  Recently, deep residual networks have been successfully applied in many
computer vision and natural language processing tasks, pushing the
state-of-the-art performance with deeper and wider architectures. In this work,
we interpret deep residual networks as ordinary differential equations (ODEs),
which have long been studied in mathematics and physics with rich theoretical
and empirical success. From this interpretation, we develop a theoretical
framework on stability and reversibility of deep neural networks, and derive
three reversible neural network architectures that can go arbitrarily deep in
theory. The reversibility property allows a memory-efficient implementation,
which does not need to store the activations for most hidden layers. Together
with the stability of our architectures, this enables training deeper networks
using only modest computational resources. We provide both theoretical analyses
and empirical results. Experimental results demonstrate the efficacy of our
architectures against several strong baselines on CIFAR-10, CIFAR-100 and
STL-10 with superior or on-par state-of-the-art performance. Furthermore, we
show our architectures yield superior results when trained using fewer training
data.
