  Convolutional neural network based systems have largely failed to be adopted
in many high-risk application areas, including healthcare, military, security,
transportation, finance, and legal, due to their highly uninterpretable
"black-box" nature. Towards solving this deficiency, we teach a novel
multi-task capsule network to improve the explainability of predictions by
embodying the same high-level language used by human-experts. Our explainable
capsule network, X-Caps, encodes high-level visual object attributes within the
vectors of its capsules, then forms predictions based solely on these
human-interpretable features. To encode attributes, X-Caps utilizes a new
routing sigmoid function to independently route information from child capsules
to parents. Further, to provide radiologists with an estimate of model
confidence, we train our network on a distribution of expert labels, modeling
inter-observer agreement and punishing over/under confidence during training,
supervised by human-experts' agreement. X-Caps simultaneously learns attribute
and malignancy scores from a multi-center dataset of over 1000 CT scans of lung
cancer screening patients. We demonstrate a simple 2D capsule network can
outperform a state-of-the-art deep dense dual-path 3D CNN at capturing
visually-interpretable high-level attributes and malignancy prediction, while
providing malignancy prediction scores approaching that of non-explainable 3D
CNNs. To the best of our knowledge, this is the first study to investigate
capsule networks for making predictions based on radiologist-level
interpretable attributes and its applications to medical image diagnosis. Code
is publicly available at https://github.com/lalonderodney/X-Caps .
