1. A system for a neural network image classifier having improved accuracy, the system comprising: a memory arranged to access a neural network image classifier, the neural network image classifier having been trained using a plurality of training images from an input space, the training images being labeled for a plurality of classes; and at least one processor that computes a plurality of adversarial images by, for each adversarial image, searching a region in the input space around one of the training images, the region being one in which the neural network is linear, to find an image which is incorrectly classified into the plurality of classes by the neural network, wherein the at least one processor applies the training image to the neural network and observes a response of the neural network, wherein the at least one processor computes a constraint system using the observed response, the constraint system approximating the region of the input space, and wherein the at least one processor further trains the neural network image classifier to have improved accuracy using at least the adversarial images.