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
Tsinghua University · Microsoft Research · Zhejiang University
Published August 31, 2026 · on the feed September 2, 2026 · ▲ 8 · arXiv 2608.30457
The 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.
The Brief
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Transcript
Learning Where Outcomes Change. Credit-Addressable Reasoning for Multimodal Geometry. By Jiani Guo and seven others, from Tsinghua University, Microsoft Research, and one other institution. Published on the thirty-first of August. No code repository is linked to it.
Multimodal geometry reasoning asks a vision-language model to extract precise visual relations from a diagram and carry them intact through many steps of deduction. Two things get in the way. Free-form reasoning traces obscure the decisions that actually determine the answer. And trajectory-level reinforcement learning takes a single signal from the end and spreads it across the entire response, so a decisive step and an incidental one are credited alike.
The proposal is credit-addressable reasoning. The semantic units a model exposes while it reasons are given a second job: they also define where learning compares alternatives and where it assigns credit. The structure of the reasoning and the structure of the training signal become one and the same.
Two components put this into practice. Code-CoT shapes the reasoning. It keeps the diagram, represents visual relations as executable code that can be addressed line by line, and organises reasoning into typed events. CE-GRPO shapes the learning. It selects event boundaries using structural priors and type-normalized entropy, samples complete continuations from shared prefixes, and converts the differences in outcome between those continuations into localized advantages. That is the sense of the title: learning where outcomes change.
Across nine geometry benchmarks, CE-GRPO reaches an average accuracy of seventy-six point zero four. That is eight point zero nine points above Qwen3-VL-8B, and three point four three points above trajectory-level GRPO. Its relative advantage also grows with the number of intermediate events.
That last pattern is the authors' main case for designing representation and optimization together. The longer and more dependency-heavy the reasoning, the more it helps when the format of a trace and the training signal agree on where the decisions are.
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Learn it by doing: make the calls the authors made, guess the result before you see it, and defend it in a viva graded on your own words. Chapter 1 is right here.
Chapter 1 🧩 · The problem
One bad assumption, one reward at the end, and no way to say which step was to blame.
You are training a vision-language model to solve geometry problems from diagrams. One wrong assumption early on, say a line wrongly taken to be perpendicular, ruins every deduction after it.
The road ahead
- 1 · The problem ~7 min Geometry from diagrams breaks on one early wrong assumption, yet the training signal arrives only at the end and lands on everything equally.
- 2 · What came before ~3 min
- 3 · The key idea ~9 min Make the reasoning's typed steps also the places where learning compares alternatives and hands out credit.
- 4 · Choose your own research ~3 min
- 5 · Build the method ~8 min Write the diagram as code, reason in typed events, pick events by structure and entropy, branch from prefixes, and credit outcome differences locally.
- 6 · The experiment ~6 min You’ll guess: Averaged over nine geometry benchmarks, by how many accuracy points did CE-GRPO beat trajectory-level GRPO?
- 7 · The viva ~5 min Three questions from the examiners, answered in your own words. Win it for the paper’s trophy.
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