Robustness of Deep ReLU Networks to Misclassification of High-Dimensional Data
This work addresses the robustness of neural networks for theoretical machine learning, but it appears incremental as it builds on existing theoretical frameworks.
The authors tackled the problem of quantifying the robustness of deep ReLU networks to random input perturbations, deriving lower bounds on local robustness in terms of input dimensionality and network units.
We present a theoretical study of the robustness of parameterized networks to random input perturbations. Specifically, we analyze local robustness at a given network input by quantifying the probability that a small additive random perturbation of the input leads to misclassification. For deep networks with rectified linear units, we derive lower bounds on local robustness in terms of the input dimensionality and the total number of network units.