Teaching a small AI model (student) by copying the reasoning steps of a larger one (teacher) runs into trouble on long answers. The student's own reasoning path drifts away from the teacher's. When this happens, the teacher's feedback on later steps becomes unreliable, making the training process unstable.
To fix this, ATI-OPD lets the teacher step in and rewrite the very first segment where the student goes wrong. The student then continues its own reasoning from the corrected path. A second safeguard watches the rest of the answer; any part that still disagrees with the teacher is simply ignored in the training update.
This keeps training stable. It reduces huge mismatches between teacher and student and improves the student's accuracy on math reasoning tests without needing to artificially limit answer length.