  We address the question of characterizing and finding optimal representations
for supervised learning. Traditionally, this question has been tackled using
the Information Bottleneck, which compresses the inputs while retaining
information about the targets, in a decoder-agnostic fashion. In machine
learning, however, our goal is not compression but rather generalization, which
is intimately linked to the predictive family or decoder of interest (e.g.
linear classifier). We propose the Decodable Information Bottleneck (DIB) that
considers information retention and compression from the perspective of the
desired predictive family. As a result, DIB gives rise to representations that
are optimal in terms of expected test performance and can be estimated with
guarantees. Empirically, we show that the framework can be used to enforce a
small generalization gap on downstream classifiers and to predict the
generalization ability of neural networks.
