Easier Said Than Done: Strangers, Impostors, and the Negatives That Teach a Small Learner to Say "I Don't Know"

How do you teach a model to say “I don’t know”? The usual recipe collects questions it cannot answer, trains it to refuse them, and checks on a held-out part of the same collection, which cannot tell a learned rule from a memorized list, nor say which kind of unknown the rule covers. A question can carry a name the model has never seen, or a name it knows attached to work that is not that task’s (as a language model can be asked an unknown attribute of a known entity). We call these identifier membership and identifier–payload binding, and test both where the answer key is exact: a 1.8M-parameter learner routing tasks to verified programs in a program-graded world, with its competence map known, test identifiers reserved from all training, and every experiment registered before launch. Supervised for refusal only on its world’s own untaught tasks, the learner refuses, on average, 39% of items with never-seen identifiers, fluctuating from 2.5% to 70% over six runs of three seeds. Adding refusal on unknown identifiers in 5% of each batch fixes this in every seed, whether the identifiers are drawn fresh or from a fixed pool of 21. But the rule it learns does not reach the payload: the same learner abstains on none of the impostors, familiar identifiers carrying another task’s work. Mismatched pairings drawn fresh (nearly the whole pairing space) teach it to refuse impostors (95.8% abstention on average across ten seeds, with a low of 92%); a fixed pool of 21 pairings does not (25.9% on average, max of 41.5%), and what it teaches sits mostly on the identifiers it contains. A ladder of fixed pools of 100, 500 and 2,000 pairings reaches 61%, 91% and 96% on pairings it never saw, though larger pools also cover more identifiers. Twenty-one negatives taught the first boundary, but the second needed broad coverage.