这篇论文提出了MIRROR方法，让视觉语言模型通过不同视角互相学习，在几何推理中表现更稳定、更准确。
论文发现视觉语言模型在几何推理中，对文本、图像和图文组合三种视图的推理结果不一致。为此构建了ODA-Data多视图几何数据集，并提出了MIRROR强化学习方法。MIRROR通过评估模型在各视图下的表现，选择最佳视图作为教师，用反向KL散度训练其他视图。在多个几何推理基准上，MIRROR比标准RL提高了准确性和模态间一致性。
MIRROR: Learning from the Other View for Multi-Modal Reasoning
Unlike large language models (LLMs) that exhibit strong reasoning capabilities, vision-language models (VLMs) struggle with visual reasoning, even on geometry problems that admit equivalent text, diagram, and combined diagram+text views. We show that these views often elicit different behaviors: a model may solve a problem from text but fail on the corresponding diagram, or succeed visually while failing textually. This inconsistency suggests that different views expose complementary reasoning paths and failure modes that standard multimodal post-training does not fully exploit. To study and exploit this phenomenon, we construct ODA-Data, a high-quality paired multimodal geometry dataset with text-dominant, image-dominant, and combined image+text views of the same problems, together with splits for training and evaluating modality-dependent reasoning behaviors. We then develop Modality-Informed Reciprocal Reasoning Optimization (MIRROR), a reinforcement learning approach for improving multimodal reasoning via self supervision. For each problem, MIRROR evaluates the model under all views, selects the best-performing view as a teacher, and trains other views with a reverse-KL objective towards the teacher. Across reasoning benchmarks that evaluate on geometry problems, MIRROR improves over standard RL and yields more accurate and consistent behavior across modalities