  Much of the field of Machine Learning exhibits a prominent set of failure
modes, including vulnerability to adversarial examples, poor
out-of-distribution (OoD) detection, miscalibration, and willingness to
memorize random labelings of datasets. We characterize these as failures of
robust generalization, which extends the traditional measure of generalization
as accuracy or related metrics on a held-out set. We hypothesize that these
failures to robustly generalize are due to the learning systems retaining too
much information about the training data. To test this hypothesis, we propose
the Minimum Necessary Information (MNI) criterion for evaluating the quality of
a model. In order to train models that perform well with respect to the MNI
criterion, we present a new objective function, the Conditional Entropy
Bottleneck (CEB), which is closely related to the Information Bottleneck (IB).
We experimentally test our hypothesis by comparing the performance of CEB
models with deterministic models and Variational Information Bottleneck (VIB)
models on a variety of different datasets and robustness challenges. We find
strong empirical evidence supporting our hypothesis that MNI models improve on
these problems of robust generalization.
