An Estimator for the Sensitivity to Perturbations of Deep Neural Networks

TL;DR

This paper introduces an estimator to predict the sensitivity of deep neural networks to perturbations, aiding in ensuring their stability for safety-critical applications by estimating their robustness to noise and errors.

Contribution

The paper derives a novel estimator based on inequalities and matrix norms that predicts a DNN's sensitivity to perturbations, similar to a condition number for the network.

Findings

Estimator tested on AlexNet and VGG-19 with ImageNet.

Estimator's tightness evaluated via random perturbations.

Potential to guide minimal bit-width precision for safety.

Abstract

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.