Intriguing properties of neural networks – https://arxiv.org/pdf/1312.6199.pdf

1. It suggests that it is the space, rather than the individual units, that contains the semantic information in the high layers of neural networks.
2. It suggests that the learnt input-output mappings by deep neural networks are fairly discontinuous. That means it is easy to fool a well trained neural networks.

See also in https://arxiv.org/pdf/1412.6572.pdf where the authors show it is easy to generate adversarial examples which are close to the original ones but are misclassified by neural networks.