Randomized smoothing has been successfully applied in high-dimensional image classification tasks to obtain models that are provably robust against input perturbations of bounded size. We extend this technique to produce certifiable robustness for vector-valued functions, i.e., bound the change in output caused by a small change in input. These functions are used in many areas of machine learning, such as image reconstruction, dimensionality reduction, super-resolution, etc., but due to the enormous dimensionality of the output space in these problems, generating meaningful robustness guarantees is difficult. We design a smoothing procedure that can leverage the local, potentially low-dimensional, behaviour of the function around an input to obtain probabilistic robustness certificates. We demonstrate the effectiveness of our method on multiple learning tasks involving vector-valued functions with a wide range of input and output dimensionalities.

翻译：在高维图像分类任务中成功地应用了随机平滑法,以获得模型,这些模型对封闭尺寸的输入扰动具有可辨别的稳健性。我们推广了这一技术,为矢量价值的函数产生可验证的稳健性,即将投入小幅变化引起的产出变化捆绑起来。这些功能用于机器学习的许多领域,如图像重建、维度降低、超分辨率等,但由于在这些问题上产出空间的高度维度,因此难以产生有意义的稳健性保证。我们设计了一个滑动程序,能够利用投入周围的局部、潜在的低维度功能,以获得概率稳健性证书。我们展示了我们利用广泛投入和输出维度的矢量价值功能开展多重学习任务的方法的有效性。