A fast learning algorithm for deep belief nets
TL;DR: A fast, greedy algorithm is derived that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory.
Abstract: We show how to use "complementary priors" to eliminate the explaining-away effects that make inference difficult in densely connected belief nets that have many hidden layers. Using complementary priors, we derive a fast, greedy algorithm that can learn deep, directed belief networks one layer at a time, provided the top two layers form an undirected associative memory. The fast, greedy algorithm is used to initialize a slower learning procedure that fine-tunes the weights using a contrastive version of the wake-sleep algorithm. After fine-tuning, a network with three hidden layers forms a very good generative model of the joint distribution of handwritten digit images and their labels. This generative model gives better digit classification than the best discriminative learning algorithms. The low-dimensional manifolds on which the digits lie are modeled by long ravines in the free-energy landscape of the top-level associative memory, and it is easy to explore these ravines by using the directed connections to display what the associative memory has in mind.
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TL;DR: In this article, an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data is described.
Abstract: High-dimensional data can be converted to low-dimensional codes by training a multilayer neural network with a small central layer to reconstruct high-dimensional input vectors. Gradient descent can be used for fine-tuning the weights in such "autoencoder" networks, but this works well only if the initial weights are close to a good solution. We describe an effective way of initializing the weights that allows deep autoencoder networks to learn low-dimensional codes that work much better than principal components analysis as a tool to reduce the dimensionality of data.
16,717 citations
Proceedings Article•
21 Jun 2010TL;DR: Restricted Boltzmann machines were developed using binary stochastic hidden units that learn features that are better for object recognition on the NORB dataset and face verification on the Labeled Faces in the Wild dataset.
Abstract: Restricted Boltzmann machines were developed using binary stochastic hidden units. These can be generalized by replacing each binary unit by an infinite number of copies that all have the same weights but have progressively more negative biases. The learning and inference rules for these "Stepped Sigmoid Units" are unchanged. They can be approximated efficiently by noisy, rectified linear units. Compared with binary units, these units learn features that are better for object recognition on the NORB dataset and face verification on the Labeled Faces in the Wild dataset. Unlike binary units, rectified linear units preserve information about relative intensities as information travels through multiple layers of feature detectors.
14,799 citations
Cites background or methods from "A fast learning algorithm for deep ..."
...Restricted Boltzmann machines (RBMs) have been used as generative models of many different types of data including labeled or unlabeled images (Hinton et al., 2006), sequences of mel-cepstral coefficients that represent speech (Mohamed & Hinton, 2010), bags of words that represent documents (Salakhutdinov & Hinton, 2009), and user ratings of movies (Salakhutdinov et al....
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...Restricted Boltzmann machines (RBMs) have been used as generative models of many different types of data including labeled or unlabeled images (Hinton et al., 2006), sequences of mel-cepstral coefficients that represent speech (Mohamed & Hinton, 2010), bags of words that represent documents…...
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...Pretraining is done for 300 epochs (in both layers), using mini-batches of 100 training examples with a learning rate of 10 applied to the average per-case CD update, along with momentum (Hinton et al., 2006)....
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...Their most important use is as learning modules that are composed to form deep belief nets (Hinton et al., 2006)....
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...Pretraining is done for 300 epochs (in both layers), using mini-batches of 100 training examples with a learning rate of 10−3 applied to the average per-case CD update, along with momentum (Hinton et al., 2006)....
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TL;DR: This historical survey compactly summarizes relevant work, much of it from the previous millennium, review deep supervised learning, unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.
14,635 citations
06 Sep 2014
TL;DR: A novel visualization technique is introduced that gives insight into the function of intermediate feature layers and the operation of the classifier in large Convolutional Network models, used in a diagnostic role to find model architectures that outperform Krizhevsky et al on the ImageNet classification benchmark.
Abstract: Large Convolutional Network models have recently demonstrated impressive classification performance on the ImageNet benchmark Krizhevsky et al. [18]. However there is no clear understanding of why they perform so well, or how they might be improved. In this paper we explore both issues. We introduce a novel visualization technique that gives insight into the function of intermediate feature layers and the operation of the classifier. Used in a diagnostic role, these visualizations allow us to find model architectures that outperform Krizhevsky et al on the ImageNet classification benchmark. We also perform an ablation study to discover the performance contribution from different model layers. We show our ImageNet model generalizes well to other datasets: when the softmax classifier is retrained, it convincingly beats the current state-of-the-art results on Caltech-101 and Caltech-256 datasets.
12,783 citations
Cites background or methods from "A fast learning algorithm for deep ..."
...As such, this is a form of supervised pre-training, which contrasts with the unsupervised pre-training methods popularized by (Hinton et al., 2006) and others (Bengio et al....
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...As such, this is a form of supervised pre-training, which contrasts with the unsupervised pre-training methods popularized by (Hinton et al., 2006) and others (Bengio et al., 2007; Vincent et al., 2008)....
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TL;DR: Recent work in the area of unsupervised feature learning and deep learning is reviewed, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks.
Abstract: The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, autoencoders, manifold learning, and deep networks. This motivates longer term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation, and manifold learning.
11,201 citations
Cites background or methods from "A fast learning algorithm for deep ..."
...Object Recognition The beginnings of deep learning in 2006 have focused on the MNIST digit image classification problem (Hinton et al., 2006; Bengio et al., 2007), breaking the supremacy of SVMs (1.4% error) on this dataset3....
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...The first proposal was to stack pre-trained RBMs into a Deep Belief Network (Hinton et al., 2006) or DBN, where the top layer is interpreted as an RBM and the lower layers as a directed sigmoid belief network....
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...One option is the wake-sleep algorithm (Hinton et al., 2006) but more work should be done to assess the efficiency of this procedure in terms of improving the generative model....
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...Contrastive Divergence (Hinton, 1999; Hinton et al., 2006), Stochastic Maximum Likelihood (Younes, 1999; Tieleman, 2008) and fast-weights persistent contrastive divergence or FPCD (Tieleman and Hinton, 2009) are all ways to avoid or reduce the need for burn-in....
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...In 2006, a breakthrough in feature learning and deep learning was initiated by Geoff Hinton and quickly followed up in the same year (Hinton et al., 2006; Bengio et al., 2007; Ranzato et al., 2007), and soon after by Lee et al. (2008) and many more later....
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References
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01 Jan 1998
TL;DR: In this article, a graph transformer network (GTN) is proposed for handwritten character recognition, which can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters.
Abstract: Multilayer neural networks trained with the back-propagation algorithm constitute the best example of a successful gradient based learning technique. Given an appropriate network architecture, gradient-based learning algorithms can be used to synthesize a complex decision surface that can classify high-dimensional patterns, such as handwritten characters, with minimal preprocessing. This paper reviews various methods applied to handwritten character recognition and compares them on a standard handwritten digit recognition task. Convolutional neural networks, which are specifically designed to deal with the variability of 2D shapes, are shown to outperform all other techniques. Real-life document recognition systems are composed of multiple modules including field extraction, segmentation recognition, and language modeling. A new learning paradigm, called graph transformer networks (GTN), allows such multimodule systems to be trained globally using gradient-based methods so as to minimize an overall performance measure. Two systems for online handwriting recognition are described. Experiments demonstrate the advantage of global training, and the flexibility of graph transformer networks. A graph transformer network for reading a bank cheque is also described. It uses convolutional neural network character recognizers combined with global training techniques to provide record accuracy on business and personal cheques. It is deployed commercially and reads several million cheques per day.
42,067 citations
Book•
01 Jan 1988TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Abstract: From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
15,671 citations
TL;DR: This paper presents work on computing shape models that are computationally fast and invariant basic transformations like translation, scaling and rotation, and proposes shape detection using a feature called shape context, which is descriptive of the shape of the object.
Abstract: We present a novel approach to measuring similarity between shapes and exploit it for object recognition. In our framework, the measurement of similarity is preceded by: (1) solving for correspondences between points on the two shapes; (2) using the correspondences to estimate an aligning transform. In order to solve the correspondence problem, we attach a descriptor, the shape context, to each point. The shape context at a reference point captures the distribution of the remaining points relative to it, thus offering a globally discriminative characterization. Corresponding points on two similar shapes will have similar shape contexts, enabling us to solve for correspondences as an optimal assignment problem. Given the point correspondences, we estimate the transformation that best aligns the two shapes; regularized thin-plate splines provide a flexible class of transformation maps for this purpose. The dissimilarity between the two shapes is computed as a sum of matching errors between corresponding points, together with a term measuring the magnitude of the aligning transform. We treat recognition in a nearest-neighbor classification framework as the problem of finding the stored prototype shape that is maximally similar to that in the image. Results are presented for silhouettes, trademarks, handwritten digits, and the COIL data set.
6,693 citations
TL;DR: A product of experts (PoE) is an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary because it is hard even to approximate the derivatives of the renormalization term in the combination rule.
Abstract: It is possible to combine multiple latent-variable models of the same data by multiplying their probability distributions together and then renormalizing. This way of combining individual "expert" models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert, because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data. A product of experts (PoE) is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary. Training a PoE by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule. Fortunately, a PoE can be trained using a different objective function called "contrastive divergence" whose derivatives with regard to the parameters can be approximated accurately and efficiently. Examples are presented of contrastive divergence learning using several types of expert on several types of data.
5,150 citations
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
"A fast learning algorithm for deep ..." refers methods in this paper
...Using local elastic deformations in a convolutional neural network, Simard, Steinkraus, and Platt (2003) achieve 0.4%, which is slightly better than the 0.63% achieved by the best hand-coded recognition algorithm (Belongie, Malik, & Puzicha, 2002)....
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...Using local elastic deformations in a convolutional neural network, Simard, Steinkraus, and Platt (2003) achieve 0.4%, which is slightly better than the 0.63% achieved by the best hand-coded recognition algorithm (Belongie, Malik, & Puzicha, 2002)....
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