Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry
2026-08-31 • Machine Learning
Machine LearningComputation and Language
AI summaryⓘ
The authors studied how to improve visual-language models (VLMs) in solving complex geometry problems that need several reasoning steps. They found that common methods don't clearly show which decisions led to the answer and have trouble giving the model feedback at the right moments. To fix this, they created a method called credit-addressable reasoning, which breaks down the problem into smaller, understandable parts, represented as code that the model can run and check step-by-step. Their approach, tested on various geometry tasks, scored better than previous models, especially when problems required many intermediate reasoning steps.
Visual-Language ModelsGeometry ReasoningCredit-AssignmentCode Chains-of-ThoughtReinforcement LearningEvent SegmentationMultimodal ReasoningEntropyExecutable CodeDependency Parsing
Authors
Jiani Guo, Junjie Wang, Jie Wu, Pengxiang Zhao, Dongdong Zhang, Shaohan Huang, Yujiu Yang, Furu Wei
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.