LatentGeo: 在潜在空间中学习可学习的辅助构造以进行多模态几何推理
LatentGeo: Learnable Auxiliary Constructions in Latent Space for Multimodal Geometric Reasoning
AI总结：
LatentGeo通过学习潜在空间中的连续视觉表示，解决多模态几何推理中辅助构造的表示问题，采用三阶段课程和强化学习方法提升几何推理任务的性能。
摘要：
尽管在多模态推理方面取得了最近的进展，但表示辅助几何构造仍然是多模态大语言模型（MLLMs）中的基本挑战。这些构造不存在于原始图中，必须在定理应用之前引入。现有方法主要依赖于显式构造范式，包括基于文本的几何规范、推理过程中的视觉令牌交错以及工具增强的几何执行。然而，这些方法要么无法忠实表示复杂的空间关系，要么导致离散符号与连续几何结构之间的表示不匹配，或者依赖外部能力，阻碍了端到端优化。为了解决这些限制，我们提出了LatentGeo，一个框架，通过学习连续的潜在视觉表示来内部化辅助几何构造，而无需像素级渲染或外部执行器。我们设计了一个三阶段的课程，通过辅助视觉监督逐步对齐和内部化这些潜在表示，随后是LaGDPO，一种具有潜在意识的强化学习过程，它在策略优化期间稳定潜在表示，同时提高端任务的正确性。为了系统评估以构造为中心的表示质量，我们引入了GeoAux，一个新的针对视觉依赖几何问题的基准，并在GeoAux和MathVerse上进行了实验。结果表明，LatentGeo在几何推理任务上取得了显著的提升，特别是那些需要辅助构造的任务。广泛的分析和消融研究进一步验证了我们框架中每个组件的有效性。
英文摘要：
Despite recent advances in multimodal reasoning, representing auxiliary geometric constructions remains a fundamental challenge for multimodal large language models (MLLMs). Such constructions are absent from the original diagram and must be introduced before theorems apply. Existing approaches predominantly rely on explicit construction paradigms, including text-based geometric specification, visual-token interleaving during reasoning, and tool-augmented geometric execution. However, these methods either fail to faithfully represent complex spatial relationships, incur representation mismatch between discrete symbols and continuous geometric structures, or rely on external capabilities that hinder end-to-end optimization. To address these limitations, we propose LatentGeo, a framework that learns continuous latent visual representations to internalize auxiliary geometric constructions without pixel-level rendering or external executors. We design a three-stage curriculum that progressively aligns and internalizes these latent representations through auxiliary visual supervision, followed by LaGDPO, a latent-aware reinforcement learning procedure that stabilizes latent representations during policy optimization while improving end-task correctness. To systematically evaluate construction-centric representation quality, we introduce GeoAux, a new benchmark targeting visually dependent geometry problems, and conduct experiments on GeoAux and MathVerse. Results show that LatentGeo achieves substantial gains on geometric reasoning tasks, particularly those requiring auxiliary constructions. Extensive analyses and ablation studies further validate the effectiveness of each component in our framework.
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