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

CVPR 2026 · Vision-language and multimodal › Multimodal LLMs · approach: Spatial reasoning in VLMs

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Proposes Socratic-Geo, a multi-agent loop where a Teacher MLLM writes parameterized Python geometry scripts (verified by Reflect and RePI) to synthesize targeted problems for a GRPO-trained Solver and a diffusion Generator distilled from code-image triplets.

Problem

Geometric reasoning in MLLMs is bottlenecked by scarce high-quality image-text pairs; existing synthesis methods are passive, randomly explore with post-hoc filtering, or are decoupled from learning.

Approach

A Teacher agent diagnoses Solver failures and programmatically modifies geometry code to invent new verified problems (Reflect for solvability, RePI for visual validity), with the Solver trained via GRPO using failure-aware positive/negative sets and the Generator fine-tuned on resulting image-code-instruction triplets.

Key results

• Socratic-Solver-Geo (Qwen2.5-VL-7B, +Stage3 with 2.5k synthetic problems) reaches 49.11 overall on five geometric benchmarks vs. 44.98 zero-shot, and beats the best baseline GeoReasoning (46.68) with fewer samples.
• Socratic-Generator-Image (Qwen-Image-based) achieves 42.4 relaxed score on GenExam-Math, versus 18.9 for base Qwen-Image and 39.8 for Seedream 4.0.
• Without the Qualify (verification) module, Solver MathVerse accuracy drops to 37.09 from 40.33 with verification, below the 39.59 zero-shot baseline.

Surprising findings

• Unverified invented problems (1.3k) reduce MathVerse accuracy below the zero-shot baseline, showing that more synthetic data can hurt.
• Instruction rewriting is essential: without it the Generator gets 0.0 strict and 20.1 relaxed on GenExam-Math.

Limitations

• Numeric inconsistencies in the paper: the abstract says Socratic-Solver surpasses baselines by 2.43 points while the text says 2.25 and the table gives 49.11 vs 46.68 (2.43) for the best baseline; the overall average is reported inconsistently (42.07 in text vs 49.11 in table).
• Generator evaluation relies on GPT-5 as judge, with only a single generator base model.
• Generalization experiments in Table 2 lack described training details and baselines beyond the base model.

Experimental setup

Datasets: 108 seed geometry problems PGPS9k Geo170k GeoReasoning-10K R-CoT synthetic data

Benchmarks: MathVerse GeomVerse GeoQA MathVision MathVista WeMath GenExam-Math ChartQA CharXiv ChartQAPro ChartMinic Design2Code

Metrics: Mean@1 accuracy Strict score Relaxed score

Baselines: R-CoT G-LLaVA / Geo170k GeoReasoning-10K PGPSNet GPT-Image-1 Gemini-2.5-Flash-Image Seedream 4.0 Qwen-Image

Builds on: Socratic-Zero GRPO Qwen-Image R-CoT GeoReasoning

Closest papers by meaning

• GGBench: A Geometric Generative Reasoning Benchmark for Unified Multimodal Models (CVPR 2026 · similarity 0.90)
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• Let Language Constrain Geometry: Vision–Language Models as Semantic and Spatial Critics for 3D Generation (ICML 2026 · similarity 0.89)
• GeoSense: Internalizing Geometric Necessity Perception for Multimodal Reasoning (ICML 2026 · similarity 0.89)
• GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training (ICLR 2025 · similarity 0.89)
• InternSpatial: A Comprehensive Dataset for Spatial Reasoning in Vision-Language Models (ICLR 2026 · similarity 0.89)