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Recently, deep residual networks have been successfully applied in manycomputer vision and natural language processing tasks, pushing thestate-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 theoreticaland empirical success. From this interpretation, we develop a theoreticalframework on stability and reversibility of deep neural networks, and derivethree reversible neural network architectures that can go arbitrarily deep intheory. The reversibility property allows a memory-efficient implementation,which does not need to store the activations for most hidden layers. Togetherwith the stability of our architectures, this enables training deeper networksusing only modest computational resources. We provide both theoretical analysesand empirical results. Experimental results demonstrate the efficacy of ourarchitectures against several strong baselines on CIFAR-10, CIFAR-100 andSTL-10 with superior or on-par state-of-the-art performance. Furthermore, weshow our architectures yield superior results when trained using fewer trainingdata.

Reversible Architectures for Arbitrarily Deep Residual Neural Networks