| Summary: | 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.
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