Post-hoc attribution methods aim to explain deep learning predictions by highlighting influential input pixels. However, these explanations are highly non-robust: small, imperceptible input perturbations can drastically alter the attribution map while maintaining the same prediction. This vulnerability undermines their trustworthiness and calls for rigorous robustness guarantees of pixel-level attribution scores. We introduce the first certification framework that guarantees pixel-level robustness for any black-box attribution method using randomized smoothing. By sparsifying and smoothing attribution maps, we reformulate the task as a segmentation problem and certify each pixel's importance against ₂-bounded perturbations. We further propose three evaluation metrics to assess certified robustness, localization, and faithfulness. An extensive evaluation of 12 attribution methods across 5 ImageNet models shows that our certified attributions are robust, interpretable, and faithful, enabling reliable use in downstream tasks. Our code is at https: //github. com/AlaaAnani/certified-attributions.
Anani et al. (Wed,) studied this question.