Fable
Inferring the secret recipe from the taste of the soup
The pharmacy published the efficacy of its pills for various illnesses, but promised not to reveal patients' prescriptions. The out-of-town doctor did not ask for formulas, but repeatedly asked about extremely rare illnesses, carefully noting tiny changes in the efficacy table each time.
At first the shopkeeper thought what was made public was aggregate numbers and would not hurt anyone. But when a rare illness appeared, the doctor pieced several answers together and actually inferred the medicinal materials that patient had used.
The manager then stopped overly granular group reporting, merged results with too few samples, and limited abnormally frequent follow-up queries. Queries involving sensitive medical conditions also had to go through review, to prevent someone from piecing together a personal profile from a string of seemingly ordinary questions.
The apothecary still publishes useful efficacy information, but no longer treats every detail as harmless. Looking only at the output of a model or system, someone may also trace the traces backward to infer secrets in the input.