  The process of aggregation is ubiquitous in almost all deep nets models. It
functions as an important mechanism for consolidating deep features into a more
compact representation, whilst increasing robustness to overfitting and
providing spatial invariance in deep nets. In particular, the proximity of
global aggregation layers to the output layers of DNNs mean that aggregated
features have a direct influence on the performance of a deep net. A better
understanding of this relationship can be obtained using information theoretic
methods. However, this requires the knowledge of the distributions of the
activations of aggregation layers. To achieve this, we propose a novel
mathematical formulation for analytically modelling the probability
distributions of output values of layers involved with deep feature
aggregation. An important outcome is our ability to analytically predict the
KL-divergence of output nodes in a DNN. We also experimentally verify our
theoretical predictions against empirical observations across a range of
different classification tasks and datasets.
