For Deep Neural Networks (DNNs) to become useful in safety-critical applications, such as self-driving cars and disease diagnosis, they must be stable to perturbations in input and model parameters. Characterizing the sensitivity of a DNN to perturbations is necessary to determine minimal bit-width precision that may be used to safely represent the network. However, no general result exists that is capable of predicting the sensitivity of a given DNN to round-off error, noise, or other perturbations in input. This paper derives an estimator that can predict such quantities. The estimator is derived via inequalities and matrix norms, and the resulting quantity is roughly analogous to a condition number for the entire neural network. An approximation of the estimator is tested on two Convolutional Neural Networks, AlexNet and VGG-19, using the ImageNet dataset. For each of these networks, the tightness of the estimator is explored via random perturbations and adversarial attacks.

翻译：为使深度神经网络（DNNs）能够应用于安全关键型场景，例如自动驾驶汽车和疾病诊断，它们必须对输入和模型参数的扰动保持稳定。表征DNN对扰动的敏感性，对于确定可安全表示网络所需的最小位宽精度至关重要。然而，目前尚无通用方法能够预测给定DNN对舍入误差、噪声或其他输入扰动的敏感性。本文推导出一种可预测此类量的估计器。该估计器通过不等式和矩阵范数推导得出，其结果大致类似于整个神经网络的状况数。该估计器的一种近似形式在两种卷积神经网络（AlexNet和VGG-19）上进行了测试，并使用了ImageNet数据集。针对上述每种网络，通过随机扰动和对抗攻击探究了该估计器的紧密性。