Learning representations by back-propagating errors
TL;DR: Back-propagation repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector, which helps to represent important features of the task domain.
Abstract: We describe a new learning procedure, back-propagation, for networks of neurone-like units. The procedure repeatedly adjusts the weights of the connections in the network so as to minimize a measure of the difference between the actual output vector of the net and the desired output vector. As a result of the weight adjustments, internal ‘hidden’ units which are not part of the input or output come to represent important features of the task domain, and the regularities in the task are captured by the interactions of these units. The ability to create useful new features distinguishes back-propagation from earlier, simpler methods such as the perceptron-convergence procedure1.
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Proceedings Article•
31 Mar 2010TL;DR: The objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future.
Abstract: Whereas before 2006 it appears that deep multilayer neural networks were not successfully trained, since then several algorithms have been shown to successfully train them, with experimental results showing the superiority of deeper vs less deep architectures. All these experimental results were obtained with new initialization or training mechanisms. Our objective here is to understand better why standard gradient descent from random initialization is doing so poorly with deep neural networks, to better understand these recent relative successes and help design better algorithms in the future. We first observe the influence of the non-linear activations functions. We find that the logistic sigmoid activation is unsuited for deep networks with random initialization because of its mean value, which can drive especially the top hidden layer into saturation. Surprisingly, we find that saturated units can move out of saturation by themselves, albeit slowly, and explaining the plateaus sometimes seen when training neural networks. We find that a new non-linearity that saturates less can often be beneficial. Finally, we study how activations and gradients vary across layers and during training, with the idea that training may be more difficult when the singular values of the Jacobian associated with each layer are far from 1. Based on these considerations, we propose a new initialization scheme that brings substantially faster convergence. 1 Deep Neural Networks Deep learning methods aim at learning feature hierarchies with features from higher levels of the hierarchy formed by the composition of lower level features. They include Appearing in Proceedings of the 13 International Conference on Artificial Intelligence and Statistics (AISTATS) 2010, Chia Laguna Resort, Sardinia, Italy. Volume 9 of JMLR: WC Weston et al., 2008). Much attention has recently been devoted to them (see (Bengio, 2009) for a review), because of their theoretical appeal, inspiration from biology and human cognition, and because of empirical success in vision (Ranzato et al., 2007; Larochelle et al., 2007; Vincent et al., 2008) and natural language processing (NLP) (Collobert & Weston, 2008; Mnih & Hinton, 2009). Theoretical results reviewed and discussed by Bengio (2009), suggest that in order to learn the kind of complicated functions that can represent high-level abstractions (e.g. in vision, language, and other AI-level tasks), one may need deep architectures. Most of the recent experimental results with deep architecture are obtained with models that can be turned into deep supervised neural networks, but with initialization or training schemes different from the classical feedforward neural networks (Rumelhart et al., 1986). Why are these new algorithms working so much better than the standard random initialization and gradient-based optimization of a supervised training criterion? Part of the answer may be found in recent analyses of the effect of unsupervised pretraining (Erhan et al., 2009), showing that it acts as a regularizer that initializes the parameters in a “better” basin of attraction of the optimization procedure, corresponding to an apparent local minimum associated with better generalization. But earlier work (Bengio et al., 2007) had shown that even a purely supervised but greedy layer-wise procedure would give better results. So here instead of focusing on what unsupervised pre-training or semi-supervised criteria bring to deep architectures, we focus on analyzing what may be going wrong with good old (but deep) multilayer neural networks. Our analysis is driven by investigative experiments to monitor activations (watching for saturation of hidden units) and gradients, across layers and across training iterations. We also evaluate the effects on these of choices of activation function (with the idea that it might affect saturation) and initialization procedure (since unsupervised pretraining is a particular form of initialization and it has a drastic impact).
9,500 citations
Cites background or methods from "Learning representations by back-pr..."
...1 Effect of the Cost Function We have found that the logistic regression or conditional log-likelihood cost function ( log P (y|x) coupled with softmax outputs) worked much better (for classification problems) than the quadratic cost which was traditionally used to train feedforward neural networks (Rumelhart et al., 1986)....
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...Most of the recent experimental results with deep architecture are obtained with models that can be turned into deep supervised neural networks, but with initialization or training schemes different from the classical feedforward neural networks (Rumelhart et al., 1986)....
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TL;DR: This article provides an overview of progress and represents the shared views of four research groups that have had recent successes in using DNNs for acoustic modeling in speech recognition.
Abstract: Most current speech recognition systems use hidden Markov models (HMMs) to deal with the temporal variability of speech and Gaussian mixture models (GMMs) to determine how well each state of each HMM fits a frame or a short window of frames of coefficients that represents the acoustic input. An alternative way to evaluate the fit is to use a feed-forward neural network that takes several frames of coefficients as input and produces posterior probabilities over HMM states as output. Deep neural networks (DNNs) that have many hidden layers and are trained using new methods have been shown to outperform GMMs on a variety of speech recognition benchmarks, sometimes by a large margin. This article provides an overview of this progress and represents the shared views of four research groups that have had recent successes in using DNNs for acoustic modeling in speech recognition.
9,091 citations
Cites background from "Learning representations by back-pr..."
...DNNs can be discriminatively trained (DT) by backpropagating derivatives of a cost function that measures the discrepancy between the target outputs and the actual outputs produced for each training case [14]....
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07 Jun 2015
TL;DR: A system that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure offace similarity, and achieves state-of-the-art face recognition performance using only 128-bytes perface.
Abstract: Despite significant recent advances in the field of face recognition [10, 14, 15, 17], implementing face verification and recognition efficiently at scale presents serious challenges to current approaches. In this paper we present a system, called FaceNet, that directly learns a mapping from face images to a compact Euclidean space where distances directly correspond to a measure of face similarity. Once this space has been produced, tasks such as face recognition, verification and clustering can be easily implemented using standard techniques with FaceNet embeddings as feature vectors.
8,289 citations
Cites methods from "Learning representations by back-pr..."
...In all our experiments we train the CNN using Stochastic Gradient Descent (SGD) with standard backprop [8, 11] and AdaGrad [5]....
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...Both are deep convolutional networks [8, 11]....
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Book•
06 Oct 2003
TL;DR: A fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
Abstract: Fun and exciting textbook on the mathematics underpinning the most dynamic areas of modern science and engineering.
8,091 citations
Cites methods from "Learning representations by back-pr..."
...This gradient can be efficiently computed using the backpropagation algorithm (Rumelhart et al., 1986), which uses the chain rule to find the derivatives....
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18 Jun 2018
TL;DR: In this article, the non-local operation computes the response at a position as a weighted sum of the features at all positions, which can be used to capture long-range dependencies.
Abstract: Both convolutional and recurrent operations are building blocks that process one local neighborhood at a time. In this paper, we present non-local operations as a generic family of building blocks for capturing long-range dependencies. Inspired by the classical non-local means method [4] in computer vision, our non-local operation computes the response at a position as a weighted sum of the features at all positions. This building block can be plugged into many computer vision architectures. On the task of video classification, even without any bells and whistles, our nonlocal models can compete or outperform current competition winners on both Kinetics and Charades datasets. In static image recognition, our non-local models improve object detection/segmentation and pose estimation on the COCO suite of tasks. Code will be made available.
8,059 citations
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17 Jul 1986
15,313 citations