  Explanation methods for machine learning models tend not to provide any
formal guarantees and may not reflect the underlying decision-making process.
In this work, we analyze stability as a property for reliable feature
attribution methods. We prove that relaxed variants of stability are guaranteed
if the model is sufficiently Lipschitz with respect to the masking of features.
We develop a smoothing method called Multiplicative Smoothing (MuS) to achieve
such a model. We show that MuS overcomes the theoretical limitations of
standard smoothing techniques and can be integrated with any classifier and
feature attribution method. We evaluate MuS on vision and language models with
various feature attribution methods, such as LIME and SHAP, and demonstrate
that MuS endows feature attributions with non-trivial stability guarantees.
