Deeper neural networks are more difficult to train. We present a residual learning framework to ease the training of networks that are substantially deeper than those used previously. We explicitly reformulate the layers as learning residual functions with reference to the layer inputs, instead of learning unreferenced functions. We provide comprehensive empirical evidence showing that these residual networks are easier to optimize, and can gain accuracy from considerably increased depth. On the ImageNet dataset we evaluate residual nets with a depth of up to 152 layers—8× deeper than VGG nets [40] but still having lower complexity. An ensemble of these residual nets achieves 3.57% error on the ImageNet test set. This result won the 1st place on the ILSVRC 2015 classification task. We also present analysis on CIFAR-10 with 100 and 1000 layers. The depth of representations is of central importance for many visual recognition tasks. Solely due to our extremely deep representations, we obtain a 28% relative improvement on the COCO object detection dataset. Deep residual nets are foundations of our submissions to ILSVRC & COCO 2015 competitions1, where we also won the 1st places on the tasks of ImageNet detection, ImageNet localization, COCO detection, and COCO segmentation.

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Deep Residual Learning for Image Recognition

We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has little memory requirements, is invariant to diagonal rescaling of the gradients, and is well suited for problems that are large in terms of data and/or parameters. The method is also appropriate for non-stationary objectives and problems with very noisy and/or sparse gradients. The hyper-parameters have intuitive interpretations and typically require little tuning. Some connections to related algorithms, on which Adam was inspired, are discussed. We also analyze the theoretical convergence properties of the algorithm and provide a regret bound on the convergence rate that is comparable to the best known results under the online convex optimization framework. Empirical results demonstrate that Adam works well in practice and compares favorably to other stochastic optimization methods. Finally, we discuss AdaMax, a variant of Adam based on the infinity norm.

Adam: A Method for Stochastic Optimization

We trained a large, deep convolutional neural network to classify the 1.2 million high-resolution images in the ImageNet LSVRC-2010 contest into the 1000 different classes. On the test data, we achieved top-1 and top-5 error rates of 37.5% and 17.0% which is considerably better than the previous state-of-the-art. The neural network, which has 60 million parameters and 650,000 neurons, consists of five convolutional layers, some of which are followed by max-pooling layers, and three fully-connected layers with a final 1000-way softmax. To make training faster, we used non-saturating neurons and a very efficient GPU implementation of the convolution operation. To reduce overriding in the fully-connected layers we employed a recently-developed regularization method called "dropout" that proved to be very effective. We also entered a variant of this model in the ILSVRC-2012 competition and achieved a winning top-5 test error rate of 15.3%, compared to 26.2% achieved by the second-best entry.

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ImageNet Classification with Deep Convolutional Neural Networks

Learning to store information over extended time intervals by recurrent backpropagation takes a very long time, mostly because of insufficient, decaying error backflow. We briefly review Hochreiter's (1991) analysis of this problem, then address it by introducing a novel, efficient, gradient based method called long short-term memory (LSTM). Truncating the gradient where this does not do harm, LSTM can learn to bridge minimal time lags in excess of 1000 discrete-time steps by enforcing constant error flow through constant error carousels within special units. Multiplicative gate units learn to open and close access to the constant error flow. LSTM is local in space and time; its computational complexity per time step and weight is O. 1. Our experiments with artificial data involve local, distributed, real-valued, and noisy pattern representations. In comparisons with real-time recurrent learning, back propagation through time, recurrent cascade correlation, Elman nets, and neural sequence chunking, LSTM leads to many more successful runs, and learns much faster. LSTM also solves complex, artificial long-time-lag tasks that have never been solved by previous recurrent network algorithms.

Long short-term memory

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.

Very Deep Convolutional Networks for Large-Scale Image Recognition

A TYPICAL MACHINE learning program uses weighted combinations of features to discriminate between classes or to predict real-valued outcomes. The art of machine learning is in constructing the features, and a radically new method of creating features constitutes a major advance. In the 1980s, the new method was backpropagation, which uses the chain rule to backpropagate error derivatives through a multilayer, feed-forward, neural network and adjusts the weights between layers by following the gradient of the backpropagated error. This worked well for recognizing simple shapes, such as handwritten digits, especially in convolutional neural networks that use local feature detectors replicated across the image. 5 For many tasks, however, it proved extremely difficult to optimize deep neural nets with many layers of non-linear features, and a huge number of labeled training cases was required for large neural networks to generalize well to test data. In the 1990s, Support Vector Machines (SVMs) 8 introduced a very different way of creating features: the user defines a kernel function that computes the similarity between two input vectors, then a judiciously chosen subset of the training examples is used to create \" landmark \" features that measure how similar a test case is to each training case. SVMs have a clever way of choosing which training cases to use as landmarks and deciding how to weight them. They work remarkably well on many machine learning tasks even though the selected features are non-adaptive. The success of SVMs dampened the earlier enthusiasm for neural networks. More recently, however, it has been shown that multiple layers of feature detectors can be learned greedily, one layer at a time, by using unsupervised learning that does not require labeled data. The features in each layer are designed to model the statistical structure of the patterns of feature activations in the previous layer. After learning several layers of features this way without paying any attention to the final goal, many of the high-level features will be irrelevant for any particular task, but others will be highly relevant because high-order correlations are the signature of the data's true underlying causes and the labels are more directly related to these causes than to the raw inputs. A subsequent stage of fine-tuning using backpropagation then yields neural networks that work much better than those trained by backpropagation alone and better than SVMs for important tasks such as object or speech recognition. The neural …

A better way to learn features: technical perspective

Hill climbing is used to maximize an information theoretic measure of the difference betwen the actual behavior of a unit and the behavior that would be predicted by a statistician who knew the first order statistics of the inputs but believed them to be independent. This causes the unit to detect higher order correlations among its inputs. Initial simulations are presented, and seem encouraging. We describe an extension of the basic idea which makes it resemble competitive learning and which causes members of a population of these units to differentiate, each extracting different structure from the input.

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G‐maximization: an unsupervised learning procedure for discovering regularities

Animation through the numerical simulation of physicsbased graphics models offers unsurpassed realism, but it can be computationally demanding. Likewise, the search for controllers that enable physics-based models to produce desired animations usually entails formidable computational cost. This paper demonstrates the possibility of replacing the numerical simulation and control of dynamic models with a dramatically more efficient alternative. In particular, we propose the NeuroAnimator, a novel approach to creating physically realistic animation that exploits neural networks. NeuroAnimators are automatically trained off-line to emulate physical dynamics through the observation of physicsbased models in action. Depending on the model, its neural network emulator can yield physically realistic animation one or two orders of magnitude faster than conventional numerical simulation. Furthermore, by exploiting the network structure of the NeuroAnimator, we introduce a fast algorithm for learning controllers that enables either physics-based models or their neural network emulators to synthesize motions satisfying prescribed animation goals. We demonstrate NeuroAnimators for a variety of physics-based models. CR Categories: I.3.7 [Computer Graphics]: Three-Dimensional Graphics and Realism—Animation; I.6.8 [Simulation and Modeling]: Types of Simulation—Animation

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Fast Neural Network Emulation and Control of Physics-Based Models

There has been an ongoing cycle where stronger defenses against adversarial attacks are subsequently broken by a more advanced defense-aware attack. We present a new approach towards ending this cycle where we "deflect'' adversarial attacks by causing the attacker to produce an input that semantically resembles the attack's target class. To this end, we first propose a stronger defense based on Capsule Networks that combines three detection mechanisms to achieve state-of-the-art detection performance on both standard and defense-aware attacks. We then show that undetected attacks against our defense often perceptually resemble the adversarial target class by performing a human study where participants are asked to label images produced by the attack. These attack images can no longer be called "adversarial'' because our network classifies them the same way as humans do.

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Deflecting Adversarial Attacks

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Geoffrey E. Hinton

Papers

A better way to learn features: technical perspective

G‐maximization: an unsupervised learning procedure for discovering regularities

Fast Neural Network Emulation and Control of Physics-Based Models

Deflecting Adversarial Attacks

A Practical Guide to Training