We survey results on neural network expressivity described in "On the
Expressive Power of Deep Neural Networks". The paper motivates and develops
three natural measures of expressiveness, which all display an exponential
dependence on the depth of the network. In fact, all of these measures are
related to a fourth quantity, trajectory length. This quantity grows
exponentially in the depth of the network, and is responsible for the depth
sensitivity observed. These results translate to consequences for networks
during and after training. They suggest that parameters earlier in a network
have greater influence on its expressive power -- in particular, given a layer,
its influence on expressivity is determined by the remaining depth of the
network after that layer. This is verified with experiments on MNIST and
CIFAR-10. We also explore the effect of training on the input-output map, and
find that it trades off between the stability and expressivity.

本文研究神经网络的表达能力，提出了三种衡量表达能力的自然量，并探讨了神经网络层数与表达能力之间的关系，特别地找出了深度敏感性所在，同时分析了训练和输入 - 输出映射等因素对表达能力的影响。