Post-Training Leaves Behavioral Shadows on Unrelated Decisions

Post-training adapts language models to target tasks using domain-specific data. Recent work on subliminal learning reveals that information about these private updates can be implicitly transmitted through model generations on unrelated tasks. However, existing approaches are computationally heavy, relying on sampling extensive trajectories from the teacher, and remain largely confined to transferring superficial traits or preferences. **We show that capability-relevant information can be observed through single-word responses to unrelated inputs, without access to teacher logits, parameters, or target-task responses.** We call the behavioral changes that a private update induces on unrelated inputs its *behavioral shadow*. Our instrument, **A**ctive **T**askless **D**istillation (ATD), uses only the public model from which both teacher and student are initialized to find prompts where that model assigns nearly equal probabilities to two ordinary words. At these near-ties, a small private update may reverse the preferred word; ATD collects one greedy word per query from the private teacher and trains the student solely on the resulting prompt–word pairs. In the primary coding experiment with Qwen2.5-1.5B, a student trained on just 5,664 single-word teacher responses gains $5.34\mathrm{pp}$ on HumanEval+ over a control trained on the same responses with disrupted prompt–response pairings. Experiments on scientific knowledge, commonsense reasoning, and reading comprehension also show capability transfer, with further evidence across the tested model generations, sizes, and families. Functional analyses show that the learned signal is source-specific and composable, and that its strength tracks the teacher’s update strength. These results reveal that capability improvements can induce behavioral changes on unrelated boundary decisions, where even minimal, single-token observations suffice to transfer complex task skills.