# Socratic-Geo: Synthetic Data Generation and Geometric Reasoning via Multi-Agent Interaction

arXiv: https://arxiv.org/abs/2602.03414 · HTML: https://mlsanity.com/paper/2602.03414/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 31 of its 37 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)
- Multimodal LLMs / vision-language models / [Embodied and 3D vision-language models](https://mlsanity.com/mllm/embodied-and-3d-vision-language-models/)
- LLM agents and tool use / [Multimodal and embodied agents](https://mlsanity.com/agents/multimodal-and-embodied-agents/)
- Synthetic data and self-improvement for LLMs / [Self-improving MLLMs and synthetic data](https://mlsanity.com/synth/self-improving-mllms-and-synthetic-data/)

## Builds on (most cited first, 30 of 31)

- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Qwen2.5-VL Technical Report](https://mlsanity.com/paper/2502.13923/) (2025)
- [Scaling Rectified Flow Transformers for High-Resolution Image Synthesis](https://mlsanity.com/paper/2403.03206/) (2024)
- [MathVista: Evaluating Mathematical Reasoning of Foundation Models in Visual Contexts](https://mlsanity.com/paper/2310.02255/) (2023)
- [Qwen-Image Technical Report](https://mlsanity.com/paper/2508.02324/) (2025)
- [FLUX.1 Kontext: Flow Matching for In-Context Image Generation and Editing in Latent Space](https://mlsanity.com/paper/2506.15742/) (2025)
- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [Emu3: Next-Token Prediction is All You Need](https://mlsanity.com/paper/2409.18869/) (2024)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Measuring Multimodal Mathematical Reasoning with MATH-Vision Dataset](https://mlsanity.com/paper/2402.14804/) (2024)
- [Inter-GPS: Interpretable Geometry Problem Solving with Formal Language and Symbolic Reasoning](https://mlsanity.com/paper/2105.04165/) (2021)
- [BLIP3-o: A Family of Fully Open Unified Multimodal Models-Architecture, Training and Dataset](https://mlsanity.com/paper/2505.09568/) (2025)
- [Absolute Zero: Reinforced Self-play Reasoning with Zero Data](https://mlsanity.com/paper/2505.03335/) (2025)
- [We-Math: Does Your Large Multimodal Model Achieve Human-like Mathematical Reasoning?](https://mlsanity.com/paper/2407.01284/) (2024)
- [Show-o2: Improved Native Unified Multimodal Models](https://mlsanity.com/paper/2506.15564/) (2025)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [R-Zero: Self-Evolving Reasoning LLM from Zero Data](https://mlsanity.com/paper/2508.05004/) (2025)
- [G-LLaVA: Solving Geometric Problem with Multi-Modal Large Language Model](https://mlsanity.com/paper/2312.11370/) (2023)
- [Seedream 3.0 Technical Report](https://mlsanity.com/paper/2504.11346/) (2025)
- [HiDream-I1: A High-Efficient Image Generative Foundation Model with Sparse Diffusion Transformer](https://mlsanity.com/paper/2505.22705/) (2025)
- [MAVIS: Mathematical Visual Instruction Tuning with an Automatic Data Engine](https://mlsanity.com/paper/2407.08739/) (2024)
- [GeomVerse: A Systematic Evaluation of Large Models for Geometric Reasoning](https://mlsanity.com/paper/2312.12241/) (2023)
- [SPICE: Self-Play In Corpus Environments Improves Reasoning](https://mlsanity.com/paper/2510.24684/) (2025)
- [LLM2LLM: Boosting LLMs with Novel Iterative Data Enhancement](https://mlsanity.com/paper/2403.15042/) (2024)
- [A Multi-Modal Neural Geometric Solver with Textual Clauses Parsed from Diagram](https://mlsanity.com/paper/2302.11097/) (2023)
- [Vision-Zero: Scalable VLM Self-Improvement via Strategic Gamified Self-Play](https://mlsanity.com/paper/2509.25541/) (2025)
- [Theorem-Validated Reverse Chain-of-Thought Problem Generation for Geometric Reasoning](https://mlsanity.com/paper/2410.17885/) (2024)
- [Socratic-Zero : Bootstrapping Reasoning via Data-Free Agent Co-evolution](https://mlsanity.com/paper/2509.24726/) (2025)
- [GenExam: A Multidisciplinary Text-to-Image Exam](https://mlsanity.com/paper/2509.14232/) (2025)
- [TrustGeoGen: Formal-Verified Data Engine for Trustworthy Multi-modal Geometric Problem Solving](https://mlsanity.com/paper/2504.15780/) (2025)

## Built on by (most cited first, 2 of 2)

- [FormalAnalyticGeo: A Neural-Symbolic Based Framework for Multimodal Analytic Geometry Problem Generation](https://mlsanity.com/paper/2607.12982/) (2026)
- [Draw2Think: Harnessing Geometry Reasoning through Constraint Engine Interaction](https://mlsanity.com/paper/2605.20743/) (2026)

## Abstract (arXiv)

Multimodal Large Language Models (MLLMs) have significantly advanced vision-language understanding. However, even state-of-the-art models struggle with geometric reasoning, revealing a critical bottleneck: the extreme scarcity of high-quality image-text pairs. Human annotation is prohibitively expensive, while automated methods fail to ensure fidelity and training effectiveness. Existing approaches either passively adapt to available images or employ inefficient random exploration with filtering, decoupling generation from learning needs. We propose Socratic-Geo, a fully autonomous framework that dynamically couples data synthesis with model learning through multi-agent interaction. The Teacher agent generates parameterized Python scripts with reflective feedback (Reflect for solvability, RePI for visual validity), ensuring image-text pair purity. The Solver agent optimizes reasoning through preference learning, with failure paths guiding Teacher's targeted augmentation. Independently, the Generator learns image generation capabilities on accumulated "image-code-instruction" triplets, distilling programmatic drawing intelligence into visual generation. Starting from only 108 seed problems, Socratic-Solver achieves 49.11 on six benchmarks using one-quarter of baseline data, surpassing strong baselines by 2.43 points. Socratic-Generator achieves 42.4% on GenExam, establishing new state-of-the-art for open-source models, surpassing Seedream-4.0 (39.8%) and approaching Gemini-2.5-Flash-Image (43.1%).