Journal Article•
Dropout: a simple way to prevent neural networks from overfitting
TL;DR: It is shown that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.
Abstract: Deep neural nets with a large number of parameters are very powerful machine learning systems. However, overfitting is a serious problem in such networks. Large networks are also slow to use, making it difficult to deal with overfitting by combining the predictions of many different large neural nets at test time. Dropout is a technique for addressing this problem. The key idea is to randomly drop units (along with their connections) from the neural network during training. This prevents units from co-adapting too much. During training, dropout samples from an exponential number of different "thinned" networks. At test time, it is easy to approximate the effect of averaging the predictions of all these thinned networks by simply using a single unthinned network that has smaller weights. This significantly reduces overfitting and gives major improvements over other regularization methods. We show that dropout improves the performance of neural networks on supervised learning tasks in vision, speech recognition, document classification and computational biology, obtaining state-of-the-art results on many benchmark data sets.
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Book•
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TL;DR: Deep learning as mentioned in this paper is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts, and it is used in many applications such as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames.
Abstract: Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.
38,208 citations
Proceedings Article•
06 Jul 2015TL;DR: Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin.
Abstract: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.
30,843 citations
21 Jul 2017
TL;DR: DenseNet as mentioned in this paper proposes to connect each layer to every other layer in a feed-forward fashion, which can alleviate the vanishing gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters.
Abstract: Recent work has shown that convolutional networks can be substantially deeper, more accurate, and efficient to train if they contain shorter connections between layers close to the input and those close to the output. In this paper, we embrace this observation and introduce the Dense Convolutional Network (DenseNet), which connects each layer to every other layer in a feed-forward fashion. Whereas traditional convolutional networks with L layers have L connections—one between each layer and its subsequent layer—our network has L(L+1)/2 direct connections. For each layer, the feature-maps of all preceding layers are used as inputs, and its own feature-maps are used as inputs into all subsequent layers. DenseNets have several compelling advantages: they alleviate the vanishing-gradient problem, strengthen feature propagation, encourage feature reuse, and substantially reduce the number of parameters. We evaluate our proposed architecture on four highly competitive object recognition benchmark tasks (CIFAR-10, CIFAR-100, SVHN, and ImageNet). DenseNets obtain significant improvements over the state-of-the-art on most of them, whilst requiring less memory and computation to achieve high performance. Code and pre-trained models are available at https://github.com/liuzhuang13/DenseNet.
27,821 citations
Posted Content•
TL;DR: Batch Normalization as mentioned in this paper normalizes layer inputs for each training mini-batch to reduce the internal covariate shift in deep neural networks, and achieves state-of-the-art performance on ImageNet.
Abstract: Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters.
17,184 citations
Posted Content•
TL;DR: A scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs which outperforms related methods by a significant margin.
Abstract: We present a scalable approach for semi-supervised learning on graph-structured data that is based on an efficient variant of convolutional neural networks which operate directly on graphs. We motivate the choice of our convolutional architecture via a localized first-order approximation of spectral graph convolutions. Our model scales linearly in the number of graph edges and learns hidden layer representations that encode both local graph structure and features of nodes. In a number of experiments on citation networks and on a knowledge graph dataset we demonstrate that our approach outperforms related methods by a significant margin.
15,696 citations
Cites background from "Dropout: a simple way to prevent ne..."
...This assumption, however, might restrict modeling capacity, as graph edges need not necessarily encode node similarity, but could contain additional information....
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References
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01 Jan 2010
TL;DR: This work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations.
Abstract: We explore an original strategy for building deep networks, based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs. The resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders. It is however shown on a benchmark of classification problems to yield significantly lower classification error, thus bridging the performance gap with deep belief networks (DBN), and in several cases surpassing it. Higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent SVM classifiers. Qualitative experiments show that, contrary to ordinary autoencoders, denoising autoencoders are able to learn Gabor-like edge detectors from natural image patches and larger stroke detectors from digit images. This work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations.
5,303 citations
"Dropout: a simple way to prevent ne..." refers methods in this paper
...2 Unsupervised Pretraining Neural networks can be pretrained using stacks of RBMs (Hinton and Salakhutdinov, 2006), autoencoders (Vincent et al., 2010) or Deep Boltzmann Machines (Salakhutdinov and Hinton, 2009)....
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...The idea of adding noise to the states of units has previously been used in the context of Denoising Autoencoders (DAEs) by Vincent et al. (2008, 2010) where noise is added to the input units of an autoencoder and the network is trained to reconstruct the noise-free input....
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...Neural networks can be pretrained using stacks of RBMs (Hinton and Salakhutdinov, 2006), autoencoders (Vincent et al., 2010) or Deep Boltzmann Machines (Salakhutdinov and Hinton, 2009)....
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Journal Article•
TL;DR: Denoising autoencoders as mentioned in this paper are trained locally to denoise corrupted versions of their inputs, which is a straightforward variation on the stacking of ordinary autoencoder.
Abstract: We explore an original strategy for building deep networks, based on stacking layers of denoising autoencoders which are trained locally to denoise corrupted versions of their inputs. The resulting algorithm is a straightforward variation on the stacking of ordinary autoencoders. It is however shown on a benchmark of classification problems to yield significantly lower classification error, thus bridging the performance gap with deep belief networks (DBN), and in several cases surpassing it. Higher level representations learnt in this purely unsupervised fashion also help boost the performance of subsequent SVM classifiers. Qualitative experiments show that, contrary to ordinary autoencoders, denoising autoencoders are able to learn Gabor-like edge detectors from natural image patches and larger stroke detectors from digit images. This work clearly establishes the value of using a denoising criterion as a tractable unsupervised objective to guide the learning of useful higher level representations.
4,814 citations
Book•
01 Jan 1995
TL;DR: Bayesian Learning for Neural Networks shows that Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional neural network learning methods.
Abstract: From the Publisher:
Artificial "neural networks" are now widely used as flexible models for regression classification applications, but questions remain regarding what these models mean, and how they can safely be used when training data is limited. Bayesian Learning for Neural Networks shows that Bayesian methods allow complex neural network models to be used without fear of the "overfitting" that can occur with traditional neural network learning methods. Insight into the nature of these complex Bayesian models is provided by a theoretical investigation of the priors over functions that underlie them. Use of these models in practice is made possible using Markov chain Monte Carlo techniques. Both the theoretical and computational aspects of this work are of wider statistical interest, as they contribute to a better understanding of how Bayesian methods can be applied to complex problems. Presupposing only the basic knowledge of probability and statistics, this book should be of interest to many researchers in statistics, engineering, and artificial intelligence. Software for Unix systems that implements the methods described is freely available over the Internet.
3,846 citations
"Dropout: a simple way to prevent ne..." refers background in this paper
...On the other hand, Bayesian neural networks (Neal, 1996) are the proper way of doing model averaging over the space of neural network structures and parameters....
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03 Aug 2003
TL;DR: A set of concrete bestpractices that document analysis researchers can use to get good results with neural networks, including a simple "do-it-yourself" implementation of convolution with a flexible architecture suitable for many visual document problems.
Abstract: Neural networks are a powerful technology forclassification of visual inputs arising from documents.However, there is a confusing plethora of different neuralnetwork methods that are used in the literature and inindustry. This paper describes a set of concrete bestpractices that document analysis researchers can use toget good results with neural networks. The mostimportant practice is getting a training set as large aspossible: we expand the training set by adding a newform of distorted data. The next most important practiceis that convolutional neural networks are better suited forvisual document tasks than fully connected networks. Wepropose that a simple "do-it-yourself" implementation ofconvolution with a flexible architecture is suitable formany visual document problems. This simpleconvolutional neural network does not require complexmethods, such as momentum, weight decay, structure-dependentlearning rates, averaging layers, tangent prop,or even finely-tuning the architecture. The end result is avery simple yet general architecture which can yieldstate-of-the-art performance for document analysis. Weillustrate our claims on the MNIST set of English digitimages.
2,783 citations
"Dropout: a simple way to prevent ne..." refers background or methods in this paper
...Method Unit Type Architecture Error % Standard Neural Net (Simard et al., 2003) Logistic 2 layers, 800 units 1....
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...The best performing neural networks for the permutation invariant setting that do not use dropout or unsupervised pretraining achieve an error of about 1.60% (Simard et al., 2003)....
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01 Sep 2009
TL;DR: It is shown that using non-linearities that include rectification and local contrast normalization is the single most important ingredient for good accuracy on object recognition benchmarks and that two stages of feature extraction yield better accuracy than one.
Abstract: In many recent object recognition systems, feature extraction stages are generally composed of a filter bank, a non-linear transformation, and some sort of feature pooling layer Most systems use only one stage of feature extraction in which the filters are hard-wired, or two stages where the filters in one or both stages are learned in supervised or unsupervised mode This paper addresses three questions: 1 How does the non-linearities that follow the filter banks influence the recognition accuracy? 2 does learning the filter banks in an unsupervised or supervised manner improve the performance over random filters or hardwired filters? 3 Is there any advantage to using an architecture with two stages of feature extraction, rather than one? We show that using non-linearities that include rectification and local contrast normalization is the single most important ingredient for good accuracy on object recognition benchmarks We show that two stages of feature extraction yield better accuracy than one Most surprisingly, we show that a two-stage system with random filters can yield almost 63% recognition rate on Caltech-101, provided that the proper non-linearities and pooling layers are used Finally, we show that with supervised refinement, the system achieves state-of-the-art performance on NORB dataset (56%) and unsupervised pre-training followed by supervised refinement produces good accuracy on Caltech-101 (≫ 65%), and the lowest known error rate on the undistorted, unprocessed MNIST dataset (053%)
2,317 citations
"Dropout: a simple way to prevent ne..." refers background in this paper
...Replacing logistic units with rectified linear units (ReLUs) (Jarrett et al., 2009) further reduces the error to 1....
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...Replacing logistic units with rectified linear units (ReLUs) (Jarrett et al., 2009) further reduces the error to 1.25%....
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