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.

翻译：提升并保证深度学习模型的鲁棒性一直是研究热点。集成方法通过组合多个分类器构建更优模型，在泛化能力、不确定性估计、校准及缓解概念漂移影响等方面展现出显著优势。然而，集成方法对认证鲁棒性的影响机制尚未得到充分理解。本文通过引入S-利普希茨分类器对利普希茨连续性进行泛化，并以此分析集成模型的理论鲁棒性。研究得到了精确条件：当满足特定条件时，鲁棒分类器集成后的鲁棒性可能优于任意单一组成分类器，反之则可能出现鲁棒性下降的情况。