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.

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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

An Efficient Learning Procedure for Deep

Combining two methods of recognizing hand-printed digits

It is possible to combine multiple non-linear probabilistic models of the same data by multiplying the probability distributions together and then renormalizing. A “productof experts”is a very efficient way to model data that simultaneously satisfies many different constraints. It is difficult to fit a product of experts to data using maximum likelihood because the gradient of the log likelihood is intractable, but there is an efficient way of optimizing a different objective function and this produces good models of high-dimensional data.

/pdf/modeling-high-dimensional-data-by-combining-simple-experts-12ig9tquqq.pdf

Modeling High-Dimensional Data by Combining Simple Experts

Linear Relational Embedding is a method of learning a distributed representation of concepts from data consisting of binary relations between concepts. Concepts are represented as vectors, binary relations as matrices, and the operation of applying a relation to a concept as a matrix-vector multiplication that produces an approximation to the related concept. A representation for concepts and relations is learned by maximizing an appropriate discriminative goodness function using gradient ascent. On a task involving family relationships, learning is fast and leads to good generalization.

Learning Distributed Representations by Mapping Concepts and Relations into a Linear Space

Visual recognition (e.g., object, scene and action recognition) is an active area of research in computer vision due to its increasing number of real-world applications such as video (image) indexing and search, intelligent surveillance, human-machine interaction, robot navigation, etc. Effective modeling of the objects, scenes and actions is critical for visual recognition. Recently, bag of visual words (BoVW) representation, in which the image patches or video cuboids are quantized into visual words (i.e., mid-level features) based on their appearance similarity using clustering, has been widely and successfully explored. The advantages of this representation are: no explicit detection of objects or object parts and their tracking are required; the representation is somewhat tolerant to within-class deformations, and it is efficient for matching. However, the performance of the BoVW is sensitive to the size of the visual vocabulary. Therefore, computationally expensive cross-validation is needed to find the appropriate quantization granularity. This limitation is partially due to the fact that the visual words are not semantically meaningful. This limits the effectiveness and compactness of the representation. To overcome these shortcomings, in this thesis we present principled approach to learn a semantic vocabulary (i.e. high-level features) from a large amount of visual words (mid-level features). In this context, the thesis makes two major contributions. First, we have developed an algorithm to discover a compact yet discriminative semantic vocabulary. This vocabulary is obtained by grouping the visual-words based on their distribution in videos (images) into visual-word clusters. The mutual information (MI) between the clusters and the videos (images) depicts the discriminative power of the semantic vocabulary, while the MI between visual-words and visual-word clusters measures the compactness of the vocabulary. We apply the information bottleneck (IB) algorithm to find the optimal number of visual-word clusters by finding the good tradeoff between compactness and discriminative power. We tested our proposed approach on the state-of-the-art KTH

http://papers.cnl.salk.edu/PDFs/Learning%20Semantic%20Features%201984-3235.pdf

Geoffrey E. Hinton

Papers

An Efficient Learning Procedure for Deep

Combining two methods of recognizing hand-printed digits

Modeling High-Dimensional Data by Combining Simple Experts

Learning Distributed Representations by Mapping Concepts and Relations into a Linear Space

Learning semantic features