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.

本研究将深度残差网络解释为普通微分方程，并由此开发出一种稳定和可逆的深度神经网络理论框架，以及提出了三种可任意加深的可逆神经网络架构，实现了对深度网络的记忆高效实现，并且通过实验证明了本文方法在 CIFAR-10，CIFAR-100 和 STL-10 等数据集上取得了明显的优于现有强基准的性能表现，并且能够通过使用更少的训练数据来训练神经网络。