  Understanding the predictions made by Artificial Intelligence (AI) systems is
becoming more and more important as deep learning models are used for
increasingly complex and high-stakes tasks. Saliency mapping -- a popular
visual attribution method -- is one important tool for this, but existing
formulations are limited by either computational cost or architectural
constraints. We therefore propose Hierarchical Perturbation, a very fast and
completely model-agnostic method for interpreting model predictions with robust
saliency maps. Using standard benchmarks and datasets, we show that our
saliency maps are of competitive or superior quality to those generated by
existing model-agnostic methods -- and are over 20 times faster to compute.
