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

2026-09-11

AI Summary

本文通过引入GeoVAD-Bench诊断基准和开发GeoWeave-8B模型，解决了几何问题求解中视觉辅助工具的有效利用及中间过程几何有效性的问题。

Abstract

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.

Problem

• Visual Chain-of-Thought
• Geometry Problem Solving
• Intermediate Visual Aids
• Diagnostic Benchmark
• Causal Gains

Innovation

• GeoVAD-Bench
• Visual Chain-of-Thought (VCoT)
• geometric problem solving
• multimodal RL
• supervised fine-tuning (SFT)