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How RL Unlocks the Aha Moment in Geometric Interleaved Reasoning

ICML 2026 · Vision-language and multimodal › Multimodal LLMs · approach: Chain-of-thought multimodal reasoning · 0 citations (OpenAlex)

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Proposes Faire, an RL (GRPO) framework with tri-perspective verifiers (executable GeoGebra checks, VLM visual judge, semantic parser) that trains an interleaved text-plus-GeoGebra-code geometry solver from Qwen3-VL-8B, and introduces the Faire-Bench K12 geometry dataset.

Problem

Interleaving diagram construction (as executable plotting code) with textual deduction for geometry problems; naive SFT on interleaved traces degrades accuracy relative to text-only reasoning.

Approach

Replace distributional imitation of interleaved traces with RL using a gated reward that combines answer correctness, code executability, and three verifier signals (geometric assertions in GeoGebra, perceptual VLM judgment, and semantic consistency between reasoning and code), framing the diagram as a causal mediator that must be functionally useful.

Key results

• Faire (8B, from Qwen3-VL-8B) reaches 74.82 accuracy and 45.37 average verification score on Faire-Bench, versus 59.71 accuracy and 14.85 average for its SFT base Qwen3-VL-8B and 68.78 accuracy / 24.62 average for GPT-5.2.
• Interleaved SFT reduces accuracy to 62.48 vs 68.13 text-only, while after RL the interleaved variant reaches 74.83 vs 71.21 text-only.
• Verifier score correlates with human rating at r=0.9578.

Surprising findings

• Naive SFT on interleaved plot-solution traces lowers accuracy relative to text-only SFT, while the same interleaved setup under RL outperforms text-only RL.
• Gemini-2.5-Pro has the highest answer accuracy among baselines (78.24) yet a low verification average (19.86), indicating answer correctness does not imply valid constructions.

Limitations

• Benchmark is K12-focused and built with Gemini-2.5 synthesis plus expert review, so dataset-generation bias is possible.
• Verification relies on VLM and parser judges whose reliability is only partly validated by correlation with human ratings.
• Reported accuracy of Faire (74.82 in main table, 74.83 in ablation) and reward ablation labels are inconsistent in places.

Experimental setup

Datasets: Faire-Bench SFT split Faire-Bench RL split GenExam GGBench

Benchmarks: Faire-Bench GenExam GGBench

Metrics: accuracy BLEU ROUGE-L chrF PSNR SSIM LPIPS tri-perspective verification scores (Parser, Code, Judge, Av

Baselines: GPT-4o GPT-5.1 GPT-5.2 Gemini-2.5-Pro GLM-4.1V-9B Gemma3-12B InternVL3.5-8B Kimi-VL-A3B Qwen2.5-VL-7B Qwen3-VL-8B

Builds on: GRPO Qwen3-VL

Closest papers by meaning

• MINT-CoT: Enabling Interleaved Visual Tokens in Mathematical Chain-of-Thought Reasoning (NeurIPS 2025 · similarity 0.88)
• CogFlow: Bridging Perception and Reasoning through Knowledge Internalization for Visual Mathematical Problem Solving (ICLR 2026 · similarity 0.88)
• We-Math 2.0: A Versatile MathBook System for Incentivizing Visual Mathematical Reasoning (ICLR 2026 · similarity 0.87)
• GeoBench: Rethinking Multimodal Geometric Problem-Solving via Hierarchical Evaluation (ICLR 2026 · similarity 0.87)
• GeoSense: Internalizing Geometric Necessity Perception for Multimodal Reasoning (ICML 2026 · similarity 0.87)
• Reinforcing Spatial Reasoning in Vision-Language Models with Interwoven Thinking and Visual Drawing (NeurIPS 2025 · similarity 0.87)