Residual Networks with convolutional layers are widely used in the field of machine learning. Since they effectively extract features from input data by stacking multiple layers, they can achieve high accuracy in many applications. However, the stacking of many layers raises their computation costs. To address this problem, we propose Network Implosion, it erases multiple layers from Residual Networks without degrading accuracy. Our key idea is to introduce a priority term that identifies the importance of a layer; we can select unimportant layers according to the priority and erase them after the training. In addition, we retrain the networks to avoid critical drops in accuracy after layer erasure. A theoretical assessment reveals that our erasure and retraining scheme can erase layers without accuracy drop, and achieve higher accuracy than is possible with training from scratch. Our experiments show that Network Implosion can, for classification on Cifar-10 100 and ImageNet, reduce the number of layers by 24.00 to 42.86 percent without any drop in accuracy.
 Do convolutional networks really need a fixed feed-forward structure? Often, a neural network is already confident after a few layers about the high-level concept shown in the image. However, due to the fixed network structure, all remaining layers still need to be evaluated. What if the network could jump right to a layer that is specialized in fine-grained differences of the image's content? In this work, we propose Adanets, a family of convolutional networks with adaptive computation graphs. Following a high-level structure similar to residual networks (Resnets), the key difference is that for each layer a gating function determines whether to execute the layer or move on to the next one. In experiments on CIFAR-10 and ImageNet we demonstrate that Adanets efficiently allocate computational budget among layers and learn distinct layers specializing in similar categories. Adanet 50 achieves a top 5 error rate of 7.94 on ImageNet using 30 fewer computations than Resnet 34, which only achieves 8.58 . Lastly, we study the effect of adaptive computation graphs on the susceptibility towards adversarial examples. We observe that Adanets show a higher robustness towards adversarial attacks, complementing other defenses such as JPEG compression. 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. Abstract: In this work we investigate the effect of the convolutional network depth on its accuracy in the large-scale image recognition setting. Our main contribution is a thorough evaluation of networks of increasing depth using an architecture with very small (3x3) convolution filters, which shows that a significant improvement on the prior-art configurations can be achieved by pushing the depth to 16-19 weight layers. These findings were the basis of our ImageNet Challenge 2014 submission, where our team secured the first and the second places in the localisation and classification tracks respectively. We also show that our representations generalise well to other datasets, where they achieve state-of-the-art results. We have made our two best-performing ConvNet models publicly available to facilitate further research on the use of deep visual representations in computer vision.