Abstract: A system, method and computer program product for training a deep neural network. The deep neural network can be trained using a learning process that is defined to optimize both an error function of the deep neural network as well as a network mapping function of the deep neural network. The network mapping function can represent a predicted label distribution geometry property of the deep neural network. This learning process can improve the accuracy of the trained deep neural network model as well as its robustness again adversarial attacks. Optimizing the network mapping function can also provide increased insight into the operation of the trained deep neural network model, which may promote increased interpretability of the trained model and thus encourage uptake of the trained model.