Improving Gradient Regularization using Complex-Valued Neural Networks

Gradient regularization is a neural network defense technique that requires no prior knowledge of an adversarial attack and that brings only limited increase in training computational complexity. A form of complex-valued neural network (CVNN) is proposed to improve the performance of gradient regularization on classification tasks of real-valued input in adversarial settings. The activation derivatives of each layer of the CVNN are dependent on the combination of inputs to the layer, and locally stable representations can be learned for inputs the network is trained on. Furthermore, the properties of the CVNN parameter derivatives resist decrease of performance on the standard objective that is caused by competition with the gradient regularization objective. Experimental results show that the performance of gradient regularized CVNN surpasses that of real-valued neural networks with comparable storage and computational complexity. Moreover, gradient regularized complex-valued networks exhibit robust performance approaching that of real-valued networks trained with multi-step adversarial training.