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 advances in deep reinforcement learning have demonstrated the capability of learning complex control policies from many types of environments. When learning policies for safety-critical applications, it is essential to be sensitive to risks and avoid catastrophic events. Towards this goal, we propose an actor-critic framework that models the uncertainty of the future and simultaneously learns a policy based on that uncertainty model. Specifically, given a distribution of the future return for any state and action, we optimize policies for varying levels of conditional Value-at-Risk. The learned policy can map the same state to different actions depending on the propensity for risk. We demonstrate the effectiveness of our approach in the domain of driving simulations, where we learn maneuvers in two scenarios. Our learned controller can dynamically select actions along a continuous axis, where safe and conservative behaviors are found at one end while riskier behaviors are found at the other. Finally, when testing with very different simulation parameters, our risk-averse policies generalize significantly better compared to other reinforcement learning approaches.

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Worst Cases Policy Gradients

We present a novel approach for learning nonlinear dynamic models, which leads to a new set of tools capable of solving problems that are otherwise difficult. We provide theory showing this new approach is consistent for models with long range structure, and apply the approach to motion capture and high-dimensional video data, yielding results superior to standard alternatives.

Learning Nonlinear Dynamic Models

The focus of past machine learning research for Reading Comprehension tasks has been primarily on the design of novel deep learning architectures. Here we show that seemingly minor choices made on (1) the use of pre-trained word embeddings, and (2) the representation of out-of-vocabulary tokens at test time, can turn out to have a larger impact than architectural choices on the final performance. We systematically explore several options for these choices, and provide recommendations to researchers working in this area.

A Comparative Study of Word Embeddings for Reading Comprehension

The recent proliferation of richly structured probabilistic models raises the question of how to automatically determine an appropriate model for a dataset. We investigate this question for a space of matrix decomposition models which can express a variety of widely used models from unsupervised learning. To enable model selection, we organize these models into a context-free grammar which generates a wide variety of structures through the compositional application of a few simple rules. We use our grammar to generically and efficiently infer latent components and estimate predictive likelihood for nearly 2500 structures using a small toolbox of reusable algorithms. Using a greedy search over our grammar, we automatically choose the decomposition structure from raw data by evaluating only a small fraction of all models. The proposed method typically finds the correct structure for synthetic data and backs off gracefully to simpler models under heavy noise. It learns sensible structures for datasets as diverse as image patches, motion capture, 20 Questions, and U.S. Senate votes, all using exactly the same code.

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Exploiting compositionality to explore a large space of model structures

A training method of training an illumination compensation model includes extracting, from a training image, an albedo image of a face area, a surface normal image of the face area, and an illumination feature, the extracting being based on an illumination compensation model; generating an illumination restoration image based on the albedo image, the surface normal image, and the illumination feature; and training the illumination compensation model based on the training image and the illumination restoration image.

Ruslan Salakhutdinov

Papers

Worst Cases Policy Gradients

Learning Nonlinear Dynamic Models

A Comparative Study of Word Embeddings for Reading Comprehension

Exploiting compositionality to explore a large space of model structures

Method and apparatus for face recognition