Some Questions Concerning the Robustness of Neuromorphic Neural Networks

In this paper, we extend previous results on neural networks, that were obtained on simple architectures, to the more practical cases of convolutional neural networks (CNN) and consider different action functions. Similarly to what has been done before, we view multilayer and CNN architectures of neural networks as distributed systems where neurons can fail independently and any recovery learning phase is absent. We give upper bounds on the number of neurons that can fail without harming the result of a computation. We evaluate the error propagated by a neural network when a given number of components fails, taking into account only the network’s topology and the type of activation function. In the crash case, our upper bound involves the number of neurons per layer, the Lipschitz constant of the neural activation function, the number of failing neurons, the synaptic weights and the depth of the layer where the failure occurred. Our results apply to more practical and modern cases of neural network architectures.