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.

/pdf/deep-residual-learning-for-image-recognition-b75jg61qrq.pdf

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.

/pdf/imagenet-classification-with-deep-convolutional-neural-1190x9a6b9.pdf

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

There is large consent that successful training of deep networks requires many thousand annotated training samples. In this paper, we present a network and training strategy that relies on the strong use of data augmentation to use the available annotated samples more efficiently. The architecture consists of a contracting path to capture context and a symmetric expanding path that enables precise localization. We show that such a network can be trained end-to-end from very few images and outperforms the prior best method (a sliding-window convolutional network) on the ISBI challenge for segmentation of neuronal structures in electron microscopic stacks. Using the same network trained on transmitted light microscopy images (phase contrast and DIC) we won the ISBI cell tracking challenge 2015 in these categories by a large margin. Moreover, the network is fast. Segmentation of a 512x512 image takes less than a second on a recent GPU. The full implementation (based on Caffe) and the trained networks are available at http://lmb.informatik.uni-freiburg.de/people/ronneber/u-net .

/pdf/u-net-convolutional-networks-for-biomedical-image-2xoyjzggxv.pdf

U-Net: Convolutional Networks for Biomedical Image Segmentation

A method of creating translingual text representations takes in documents in a first language and in a second language and creates a matrix using the words in the documents to represent which words are present in which language. An algorithm is applied to each matrix such that like documents are placed close to each other and unlike documents are moved far from each other.

Trans-lingual representation of text documents

Methods, systems and apparatus, including computer programs encoded on computer storage media, for training a value neural network that is configured to receive an observation characterizing a state of an environment being interacted with by an agent and to process the observation in accordance with parameters of the value neural network to generate a value score. One of the systems performs operations that include training a supervised learning policy neural network; initializing initial values of parameters of a reinforcement learning policy neural network having a same architecture as the supervised learning policy network to the trained values of the parameters of the supervised learning policy neural network; training the reinforcement learning policy neural network on second training data; and training the value neural network to generate a value score for the state of the environment that represents a predicted long-term reward resulting from the environment being in the state.

Training a policy neural network and a value neural network

Convolutional gated recurrent neural networks

A system can be configured to perform tasks such as converting recorded speech to a sequence of phonemes that represent the speech, converting an input sequence of graphemes into a target sequence of phonemes, translating an input sequence of words in one language into a corresponding sequence of words in another language, or predicting a target sequence of words that follow an input sequence of words in a language (eg, a language model) In a speech recognizer, the RNN system may be used to convert speech to a target sequence of phonemes in real-time so that a transcription of the speech can be generated and presented to a user, even before the user has completed uttering the entire speech input

Generating target sequences from input sequences using partial conditioning

The kernel Perceptron is an appealing online learning algorithm that has a drawback: whenever it makes an error it must increase its support set, which slows training and testing if the number of errors is large. The Forgetron and the Randomized Budget Perceptron algorithms overcome this problem by restricting the number of support vectors the Perceptron is allowed to have. These algorithms have regret bounds whose proofs are dissimilar. In this paper we propose a unified analysis of both of these algorithms by observing that the way in which they remove support vectors can be seen as types of L2-regularization. By casting these algorithms as instances of online convex optimization problems and applying a variant of Zinkevich's theorem for noisy and incorrect gradient, we can bound the regret of these algorithms more easily than before. Our bounds are similar to the existing ones, but the proofs are less technical.

/pdf/a-simpler-unified-analysis-of-budget-perceptrons-1dj0hhhj3o.pdf

Ilya Sutskever

Papers

Trans-lingual representation of text documents

Training a policy neural network and a value neural network

Convolutional gated recurrent neural networks

Generating target sequences from input sequences using partial conditioning

A simpler unified analysis of budget perceptrons