Machine learning models often need to be robust to noisy input data. The
effect of real-world noise (which is often random) on model predictions is
captured by a model's local robustness, i.e., the consistency of model
predictions in a local region around an input. However, the na\"ive approach to
computing local robustness based on Monte-Carlo sampling is statistically
inefficient, leading to prohibitive computational costs for large-scale
applications. In this work, we develop the first analytical estimators to
efficiently compute local robustness of multi-class discriminative models using
local linear function approximation and the multivariate Normal CDF. Through
the derivation of these estimators, we show how local robustness is connected
to concepts such as randomized smoothing and softmax probability. We also
confirm empirically that these estimators accurately and efficiently compute
the local robustness of standard deep learning models. In addition, we
demonstrate these estimators' usefulness for various tasks involving local
robustness, such as measuring robustness bias and identifying examples that are
vulnerable to noise perturbation in a dataset. By developing these analytical
estimators, this work not only advances conceptual understanding of local
robustness, but also makes its computation practical, enabling the use of local
robustness in critical downstream applications.

本文提出了分析估计器，用于高效计算多类辨别模型的局部鲁棒性，并证实了这些估计器在标准深度学习模型中准确且高效地计算局部鲁棒性，突出了局部鲁棒性的概念理解的进步，并使其计算实用化，能够在关键的下游应用中使用。