# Beyond Generation and Accuracy: Diagnosing and Enhancing Visual Chain-of-Thought for Geometry Problem Solving

arXiv: https://arxiv.org/abs/2609.12606 · HTML: https://mlsanity.com/paper/2609.12606/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Spatial and embodied reasoning, one of 17 directions in LLM reasoning.
- Builds on 24 of its 52 references that are in the map.
- First posted on arXiv 11 Sep 2026.

## Placed in

- LLM reasoning / [Spatial and embodied reasoning](https://mlsanity.com/lr/spatial-and-embodied-reasoning/)

## Builds on (most cited first, 24 of 24)

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- [Janus-Pro: Unified Multimodal Understanding and Generation with Data and Model Scaling](https://mlsanity.com/paper/2501.17811/) (2025)
- [MathVerse: Does Your Multi-modal LLM Truly See the Diagrams in Visual Math Problems?](https://mlsanity.com/paper/2403.14624/) (2024)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [DeepEyes: Incentivizing "Thinking with Images" via Reinforcement Learning](https://mlsanity.com/paper/2505.14362/) (2025)
- [MM-Eureka: Exploring the Frontiers of Multimodal Reasoning with Rule-based Reinforcement Learning](https://mlsanity.com/paper/2503.07365/) (2025)
- [Visual Sketchpad: Sketching as a Visual Chain of Thought for Multimodal Language Models](https://mlsanity.com/paper/2406.09403/) (2024)
- [GeoQA: A Geometric Question Answering Benchmark Towards Multimodal Numerical Reasoning](https://mlsanity.com/paper/2105.14517/) (2021)
- [Kimi K3: Open Frontier Intelligence](https://mlsanity.com/paper/2607.24653/) (2026)
- [Reinforcing Spatial Reasoning in Vision-Language Models with Interwoven Thinking and Visual Drawing](https://mlsanity.com/paper/2506.09965/) (2025)
- [Zebra-CoT: A Dataset for Interleaved Vision Language Reasoning](https://mlsanity.com/paper/2507.16746/) (2025)
- [MathCoder-VL: Bridging Vision and Code for Enhanced Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2505.10557/) (2025)
- [MathCanvas: Intrinsic Visual Chain-of-Thought for Multimodal Mathematical Reasoning](https://mlsanity.com/paper/2510.14958/) (2025)
- [SenseNova-U1: Unifying Multimodal Understanding and Generation with NEO-unify Architecture](https://mlsanity.com/paper/2605.12500/) (2026)
- [CAPO: Towards Enhancing LLM Reasoning through Generative Credit Assignment](https://mlsanity.com/paper/2508.02298/) (2025)
- [UniRL: Self-Improving Unified Multimodal Models via Supervised and Reinforcement Learning](https://mlsanity.com/paper/2505.23380/) (2025)
- [On the Direction of RLVR Updates for LLM Reasoning: Identification and Exploitation](https://mlsanity.com/paper/2603.22117/) (2026)
- [UniGRPO: Unified Policy Optimization for Reasoning-Driven Visual Generation](https://mlsanity.com/paper/2603.23500/) (2026)
- [Future-KL Regularized GRPO: Process-Level Credit Assignment from f-Divergence Regularization](https://mlsanity.com/paper/2601.10201/) (2026)
- [GGBench: A Geometric Generative Reasoning Benchmark for Unified Multimodal Models](https://mlsanity.com/paper/2511.11134/) (2025)
- [AEM: Adaptive Entropy Modulation for Multi-Turn Agentic Reinforcement Learning](https://mlsanity.com/paper/2605.00425/) (2026)
- [Thinking with Constructions: A Benchmark and Policy Optimization for Visual-Text Interleaved Geometric Reasoning](https://mlsanity.com/paper/2603.18662/) (2026)

## Abstract (arXiv)

While multimodal reasoning has advanced rapidly, solving complex geometry problems critically hinges on active visual assistance, such as constructing auxiliary lines, spurring the rise of Visual Chain-of-Thought (VCoT). However, existing evaluations typically assess visual generation quality and final answer accuracy in isolation, failing to examine whether intermediate visual aids are geometrically valid, effectively utilized in subsequent reasoning, or causally responsible for task success. To bridge this gap, we introduce GeoVAD-Bench, a diagnostic benchmark that pairs a fine-grained five-dimensional trajectory diagnosis covering perception, auxiliary quality, utilization, deductive reasoning, and final correctness with controlled No-Aux, Auto-Aux, and GT-Aux intervention settings to systematically isolate intermediate error modes, the causal gains of visual aids, and the resulting autonomy gap. Our findings reveal that while high-quality auxiliary aids offer substantial theoretical gains for geometric problem solving, autonomous generation is frequently hampered by compounding errors across geometric perception, faithful visual manipulation, visual-state grounding, and deductive reasoning. Guided by these diagnostic insights, we establish a specialized data construction pipeline encompassing geometric perception, diagram editing, and interleaved visual-textual reasoning trajectories, and develop a progressive SFT and multimodal RL training framework. The resulting model, GeoWeave-8B, outperforms the base model by +25.3% in final geometric accuracy and achieves a +30.4% gain in process average across the four intermediate diagnostic dimensions.