  The Information Bottleneck (IB) framework is a general characterization of
optimal representations obtained using a principled approach for balancing
accuracy and complexity. Here we present a new framework, the Dual Information
Bottleneck (dualIB), which resolves some of the known drawbacks of the IB. We
provide a theoretical analysis of the dualIB framework; (i) solving for the
structure of its solutions (ii) unraveling its superiority in optimizing the
mean prediction error exponent and (iii) demonstrating its ability to preserve
exponential forms of the original distribution. To approach large scale
problems, we present a novel variational formulation of the dualIB for Deep
Neural Networks. In experiments on several data-sets, we compare it to a
variational form of the IB. This exposes superior Information Plane properties
of the dualIB and its potential in improvement of the error.
