Title: Does the Half Adversarial Robustness Represent the Whole? It Depends... A Theoretical Perspective of Subnetwork Robustness. Abstract: Adversarial robustness of deep neural networks has been studied extensively and can bring security against adversarial attacks/examples. However, adversarially robust training approaches require a training mechanism on the entire deep network which can come at the cost of efficiency and computational complexity such as runtime. As a pilot study, we develop in this paper a novel theoretical framework that aims to answer the question of how can we make a whole model robust to adversarial examples by making part of a model robust? Toward promoting subnetwork robustness, we propose for the first time a new concept of semirobustness, which indicates adversarial robustness of a part of the network. We provide a theoretical analysis to show that if a subnetwork is robust and highly correlated with the rest of the network, then the remaining layers are also guaranteed to be robust. To guide the empirical investigation of our theoretical findings, we implemented our method at multiple layer depths and across multiple common image classification datasets. Experiments demonstrate that our method, with sufficient dependency between subnetworks, successfully utilizes subnetwork robustness to match fully-robust models' performance across AlexNet, VGG16, and ResNet50 benchmarks, for attack types FGSM, I-FGSM, PGD, and C&W.