  Diagnostic imaging often requires the simultaneous identification of a
multitude of findings of varied size and appearance. Beyond global indication
of said findings, the prediction and display of localization information
improves trust in and understanding of results when augmenting clinical
workflow. Medical training data rarely includes more than global image-level
labels as segmentations are time-consuming and expensive to collect. We
introduce an approach to managing these practical constraints by applying a
novel architecture which learns at multiple resolutions while generating
saliency maps with weak supervision. Further, we parameterize the Log-Sum-Exp
pooling function with a learnable lower-bounded adaptation (LSE-LBA) to build
in a sharpness prior and better handle localizing abnormalities of different
sizes using only image-level labels. Applying this approach to interpreting
chest x-rays, we set the state of the art on 9 abnormalities in the NIH's CXR14
dataset while generating saliency maps with the highest resolution to date.
