  Distributed deep neural networks (DNNs) have been shown to reduce the
computational burden of mobile devices and decrease the end-to-end inference
latency in edge computing scenarios. While distributed DNNs have been studied,
to the best of our knowledge the resilience of distributed DNNs to adversarial
action still remains an open problem. In this paper, we fill the existing
research gap by rigorously analyzing the robustness of distributed DNNs against
adversarial action. We cast this problem in the context of information theory
and introduce two new measurements for distortion and robustness. Our
theoretical findings indicate that (i) assuming the same level of information
distortion, latent features are always more robust than input representations;
(ii) the adversarial robustness is jointly determined by the feature dimension
and the generalization capability of the DNN. To test our theoretical findings,
we perform extensive experimental analysis by considering 6 different DNN
architectures, 6 different approaches for distributed DNN and 10 different
adversarial attacks to the ImageNet-1K dataset. Our experimental results
support our theoretical findings by showing that the compressed latent
representations can reduce the success rate of adversarial attacks by 88% in
the best case and by 57% on the average compared to attacks to the input space.
