HDL locates branch points by hindsight divergence, cutting generated tokens 35–61% and lifting agent tasks by up to 12.46 points
The work introduces Hindsight-Divergence Localization (HDL), which picks branch points in a trajectory by how much token log-likelihoods change once verifier feedback and a reflection are added, then builds each training group from a few complete root trajectories plus continuations that reuse the root prefix; across math, code, and agent tasks with three models it cuts generated tokens by 35–61% and rollout wall-clock time by 18–45% relative to GRPO while improving task performance, with gains up to 12.46 percentage points on agent tasks.