  Despite the wide applications of neural networks, there have been increasing
concerns about their vulnerability issue. While numerous attack and defense
techniques have been developed, this work investigates the robustness issue
from a new angle: can we design a self-healing neural network that can
automatically detect and fix the vulnerability issue by itself? A typical
self-healing mechanism is the immune system of a human body. This
biology-inspired idea has been used in many engineering designs but is rarely
investigated in deep learning. This paper considers the post-training
self-healing of a neural network, and proposes a closed-loop control
formulation to automatically detect and fix the errors caused by various
attacks or perturbations. We provide a margin-based analysis to explain how
this formulation can improve the robustness of a classifier. To speed up the
inference of the proposed self-healing network, we solve the control problem
via improving the Pontryagin Maximum Principle-based solver. Lastly, we present
an error estimation of the proposed framework for neural networks with
nonlinear activation functions. We validate the performance on several network
architectures against various perturbations. Since the self-healing method does
not need a-priori information about data perturbations/attacks, it can handle a
broad class of unforeseen perturbations.
