论文标题
Riemannian数据依赖于神经网络认证的随机平滑
Riemannian data-dependent randomized smoothing for neural networks certification
论文作者
论文摘要
神经网络的认证是一个重要且具有挑战性的问题，几年以来就引起了机器学习社区的关注。在本文中，我们专注于随机平滑（RS），该平滑度被认为是获得可靠的稳健神经网络的最新方法。特别是，最近引入的一种新的与数据相关的RS技术可用于在神经网络的每个输入数据附近证明具有正交轴的椭圆形。在这项工作中，我们指出，在输入数据的旋转下，ANCER并不是不变的，并提出了一种新的旋转不变的公式，该公式可以在其轴线上对椭圆进行认证。我们称为Riemannian数据依赖的随机平滑（RDDR）的方法依赖于协方差矩阵流形的信息几何技术，并且可以根据MNIST数据集的实验来证明比ANCer更大的区域。
Certification of neural networks is an important and challenging problem that has been attracting the attention of the machine learning community since few years. In this paper, we focus on randomized smoothing (RS) which is considered as the state-of-the-art method to obtain certifiably robust neural networks. In particular, a new data-dependent RS technique called ANCER introduced recently can be used to certify ellipses with orthogonal axis near each input data of the neural network. In this work, we remark that ANCER is not invariant under rotation of input data and propose a new rotationally-invariant formulation of it which can certify ellipses without constraints on their axis. Our approach called Riemannian Data Dependant Randomized Smoothing (RDDRS) relies on information geometry techniques on the manifold of covariance matrices and can certify bigger regions than ANCER based on our experiments on the MNIST dataset.
