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Fork Where the Model Changes Its Mind: Belief-Shift Branching for Tree-Structured Reinforcement Learning
摘要
arXiv:2609.11061v1 Announce Type: new Abstract: Tree-structured rollouts give critic-free reinforcement learning with verifiable rewards (RLVR) step-level credit: fork a chain at an intermediate point, and sibling outcome differences estimate step value. Each fork adds sampling cost, so realistic budgets typically allow only a few forks per chain. A fork placed where the outcome is already largely settled yields siblings that mostly agree and provide almost no credit signal; hence, for a given tree size, where forks are placed largely determines how much step-level RL can gain. Most existing mainstream methods place forks by structure, such as fixed lengths, midpoints, and delimiters, or by next-token entropy. We formalize fork placement as locating the \emph{pivots} of the chain's value curve, where the expected outcome turns. We propose \emph{belief-shift branching}: read the model's answer belief at candidate boundaries and fork just before the step where consecutive beliefs diverge most. Three instantiations, none needing step-level supervision, span access levels: a black-box probe, a logit-lens depth profile, and a learned activation direction, which is fit offline and therefore used only in the validation before RL training. The signal only \emph{places} forks, and the probe costs about $1\%$ of step compute on mathematics and under $5\%$ on code when it runs inside the rollout engine. In that validation, against Monte-Carlo value curves, a belief-shift signal ranks f