Table 1 The average inner products \(d_{i}\) of sample pairs from the same class (MNIST dataset). The first row describes the average inner products for sample pairs before training, and the second row depicts the inner products for sample pairs after training. The first two columns represent the average inner products for training and test sample pairs, respectively, where adversarial samples are not added to the training set. The last column represent the average inner products for training and test sample pairs, respectively, where adversarial samples are added to the training set