Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry

Jiani Guo; Junjie Wang; Jie Wu; Pengxiang Zhao; Dongdong Zhang; Shaohan Huang; Yujiu Yang; Furu Wei

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arXiv · 2608.30457

Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry

Jiani Guo·Junjie Wang·Jie Wu·Pengxiang Zhao·Dongdong Zhang·Shaohan Huang·Yujiu Yang·Furu Wei

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Abstract

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.

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Jiani Guo, Junjie Wang, Jie Wu, Pengxiang Zhao, Dongdong Zhang, Shaohan Huang, Yujiu Yang, Furu Wei. 2026-08-31. Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry. https://arxiv.org/abs/2608.30457

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