  Interpretability is an emerging area of research in trustworthy machine
learning. Safe deployment of machine learning system mandates that the
prediction and its explanation be reliable and robust. Recently, it has been
shown that the explanations could be manipulated easily by adding visually
imperceptible perturbations to the input while keeping the model's prediction
intact. In this work, we study the problem of attributional robustness (i.e.
models having robust explanations) by showing an upper bound for attributional
vulnerability in terms of spatial correlation between the input image and its
explanation map. We propose a training methodology that learns robust features
by minimizing this upper bound using soft-margin triplet loss. Our methodology
of robust attribution training (\textit{ART}) achieves the new state-of-the-art
attributional robustness measure by a margin of $\approx$ 6-18 $\%$ on several
standard datasets, ie. SVHN, CIFAR-10 and GTSRB. We further show the utility of
the proposed robust training technique (\textit{ART}) in the downstream task of
weakly supervised object localization by achieving the new state-of-the-art
performance on CUB-200 dataset.
