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.
On-policy distillation provides dense supervision for multimodal reasoners, but its trajectory-level reward cannot determine whether a failed answer arose from perception or subsequent reasoning. Perception Success Rate (PSR), estimated from multiple reasonings sharing one perception, remains ambiguous because low success conflates perceptual insufficiency with reasoning difficulty. We introduce \textbf{Perception-Correction Distillation (PCD)}, a label-free method that identifies correctable perception failures using downstream failure and teacher--student disagreement as complementary witnesses. Their product, , forms a soft AND gate that strengthens distillation only when both witnesses are present. We motivate this rule through Bayesian evidence combination and show that multiplication is the unique normalized bilinear gate that vanishes when either witness is absent. PCD uses separated perception--reasoning rollouts and mean-preserving weights, leaving the reasoning objective unchanged. Across eight benchmarks, PCD improves the 8B 2B macro average from 44.50 with OPD to 47.28 and the 32B 8B result from 56.94 to 61.22. In matched 2B ablations, removing PCD and separated rollout reduces held-out average by 2.22 and 0.88 points, respectively. Effective multimodal distillation therefore depends not only on what the teacher predicts, but also on identifying when perception is the appropriate target of correction.
We identify and formally characterize credit misassignment as a systematic failure mode of GRPO in tool-augmented multimodal search agents: its uniform broadcast of trajectory-level advantages to all tokens causes valuable tool-use steps in failing trajectories to be penalized no differently from valueless ones. We further empirically quantify the scale of this phenomenon. Over half of failing trajectories and failing tool-use actions exhibit correctable credit misassignment, demonstrating that the wasted training signal is both substantial and structurally exploitable. Building on this insight, we propose Tool-Aware Policy Optimization (TAPO), which exploits the parameter-determinism property of information-acquisition tools: similar call parameters define equivalent information-acquisition actions and should therefore share comparable action credit. TAPO constructs counterfactual witnesses within the current training batch and compensates misassigned negative credit via confidence-gated conservative advantage correction. It requires no additional annotation, models, or sampling, and introduces negligible computational overhead. Across multiple multimodal search benchmarks, TAPO delivers consistent, plug-and-play improvements over strong baselines for three mainstream RL algorithms (GRPO, GSPO, and SAPO). Our code and models will be publicly released upon acceptance.