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We regard pre-trained residual networks (ResNets) as nonlinear systems anduse linearization, a common method used in the qualitative analysis ofnonlinear systems, to understand the behavior of the networks under smallperturbations of the input images. We work with ResNet-56 and ResNet-110trained on the CIFAR-10 data set. We linearize these networks at the level ofresidual units and network stages, and the singular value decomposition is usedin the stability analysis of these components. It is found that most of thesingular values of the linearizations of residual units are 1 and, in spite ofthe fact that the linearizations depend directly on the activation maps, thesingular values differ only slightly for different input images. However,adjusting the scaling of the skip connection or the values of the weights in aresidual unit has a significant impact on the singular value distributions.Inspection of how random and adversarial perturbations of input imagespropagate through the network reveals that there is a dramatic jump in themagnitude of adversarial perturbations towards the end of the final stage ofthe network that is not present in the case of random perturbations. We attemptto gain a better understanding of this phenomenon by projecting theperturbations onto singular vectors of the linearizations of the residualunits.

Residual Networks as Nonlinear Systems: Stability Analysis using Linearization