# Behavioral Shadow of Post-Training

The work introduces Active Taskless Distillation (ATD), which uses a public ancestor model to select unrelated prompts on which it is nearly indifferent between two ordinary words, has a privately post-trained teacher return a single word per prompt, and trains a same-ancestor student only on those prompt-word pairs; in the primary Qwen2.5-1.5B coding experiment, 5,664 single-word responses yield a 5.34 percentage-point gain on HumanEval+ over an exact nuisance-matched control, with positive mean gains also observed in scientific knowledge, commonsense reasoning, and reading comprehension across additional model generations, sizes, and families.

The work introduces Active Taskless Distillation (ATD), which uses a public ancestor model to select unrelated prompts on which it is nearly indifferent between two ordinary words, has a privately post-trained teacher return a single word per prompt, and trains a same-ancestor student only on those prompt-word pairs; in the primary Qwen2.5-1.5B coding experiment, 5,664 single-word responses yield a 5.34 percentage-point gain on HumanEval+ over an exact nuisance-matched control, with positive mean gains also observed in scientific knowledge, commonsense reasoning, and reading comprehension across additional model generations, sizes, and families.