  Improving and guaranteeing the robustness of deep learning models has been a
topic of intense research. Ensembling, which combines several classifiers to
provide a better model, has shown to be beneficial for generalisation,
uncertainty estimation, calibration, and mitigating the effects of concept
drift. However, the impact of ensembling on certified robustness is less well
understood. In this work, we generalise Lipschitz continuity by introducing
S-Lipschitz classifiers, which we use to analyse the theoretical robustness of
ensembles. Our results are precise conditions when ensembles of robust
classifiers are more robust than any constituent classifier, as well as
conditions when they are less robust.
