  We information-theoretically reformulate two measures of capacity from
statistical learning theory: empirical VC-entropy and empirical Rademacher
complexity. We show these capacity measures count the number of hypotheses
about a dataset that a learning algorithm falsifies when it finds the
classifier in its repertoire minimizing empirical risk. It then follows from
that the future performance of predictors on unseen data is controlled in part
by how many hypotheses the learner falsifies. As a corollary we show that
empirical VC-entropy quantifies the message length of the true hypothesis in
the optimal code of a particular probability distribution, the so-called actual
repertoire.
