Computation of CNN’s Sensitivity to Input Perturbation

Abstract

Although Convolutional Neural Networks (CNNs) are considered as being "approximately invariant" to nuisance perturbations such as image transformation, shift, scaling, and other small deformations, some existing studies show that intense noises can cause noticeable variation to CNNs’ outputs. This paper focuses on exploring a method of measuring sensitivity by observing corresponding output variation to input perturbation on CNNs. The sensitivity is statistically defined in a bottom-up way from neuron to layer, and finally to the entire CNN network. An iterative algorithm is proposed for approximating the defined sensitivity. On the basic architecture of CNNs, the theoretically computed sensitivity is verified on the MNIST database with four types of commonly used noise distributions: Gaussian, Uniform, Salt and Pepper, and Rayleigh. Experimental results show the theoretical sensitivity is on the one hand in agreement with the actual output variation what on the maps, layers or entire networks are, and on the other hand an applicable quantitative measure for robust network selection.