学习结果变化之处：面向多模态几何的可寻址归因推理

摘要

多模态几何推理要求视觉语言模型提取精确的视觉关系，并在多步推理中保持这些关系。现有的自由形式推理轨迹掩盖了决定答案的决策，而轨迹级强化学习则将单一的最终信号分配至整个响应。我们提出信用可寻址推理（credit-addressable reasoning）。在该原则下，推理过程中展现的语义单元同时界定了学习在何处比较备选方案并分配信用。我们以Code-CoT和CE-GRPO实例化这一原则：Code-CoT保留图形，将视觉关系表示为可逐行寻址的可执行代码，并将推理组织为类型化事件；CE-GRPO利用结构先验和类型归一化熵选择事件边界，从共享前缀中采样完整的后续生成，并将结果差异转化为局部优势。在九个几何基准上，CE-GRPO的平均准确率达到76.04，分别比Qwen3-VL-8B和轨迹级GRPO高出8.09和3.43个百分点。其相对优势随中间事件数量的增加而增大，这证明了表示与优化协同设计对于长链条、高依赖性的多模态推理的价值。

English

Multimodal geometry reasoning requires VLMs to extract precise visual relations and preserve them through multi-step deduction. Existing free-form traces obscure the decisions that determine the answer, and trajectory-level reinforcement learning distributes a single terminal signal across the entire response. We introduce credit-addressable reasoning, in which the semantic units exposed during inference also define where learning compares alternatives and assigns credit. We instantiate this principle with Code-CoT, which retains the diagram, represents visual relations as line-addressable executable code, and organizes reasoning into typed events, and CE-GRPO, which selects event boundaries using structural priors and type-normalized entropy, samples complete continuations from shared prefixes, and converts outcome differences into localized advantages. Across nine geometry benchmarks, CE-GRPO achieves an average accuracy of 76.04, outperforming Qwen3-VL-8B and trajectory-level GRPO by 8.09 and 3.43 points, respectively. Its relative advantage increases with the number of intermediate events, demonstrating the value of representation--optimization co-design for long, dependency-heavy multimodal reasoning.