  We introduce a new notion of the stability of computations, which holds under
post-processing and adaptive composition. We show that the notion is both
necessary and sufficient to ensure generalization in the face of adaptivity,
for any computations that respond to bounded-sensitivity linear queries while
providing accuracy with respect to the data sample set. The stability notion is
based on quantifying the effect of observing a computation's outputs on the
posterior over the data sample elements. We show a separation between this
stability notion and previously studied notion and observe that all
differentially private algorithms also satisfy this notion.
