  The performance of modern algorithms on certain computer vision tasks such as
object recognition is now close to that of humans. This success was achieved at
the price of complicated architectures depending on millions of parameters and
it has become quite challenging to understand how particular predictions are
made. Interpretability methods propose to give us this understanding. In this
paper, we study LIME, perhaps one of the most popular. On the theoretical side,
we show that when the number of generated examples is large, LIME explanations
are concentrated around a limit explanation for which we give an explicit
expression. We further this study for elementary shape detectors and linear
models. As a consequence of this analysis, we uncover a connection between LIME
and integrated gradients, another explanation method. More precisely, the LIME
explanations are similar to the sum of integrated gradients over the
superpixels used in the preprocessing step of LIME.
