  In this paper, we challenge the common assumption that collapsing the spatial
dimensions of a 3D (spatial-channel) tensor in a convolutional neural network
(CNN) into a vector via global pooling removes all spatial information.
Specifically, we demonstrate that positional information is encoded based on
the ordering of the channel dimensions, while semantic information is largely
not. Following this demonstration, we show the real world impact of these
findings by applying them to two applications. First, we propose a simple yet
effective data augmentation strategy and loss function which improves the
translation invariance of a CNN's output. Second, we propose a method to
efficiently determine which channels in the latent representation are
responsible for (i) encoding overall position information or (ii)
region-specific positions. We first show that semantic segmentation has a
significant reliance on the overall position channels to make predictions. We
then show for the first time that it is possible to perform a `region-specific'
attack, and degrade a network's performance in a particular part of the input.
We believe our findings and demonstrated applications will benefit research
areas concerned with understanding the characteristics of CNNs.
