  The expansion of explainable artificial intelligence as a field of research
has generated numerous methods of visualizing and understanding the black box
of a machine learning model. Attribution maps are generally used to highlight
the parts of the input image that influence the model to make a specific
decision. On the other hand, the robustness of machine learning models to
natural noise and adversarial attacks is also being actively explored. This
paper focuses on evaluating methods of attribution mapping to find whether
robust neural networks are more explainable. We explore this problem within the
application of classification for medical imaging. Explainability research is
at an impasse. There are many methods of attribution mapping, but no current
consensus on how to evaluate them and determine the ones that are the best. Our
experiments on multiple datasets (natural and medical imaging) and various
attribution methods reveal that two popular evaluation metrics, Deletion and
Insertion, have inherent limitations and yield contradictory results. We
propose a new explainability faithfulness metric (called EvalAttAI) that
addresses the limitations of prior metrics. Using our novel evaluation, we
found that Bayesian deep neural networks using the Variational Density
Propagation technique were consistently more explainable when used with the
best performing attribution method, the Vanilla Gradient. However, in general,
various types of robust neural networks may not be more explainable, despite
these models producing more visually plausible attribution maps.
