Adaptive Semantic Branching: Disagreement-Localized Cross-Trajectory Regeneration for Reasoning Candidate Expansion

Reasoning trajectories generated for the same problem often arrive at conflicting answers. These disagreements reveal alternative intermediate decisions that can be reused to explore new solutions. We introduce Adaptive Semantic Branching (ASB), a training-free inference procedure that turns cross-trajectory disagreement into targeted candidate generation. ASB first groups independently sampled trajectories by extracted final answer, selects a representative from each group, and aligns their reasoning steps with a monotonic dynamic program. A persistent-divergence objective identifies the point at which initially similar reasoning paths develop different continuations. For each selected directed pair, ASB retains the source trajectory's textual prefix, extracts a short reasoning window from a competing donor trajectory, and generates a fresh solution conditioned on both. A diversity-aware policy allocates up to three additional generations according to the answer-cluster structure. In a 500-problem MATH evaluation with Qwen2.5-7B-Instruct, ASB increases oracle candidate coverage from 445/500 (89.0%) with seven initial samples to 455/500 (91.0%), recovering correct candidates for 10 of the 55 initially uncovered problems. The method uses 576 additional generation calls across the evaluation set, averaging 8.152 calls per problem. We provide a precise specification of the branching operator, alignment objective, generation policy, and experimental configuration.