Abstract: Despite their success in massive engineering applications, deep neural
networks are vulnerable to various perturbations due to their black-box nature.
Recent study has shown that a deep neural network can misclassify the data even
if the input data is perturbed by an imperceptible amount. In this paper, we
address the robustness issue of neural networks by a novel close-loop control
method from the perspective of dynamic systems. Instead of modifying the
parameters in a fixed neural network architecture, a close-loop control process
is added to generate control signals adaptively for the perturbed or corrupted
data. We connect the robustness of neural networks with optimal control using
the geometrical information of underlying data to design the control objective.
The detailed analysis shows how the embedding manifolds of state trajectory
affect error estimation of the proposed method. Our approach can simultaneously
maintain the performance on clean data and improve the robustness against many
types of data perturbations. It can also further improve the performance of
robustly trained neural networks against different perturbations. To the best
of our knowledge, this is the first work that improves the robustness of neural
networks with close-loop control.