Residual Networks (ResNets) have demonstrated significant improvement over traditional Convolutional Neural Networks (CNNs) on image classification, increasing in performance as networks grow both deeper and wider. However, memory consumption becomes a bottleneck as one needs to store all the intermediate activations for calculating gradients using backpropagation. In this work, we present the Reversible Residual Network (RevNet), a variant of ResNets where each layer's activations can be reconstructed exactly from the next layer's. Therefore, the activations for most layers need not be stored in memory during backprop. We demonstrate the effectiveness of RevNets on CIFAR and ImageNet, establishing nearly identical performance to equally-sized ResNets, with activation storage requirements independent of depth.

We study randomly initialized residual networks using mean field theory and the theory of difference equations.

Two-stream Convolutional Networks (ConvNets) have shown strong performance for human action recognition in videos. Recently, Residual Networks (ResNets) have arisen as a new technique to train extremely deep architectures. In this paper, we introduce spatiotemporal ResNets as a combination of these two approaches.

In this work we propose a novel interpretation of residual networks showing that they can be seen as a collection of many paths of differing length. Moreover, residual networks seem to enable very deep networks by leveraging only the short paths during training. To support this observation, we rewrite residual networks as an explicit collection of paths. Unlike traditional models, paths through residual networks vary in length. Further, a lesion study reveals that these paths show ensemble-like behavior in the sense that they do not strongly depend on each other. Finally, and most surprising, most paths are shorter than one might expect, and only the short paths are needed during training, as longer paths do not contribute any gradient. For example, most of the gradient in a residual network with 110 layers comes from paths that are only 10-34 layers deep. Our results reveal one of the key characteristics that seem to enable the training of very deep networks: Residual networks avoid the vanishing gradient problem by introducing short paths which can carry gradient throughout the extent of very deep networks.

Some recent results do consider residual-like elements (see discussion of related work below),butgenerallydonotapply tostandard architectures.

We also show that the network width alleviates these issues.

We start by providing motivation for the unconstrained Jacobians problem introduced in the main text. We will continue our proof using contradiction. Figure 1: Fully-connected ResNet34 (Type 1 model) trained on MNIST.Figure 2: Fully-connected ResNet34 (Type 1 model) trained on FashionMNIST. Figure 10: Fully-connected ResNet34 (Type 1 model) trained on MNIST. Figure 24: Fully-connected ResNet34 (Type 1 model) trained on MNIST.

In recommender systems, the collected data used for training is always subject to selection bias, which poses a great challenge for unbiased learning.