Method and system for probably robust classification with detection of adversarial examples

Abstract

A computer-implemented method for training a machine-learning network includes receiving an input data from a sensor, wherein the input data includes a perturbation, wherein the input data is indicative of image, radar, sonar, or sound information, obtain a worst-case bound on a classification error and loss for perturbed versions of the input data, utilizing at least bounding of one or more hidden layer values, in response to the input data, train a classifier, wherein the classifier includes a plurality of classes, including an additional abstain class, wherein the abstain class is determined in response to at least bounding the input data, outputting a classification in response to the input data, and output a trained classifier configured to detect the additional abstain class in response to the input data classifier with a plurality of classes, including an additional abstain class.