從結果變化中學習：多模態幾何的信用可定址推理

摘要

多模態幾何推理要求視覺語言模型（VLM）擷取精確的視覺關係，並在多步驟演繹過程中加以保留。現有的自由形式軌跡模糊了決定最終答案的關鍵判斷，而軌跡層級的強化學習則將單一終端訊號分配至整個回應之中。我們提出可歸因信用推理（credit-addressable reasoning），其核心概念在於推論過程中所暴露的語義單元，同時也界定學習過程中比較替代方案與指派信用的位置。我們以兩項具體實作來落實此原則：其一為 Code-CoT，它保留圖形、將視覺關係表示為可逐行定址的可執行程式碼，並將推理過程組織為型別化事件；其二為 CE-GRPO，它利用結構先驗與型別正規化熵來選定事件邊界，從共享前綴取樣完整的後續生成，並將結果差異轉化為局部化優勢。在九個幾何基準測試中，CE-GRPO 達到 76.04 的平均準確率，分別優於 Qwen3-VL-8B 與軌跡層級 GRPO 達 8.09 與 3.43 個百分點。其相對優勢隨著中間事件數量的增加而擴大，彰顯了表徵與最佳化協同設計（representation–optimization co-design）對於冗長且高度依賴關係的多模態推理之價值。

English

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.