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

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

In the unsupervised learning paradigm, a network of neuron-like units is presented with an ensemble of input patterns from a structured environment, such as the visual world, and learns to represent the regularities in that input. The major goal in developing unsupervised learning algorithms is to find objective functions that characterize the quality of the network's representation without explicitly specifying the desired outputs of any of the units. The sort of objective functions considered cause a unit to become tuned to spatially coherent features of visual images (such as texture, depth, shading, and surface orientation), by learning to predict the outputs of other units which have spatially adjacent receptive fields. Simulations show that using an information-theoretic algorithm called IMAX, a network can be trained to represent depth by observing random dot stereograms of surfaces with continuously varying disparities. Once a layer of depth-tuned units has developed, subsequent layers are trained to perform surface interpolation of curved surfaces, by learning to predict the depth of one image region based on depth measurements in surrounding regions. An extension of the basic model allows a population of competing neurons to learn a distributed code for disparity, which naturally gives rise to a representation of discontinuities.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.

Learning spatially coherent properties of the visual world in connectionist networks

We present Pix2Seq, a simple and generic framework for object detection. Unlike existing approaches that explicitly integrate prior knowledge about the task, we cast object detection as a language modeling task conditioned on the observed pixel inputs. Object descriptions (e.g., bounding boxes and class labels) are expressed as sequences of discrete tokens, and we train a neural network to perceive the image and generate the desired sequence. Our approach is based mainly on the intuition that if a neural network knows about where and what the objects are, we just need to teach it how to read them out. Beyond the use of task-specific data augmentations, our approach makes minimal assumptions about the task, yet it achieves competitive results on the challenging COCO dataset, compared to highly specialized and well optimized detection algorithms.1 Pix2Seq ymin=9 xmin=7 ymax=67 xmax=98 train ...... ymin=8 xmin=4 ymax=99 xmax=97 motocycle ...... ymin=1 xmin=57 ymax=99 xmax=72 Person ...... Cmd: detect objects Figure 1: Illustration of Pix2Seq framework for object detection. The neural net perceives an image and generates a sequence of tokens that correspond to bounding boxes and class labels.

P ix 2 seq : a l anguage m odeling f ramework for o bject d etection

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B- splines with Gaussian "ink generators" spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. 1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. 2) During the process of explaining the image, generative models can perform recognition driven segmentation. 3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. 4) Unlike many other recognition schemes, it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques. Index Terms-Deformable model, elastic net, optical character recognition, generative model, probabilistic model, mixture model

http://eprints.aston.ac.uk/664/1/getPDF.pdf

nerative Models for andwritten Digit Recognition

Object discovery in images through categorizing object parts

Methods and systems for learning long-term dependencies in recurrent neural networks. In one aspect, a neural network system is configured to receive a respective input for each of a plurality of time steps and to generate a respective output for each time step, the neural network system comprising one or more recurrent neural network layers, wherein, for each of the time steps, each of the recurrent neural network layers is configured to receive a layer input for the time step; apply an input weight matrix to the layer input to generate a first output; apply a recurrent weight matrix to a hidden state of the recurrent neural network layer for the time step to generate a second output; combine the first and second outputs to generate a combined output; and apply a rectified linear unit activation function to the combined output to generate a layer output for the time step.

Geoffrey E. Hinton

Papers

Learning spatially coherent properties of the visual world in connectionist networks

P ix 2 seq : a l anguage m odeling f ramework for o bject d etection

nerative Models for andwritten Digit Recognition

Object discovery in images through categorizing object parts

Recurrent neural networks with rectified linear units