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We introduce a new notion of the stability of computations, which holds underpost-processing and adaptive composition. We show that the notion is bothnecessary and sufficient to ensure generalization in the face of adaptivity,for any computations that respond to bounded-sensitivity linear queries whileproviding accuracy with respect to the data sample set. The stability notion isbased on quantifying the effect of observing a computation's outputs on theposterior over the data sample elements. We show a separation between thisstability notion and previously studied notion and observe that alldifferentially private algorithms also satisfy this notion.

A necessary and sufficient stability notion for adaptive generalization