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

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

Recent research shows that for training with $\ell_2$ loss, convolutional neural networks (CNNs) whose width (number of channels in convolutional layers) goes to infinity correspond to regression with respect to the CNN Gaussian Process kernel (CNN-GP) if only the last layer is trained, and correspond to regression with respect to the Convolutional Neural Tangent Kernel (CNTK) if all layers are trained. An exact algorithm to compute CNTK (Arora et al., 2019) yielded the finding that classification accuracy of CNTK on CIFAR-10 is within 6-7% of that of that of the corresponding CNN architecture (best figure being around 78%) which is interesting performance for a fixed kernel. Here we show how to significantly enhance the performance of these kernels using two ideas. (1) Modifying the kernel using a new operation called Local Average Pooling (LAP) which preserves efficient computability of the kernel and inherits the spirit of standard data augmentation using pixel shifts. Earlier papers were unable to incorporate naive data augmentation because of the quadratic training cost of kernel regression. This idea is inspired by Global Average Pooling (GAP), which we show for CNN-GP and CNTK is equivalent to full translation data augmentation. (2) Representing the input image using a pre-processing technique proposed by Coates et al. (2011), which uses a single convolutional layer composed of random image patches. On CIFAR-10, the resulting kernel, CNN-GP with LAP and horizontal flip data augmentation, achieves 89% accuracy, matching the performance of AlexNet (Krizhevsky et al., 2012). Note that this is the best such result we know of for a classifier that is not a trained neural network. Similar improvements are obtained for Fashion-MNIST.

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Enhanced Convolutional Neural Tangent Kernels

The sample inefficiency of standard deep reinforcement learning methods precludes their application to many real-world problems. Methods which leverage human demonstrations require fewer samples but have been researched less. As demonstrated in the computer vision and natural language processing communities, large-scale datasets have the capacity to facilitate research by serving as an experimental and benchmarking platform for new methods. However, existing datasets compatible with reinforcement learning simulators do not have sufficient scale, structure, and quality to enable the further development and evaluation of methods focused on using human examples. Therefore, we introduce a comprehensive, large-scale, simulator-paired dataset of human demonstrations: MineRL. The dataset consists of over 60 million automatically annotated state-action pairs across a variety of related tasks in Minecraft, a dynamic, 3D, open-world environment. We present a novel data collection scheme which allows for the ongoing introduction of new tasks and the gathering of complete state information suitable for a variety of methods. We demonstrate the hierarchality, diversity, and scale of the MineRL dataset. Further, we show the difficulty of the Minecraft domain along with the potential of MineRL in developing techniques to solve key research challenges within it.

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MineRL: A Large-Scale Dataset of Minecraft Demonstrations

Three years ago, we released the Omniglot dataset for one-shot learning, along with five challenge tasks and a computational model that addresses these tasks. The model was not meant to be the final word on Omniglot; we hoped that the community would build on our work and develop new approaches. In the time since, we have been pleased to see wide adoption of the dataset. There has been notable progress on one-shot classification, but researchers have adopted new splits and procedures that make the task easier. There has been less progress on the other four tasks. We conclude that recent approaches are still far from human-like concept learning on Omniglot, a challenge that requires performing many tasks with a single model.

The Omniglot challenge: a 3-year progress report

Many problems in NLP require aggregating information from multiple mentions of the same entity which may be far apart in the text. Existing Recurrent Neural Network (RNN) layers are biased towards short-term dependencies and hence not suited to such tasks. We present a recurrent layer which is instead biased towards coreferent dependencies. The layer uses coreference annotations extracted from an external system to connect entity mentions belonging to the same cluster. Incorporating this layer into a state-of-the-art reading comprehension model improves performance on three datasets – Wikihop, LAMBADA and the bAbi AI tasks – with large gains when training data is scarce.

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Neural Models for Reasoning over Multiple Mentions using Coreference

Deep generative models have achieved impressive success in recent years. Generative Adversarial Networks (GANs) and Variational Autoencoders (VAEs), as emerging families for generative model learning, have largely been considered as two distinct paradigms and received extensive independent studies respectively. This paper aims to establish formal connections between GANs and VAEs through a new formulation of them. We interpret sample generation in GANs as performing posterior inference, and show that GANs and VAEs involve minimizing KL divergences of respective posterior and inference distributions with opposite directions, extending the two learning phases of classic wake-sleep algorithm, respectively. The unified view provides a powerful tool to analyze a diverse set of existing model variants, and enables to transfer techniques across research lines in a principled way. For example, we apply the importance weighting method in VAE literatures for improved GAN learning, and enhance VAEs with an adversarial mechanism that leverages generated samples. Experiments show generality and effectiveness of the transferred techniques.

Ruslan Salakhutdinov

Papers

Enhanced Convolutional Neural Tangent Kernels

MineRL: A Large-Scale Dataset of Minecraft Demonstrations

The Omniglot challenge: a 3-year progress report

Neural Models for Reasoning over Multiple Mentions using Coreference

On Unifying Deep Generative Models