Adversarially trained models exhibit a large generalization gap: they can interpolate the training set even for large perturbation radii, but at the cost of large test error on clean samples. To investigate this gap, we decompose the test risk into its bias and variance components. We find that the bias increases monotonically with perturbation size and is the dominant term in the risk. Meanwhile, the variance is unimodal, peaking near the interpolation threshold for the training set. In contrast, we show that popular explanations for the generalization gap instead predict the variance to be monotonic, which leaves an unresolved mystery. We show that the same unimodal variance appears in a simple high-dimensional logistic regression problem, as well as for randomized smoothing. Overall, our results highlight the power of bias-variance decompositions in modern settings--by providing two measurements instead of one, they can rule out some theories and clarify others.

通过偏差方差分解研究对抗性训练扰动半径对模型测试误差的影响，发现模型的偏差随扰动半径增加单调增加，方差则在训练集插值阈值附近单峰；同时，偏差和方差可用于指导缩小泛化间隔的方法，即预训练和使用无标签数据。

通过偏差-方差分解了解对抗训练的泛化