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

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.

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2608.30457 [cs.LG]

(or arXiv:2608.30457v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2608.30457 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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