Noise Optimization in Artificial Neural Networks

Artificial neural network (ANN) has been widely used in automation. However, the vulnerability of ANN under certain attacks poses security threat for critical automation systems. Adding noises to artificial neural network has been shown to be able to improve robustness in previous work. In this work, we propose a new technique to compute the pathwise stochastic gradient estimate with respect to the standard deviation of the Gaussian noise added to each neuron of the ANN. By our proposed technique, the gradient estimation with respect to noise levels is a byproduct of the back propagation algorithm for estimating gradient with respect to synaptic weights in ANN. Thus, the noise level for each neuron can be optimized simultaneously in the processing of training the synaptic weights at nearly no extra computational cost. In numerical experiments, our proposed method can achieve significant performance improvement on robustness of several popular ANN structures under both black box and white box attacks.