# Robustness of Artificial Neural Networks Based on Weight Alterations Used for Prediction Purposes
## 2 Background and Related Research  
ANNs and robustness are very popular and active research topics in the literature. Due to adversarial attacks, many approaches have been developed regarding the fault tolerance and robustness of ANNs. The authors of [2] proposed a method based on neural networks in order to detect malicious hosts based on the SYN packets that are exchanged. With the aid of appropriate training, this method achieved 98% accuracy based on specific test data. Moreover, the authors of [3] found that powerful attacks can defeat defensive distillation, demonstrating that by systematically evaluating several possible attacks, better adversarial examples can be found than those in existing approaches. This study also concludes that constructing defenses that are robust to adversarial examples remains challenging. The study of [4] presents a survey on the robustness of deep networks to changes that may affect the samples in practice, such as adversarial perturbations, random noise, and transformations. The authors also discuss different solutions that attempt to increase the robustness of deep networks. Additionally, the authors of [7] study the effectiveness of different types of attacks and propose methods for training a deep-learning-based IDS with the use of different types of neural networks in order to increase the robustness of the networks based on a thread model. Furthermore, n-MR schemes and redundancy have been proposed as methods for increasing the robustness of ANNs. The authors of [5] propose a novel dual modular redundance framework for DNNs. D2 NN checks the fault sensitivity of each neuron in the target DNN based on performance degradation and shows if the neuron is faulty. Next, D2 NN duplicates the more sensitive neurons to construct the completed DMR (dual modular redundancy). Furthermore, theoretical studies and works based on robust metrics have taken into account fault tolerance and robustness. The authors of [9] present a theoretical survey on different defenses against adversarial inputs of machine learning. The following defenses are discussed: techniques based on model training, input validation techniques, and architectural modification techniques. In this study, only the theoretical aspects are presented to show the importance of robustness against adversarial examples and the need for strong, practical countermeasures in the future. The authors of [10] propose a theoretical fault tolerance solution for ANNs based on an evaluation of the different elements of an ANN, which are more appropriate for single faults. Based on this evaluation, they propose the duplication of different parts of an ANN architecture. Furthermore, the authors of [11] present a new version of the communication robustness (CR) metric, simplified communication robustness (SCR), which helps with the calculation of the CR robustness metric for different network topologies. Additionally, this study provides evaluations and discussion about different robustness metrics. Studies that provide certifications for the robustness of neural networks are presented next. The authors of [8] present a defense method for neural networks with one hidden layer. This is based on certifications that, for a given network and test input, there is no attack that can force the error to exceed a certain threshold: the computation of an upper bound in the worst-case loss scenario. Additionally, they optimized this method with different network parameters, providing an adaptive regularizer that helps robustness. Additionally, the authors of [12] studied the sensitivity of neural networks to weight perturbations. They proposed an efficient approach to compute a certified robustness bound of weight perturbations within neural networks that do not have erroneous outputs. The authors provided a certified weight perturbation region such that DNNs maintained their accuracy if weight perturbations were within that region. Lastly, different novel robust techniques for neural networks have been presented.