This work introduces <strong>credit-addressable reasoning</strong> for multimodal geometry, aiming to localize learning signals to the reasoning steps that actually change outcomes. We propose <strong>Code-CoT</strong> for structured, executable reasoning and <strong>CE-GRPO</strong> for event-level credit assignment, achieving <strong>76.04% average accuracy across nine geometry benchmarks</strong> and outperforming trajectory-level GRPO by <strong>3.43 points</strong>.</p>\n","updatedAt":"2026-09-02T12:34:19.123Z","author":{"_id":"62579c55b98dcaa7e0de285d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/62579c55b98dcaa7e0de285d/0YUd5nloul_bW9yolDGGo.jpeg","fullname":"wangjunjie","name":"wanng","type":"user","isPro":false,"isHf":false,"isHfAdmin":false,"isMod":false,"followerCount":37,"isUserFollowing":false}},"numEdits":0,"identifiedLanguage":{"language":"en","probability":0.8402835726737976},"editors":["wanng"],"editorAvatarUrls":["https://cdn-avatars.huggingface.co/v1/production/uploads/62579c55b98dcaa7e0de285d/0YUd5nloul_bW9yolDGGo.jpeg"],"reactions":[],"isReport":false}}],"primaryEmailConfirmed":false,"paper":{"id":"2608.30457","authors":[{"_id":"6a9817968f0d5830367c38c1","name":"Jiani Guo","hidden":false},{"_id":"6a9817968f0d5830367c38c2","name":"Junjie Wang","hidden":false},{"_id":"6a9817968f0d5830367c38c3","name":"Jie Wu","hidden":false},{"_id":"6a9817968f0d5830367c38c4","name":"Pengxiang Zhao","hidden":false},{"_id":"6a9817968f0d5830367c38c5","name":"Dongdong Zhang","hidden":false},{"_id":"6a9817968f0d5830367c38c6","name":"Shaohan Huang","hidden":false},{"_id":"6a9817968f0d5830367c38c7","name":"Yujiu Yang","hidden":false},{"_id":"6a9817968f0d5830367c38c8","name":"Furu Wei","hidden":false}],"publishedAt":"2026-08-31T00:00:00.000Z","submittedOnDailyAt":"2026-09-02T00:00:00.000Z","title":"Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry","submittedOnDailyBy":{"_id":"62579c55b98dcaa7e0de285d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/62579c55b98dcaa7e0de285d/0YUd5nloul_bW9yolDGGo.jpeg","isPro":false,"fullname":"wangjunjie","user":"wanng","type":"user","name":"wanng"},"summary":"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.","upvotes":1,"discussionId":"6a9817968f0d5830367c38c9","ai_summary":"Credit-addressable reasoning via executable code traces and localized reinforcement learning improves multimodal geometry reasoning by aligning credit assignment with structured reasoning events.","ai_keywords":["multimodal geometry reasoning","VLMs","credit-addressable reasoning","Code-CoT","executable code","typed events","CE-GRPO","trajectory-level reinforcement learning","structural priors","type-normalized entropy"],"ai_summary_model":"thinkingmachines/Inkling-Small","organization":{"_id":"66f55d53853f0506904d1922","name":"IIGroup","fullname":"Tsinghua IIGroup","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/62579c55b98dcaa7e0de285d/A1SKeBEvaODFnkAZusICK.png"}},"canReadDatabase":false,"canManagePapers":false,"canSubmit":false,"hasHfLevelAccess":false,"upvoted":false,"upvoters":[{"_id":"62579c55b98dcaa7e0de285d","avatarUrl":"https://cdn-avatars.huggingface.co/v1/production/uploads/62579c55b98dcaa7e0de285d/0YUd5nloul_bW9yolDGGo.jpeg","isPro":false,"fullname":"wangjunjie","user":"wanng","type":"user"}],"acceptLanguages":["en"],"dailyPaperRank":0,"organization":{"_id":"66f55d53853f0506904d1922","name":"IIGroup","fullname":"Tsinghua IIGroup","avatar":"https://cdn-avatars.huggingface.co/v1/production/uploads/62579c55b98dcaa7e0de285d/A1SKeBEvaODFnkAZusICK.png"},"markdownContentUrl":"https://huggingface.co/buckets/huggingchat/papers-content/resolve/2608/2608.30457.md","query":{}}">
Learning Where Outcomes Change:Credit-Addressable Reasoning for Multimodal Geometry
Abstract
Credit-addressable reasoning via executable code traces and localized reinforcement learning improves multimodal geometry reasoning by aligning credit assignment with structured reasoning events.
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.
Community
This work introduces credit-addressable reasoning for multimodal geometry, aiming to localize learning signals to the reasoning steps that actually change outcomes. We propose Code-CoT for structured, executable reasoning and CE-GRPO for event-level credit assignment, achieving 76.04% average accuracy across nine geometry benchmarks and outperforming trajectory-level GRPO by 3.43 points.
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