euclid30K consists of 29,695 diagram-question-answer triples. These are divided into 18,577 planar geometry and 11,118 solid geometry questions. The collection encompasses a comprehensive curriculum including shape identification, mental rotation, relational reasoning, containment/intersection, numerosity estimation, and dynamic or moving-point problems. Categories span core K–12 as well as advanced Olympiad content; problem types reflect diverse cognitive demands, such as:

• Shape identification and classification: e.g., face type queries for polyhedra.
• Mental rotation and perspective: e.g., predicting views after spatial transformations.
• Relational reasoning: e.g., establishing parallelism, perpendicularity, or determining angles using classical geometry theorems.
• Containment/intersection: e.g., reasoning about inscribed or circumscribed figures.
• Measurement/numerosity: e.g., object counting; area, length, and volume calculations.
• Dynamic/folding problems: e.g., point movement along a locus, unfolding solid figures.

Answer formats are systematically categorized as mathematical expressions (LaTeX-based, 16,804 instances), numeric values (6,321), or multiple-choice (2,618), supporting symbolic, discrete, and evaluative task formats.

2. Construction and Quality Control

Problem data was assembled from filtered corpora (Geometry3K, MMK12, SolidGeo, WeMath2), yielding about 32,500 initial candidates. Classification into planar versus solid geometry leveraged the Qwen2.5-VL-72B model as automated annotator. To address coverage imbalance, an additional 4,500 solid geometry problems were transcribed from textbooks and competition workbooks, correcting a 7,000-item shortfall.

The dataset underwent rigorous three-stage quality control:

1. Diagram de-duplication using perceptual hashing.
2. Prompt normalization and splitting by the GPT-4o API to ensure atomic question granularity.
3. LaTeX and answer normalization utilizing DeepSeek-V3.1 and symbolic-check compatibility with MathVerify.

Each instance is represented as ⟨images i, problem text p, answer a⟩; figures are supplied in PNG/JPEG (average 1.1 images/problem, up to 8), with answers presented in LaTeX (symbolic), as numbers (float/integer), or as indices.

3. Dataset Structure and Statistics

Euclid30K is released as an undivided training corpus; typical downstream protocols reserve 5–10% for validation. The JSON schema provides: a unique id, image array, UTF-8 text (with embedded LaTeX), and a single answer field. Text length averages 229.8 characters (max 1,598), and figures per problem average 1.1 (max 8). Answer string length averages 8.9 characters (max 501). Problem distributions are 63% planar and 37% solid; symbolic, numeric, and multiple-choice answers constitute 57%, 21%, and 9%, respectively.

Category	Count/Proportion	Representative Data
Problems (total)	29,695	100%
Planar (2D)	18,577 (63%)
Solid (3D)	11,118 (37%)
Symbolic	16,804 (57%)	LaTeX expressions
Numeric	6,321 (21%)	Integer/float answers
Multiple-choice	2,618 (9%)	Indexed answer selection

4. Application in Model Training and Evaluation

Euclid30K acts as a surrogate task for curriculum-based pretraining and fine-tuning in state-of-the-art VLMs, including Qwen2.5VL (3B/7B/72B) and RoboBrain2.0 (7B/32B) series, with Group Relative Policy Optimization (GRPO) as the training algorithm. Models trained via Euclid30K demonstrate substantial zero-shot transfer without task-specific adaptation.

Key benchmark results:

• Super-CLEVR: +5–10% absolute gain in 2D visual robustness.
• Omni3DBench: +2–7% improvement on 3D object-location and size queries.
• VSI-Bench (4 spatial tasks): Mean accuracy from 34.5% to 40.5%; RoboBrain2.0-Euclid-7B reaches 49.6%, surpassing previous SOTA (Spatial-MLLM).
• MindCube: +4–18% on “Rotation,” “Among,” and “Around” subtasks.

Ablation studies indicate a geometry-specific effect: replacing Euclid30K with an equal-sized split from Clevr-CoGenT for GRPO provides little or no transfer, suggesting that Euclidean problems are critical for imparting spatial priors.

5. Access, Licensing, and Example Instances

Euclid30K is openly distributed under an MIT-style license for unrestricted research use at https://zgca-ai4edu.github.io/Euclids_Gift, with full dataset JSON, images, and inspection code. No commercial limitations are imposed.

Representative cases:

• Triangle Area (Symbolic): Images: triangle_45deg.png Text: “In ΔABC, AB=BC and ∠ABC=90°. Find the area of ΔABC if AB=2.” Answer: $\boxed{2}$
• Solid Rotation (Multiple-choice): Images: prism_rotate.png Text: “A right triangular prism is rotated 90° around edge EF. Which face is now in front? (1) ABC, (2) BCD, (3) AEF, (4) DEF.” Answer: 3
• Circle Arc Length (Numeric): Images: circle_arc.png Text: “Given circle center O with radius 5 and ∠AOB=72°, compute the length of arc AB.” Answer: 6.283

6. Limitations and Future Directions

Euclid30K exclusively contains static diagrams; thus, it does not facilitate improvement on temporal ordering tasks (e.g., “Appearance Order” in VSI-Bench). Gains on pure mental-rotation tasks remain limited, as planar problem distribution insufficiently demands 3D rotation generalization. Planned extensions involve incorporation of video/animation for spatio-temporal reasoning, expanded solid-geometry (e.g., polyhedron nets, CAD-style blueprints), and multi-stage RL schedules. A plausible implication is that such extensions could further augment transferable spatial skills in MLLMs.

7. Impact and Prospective Research

Euclid30K systematically demonstrates that geometry-centric fine-tuning can endow VLMs with broad, transferable spatial competencies, effecting zero-shot gains on unseen benchmarks without modifying underlying model architectures. The dataset’s public availability is designed to accelerate progress at the intersection of geometric reasoning, spatial perception, and multimodal AI (Lian et al., 29 Sep 2025).