Title: Robust attributions require rethinking robustness metrics. Abstract: For machine learning models to be reliable and trustworthy, their decisions must be interpretable. As these models find increasing use in safety-critical applications, it is important that not just the model predictions but also their explanations (as feature attributions) be robust to small human-imperceptible input perturbations. Recent works have shown that many attribution methods are fragile and have proposed improvements in either the attribution methods or the model training. Existing works measure attributional robustness by metrics such as top-$k$ intersection, Spearman's rank-order correlation (or Spearman's $\rho$) or Kendall's rank-order correlation (or Kendall's $\tau$) to quantify the change in feature attributions under input perturbation. However, we show that these metrics are fragile. That is, under such metrics, a simple random perturbation attack can seem to be as significant as more principled attributional attacks. We instead propose Locality-sENSitive (LENS) improvements of the above metrics, namely, LENS-top-$k$, LENS-Spearman and LENS-Kendall, that incorporate the locality of attributions along with their rank order. Our locality-sensitive metrics provide tighter bounds on attributional robustness and do not disproportionately penalize attribution methods for reasonable local changes. We show that the robust attribution methods proposed in recent works also reflect this premise of locality, thus highlighting the need for a locality-sensitive metric for progress in the field. Our empirical results on well-known benchmark datasets using well-known models and attribution methods support our observations and conclusions in this work.