Building a robust deep neural network (DNN) framework turns out to be a very difficult task as adaptive attacks are developed that break a robust DNN strategy. In this work we first study the bootstrap distribution of DNN weights and biases. We bootstrap three DNN models: a simple three layer convolutional neural network (CNN), VGG16 with 13 convolutional layers and 3 fully connected layers, and Inception v3 with 42 layers. Both VGG16 and Inception v3 are trained on CIFAR10 in order for

more »

... pping networks to converge. We then compare the bootstrap NN parameter distributions with those from training DNN with different random initial seeds. We discover that the bootstrap DNN parameter distributions change as the DNN model size increases. And the bootstrap DNN parameter distributions are very close to those obtained from training with different random initial seeds. The bootstrap DNN parameter distributions are used to create a graybox defense strategy. We randomize a certain percentage of the weights of the first convolutional layers of a DNN model, and create a random ensemble of DNNs. Based on one trained DNN, we have infinitely many random DNN ensembles. The adaptive attacks lose the target. A random DNN ensemble is resilient to the adversarial attacks and maintains performance on clean data.