Quelltext der Seite Benutzer:Schartey/Deep learning

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{{Hatnote|For deep versus shallow learning in educational psychology, see [[Student approaches to learning]]}}
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'''Deep learning''' ('''deep structured learning''', '''hierarchical learning''' oder '''deep machine learning''') stellt einen Zweig des maschinellen Lernens dar und basiert auf einer Reihe von Algorithmen, welche hohe Abstraktionen in Daten durch mehrere Prozessschichten mit komplexen Strukturen oder mehreren nicht-linearen Transformationen modellieren. <!--is a branch of [[machine learning]] based on a set of [[algorithm]]s that attempt to model high-level abstractions in data by using multiple processing layers, with complex structures or otherwise, composed of multiple non-[[linear transformation]]s.--><ref name="BOOK2014">{{cite journal |last1=Deng |first1=L. |last2=Yu |first2=D. |year=2014 |title=Deep Learning: Methods and Applications |url=http://research.microsoft.com/pubs/209355/DeepLearning-NowPublishing-Vol7-SIG-039.pdf |journal=Foundations and Trends in Signal Processing |volume=7 |pages=3–4 |doi=10.1561/2000000039}}</ref><ref name="BENGIODEEP">{{cite journal |first=Yoshua |last=Bengio |year=2009 |title=Learning Deep Architectures for AI |url=http://sanghv.com/download/soft/machine%20learning,%20artificial%20intelligence,%20mathematics%20ebooks/ML/learning%20deep%20architectures%20for%20AI%20%282009%29.pdf |journal=Foundations and Trends in Machine Learning |volume=2 |issue=1 |pages=1–127 |doi=10.1561/2200000006}}</ref><ref name="BENGIO2012">{{cite journal |last1=Bengio |first1=Y. |last2=Courville |first2=A. |last3=Vincent |first3=P. |year=2013 |title=Representation Learning: A Review and New Perspectives |journal=IEEE Transactions on Pattern Analysis and Machine Intelligence |volume=35 |issue=8 |pages=1798–1828 |arxiv=1206.5538 |doi=10.1109/tpami.2013.50}}</ref><ref name="SCHIDHUB">{{cite journal |last=Schmidhuber |first=J. |year=2015 |title=Deep Learning in Neural Networks: An Overview |journal=Neural Networks |volume=61 |pages=85–117 |arxiv=1404.7828 |doi=10.1016/j.neunet.2014.09.003}}</ref><ref name="NatureBengio">{{cite journal |last1=Bengio |first1=Yoshua |last2=LeCun |first2= Yann| last3=Hinton | first3= Geoffrey|year=2015 |title=Deep Learning |journal=Nature |volume=521 |pages=436–444 |doi=10.1038/nature14539}}</ref><ref>Deep Machine Learning – A New Frontier in Artificial Intelligence Research – a survey paper by Itamar Arel, Derek C. Rose, and Thomas P. Karnowski. IEEE Computational Intelligence Magazine, 2013</ref>

Deep learning ist Teil einer breitgefächerten Familie von Methoden für maschinelles Lernen basierend auf der lernenden Repräsentation von Daten. Eine Beobachtung (z.B. ein Bild) kann in vielen Arten dargestellt werden, wie einem Vektor von Intensitätswerten pro Pixel, oder in einem abstrakteren Weg als Kanten, Regionen einer bestimmten Form, etc. Manche Repräsentationen eignen sich dabei besser für Lernaufgaben durch Muster als andere (z.B. Gesichtserkennung oder Gesichtsmimik-Erkennung). Aufgrund von Deep learning verspricht man sich den Ersatz von handgemachten Funktionen mit effizienten Algorithmen durch (teilweise) unbeaufsichtiges Lernen von Funktionen und hierachische Funktionsextraktion. <!--Deep learning is part of a broader family of [[machine learning]] methods based on [[learning representation]]s of data. An observation (e.g., an image) can be represented in many ways such as a [[Vector space|vector]] of intensity values per pixel, or in a more abstract way as a set of edges, regions of particular shape, [[Scale-invariant feature transform|etc.]] Some representations are better than others at simplifying the learning task (e.g., face recognition or facial expression recognition--><ref>{{cite thesis |last=Glauner |first=P. |year=2015 |title=Deep Convolutional Neural Networks for Smile Recognition |arxiv=1508.06535 |type=MSc Thesis |publisher=[[Imperial College London]], Department of Computing}}</ref>) from examples. One of the promises of deep learning is replacing handcrafted [[Feature (machine learning)|features]] with efficient algorithms for [[Unsupervised learning|unsupervised]] or [[Semi-supervised learning|semi-supervised]] [[feature learning]] and hierarchical [[feature extraction]].<ref>{{cite book |last1=Song |first1=H.A. |last2=Lee |first2=S. Y. |year=2013 |chapter=Hierarchical Representation Using NMF |title=Neural Information Processing |series=Lectures Notes in Computer Sciences |volume=8226 |issue= |pages=466–473 |publisher=[[Springer Berlin Heidelberg]] |isbn=978-3-642-42053-5 |doi=10.1007/978-3-642-42054-2_58}}</ref>
 
Forschungen in diesem Gebiet versuchen diese Repräsentationen zu verbessern und erstellen Modelle um sie von vielen verschiedenen unbestimmten Daten zu lernen. Manche dieser Darstellungen sind durch Entwicklungen in der Neurowissenschaft inspiriert und basieren etwas auf der Interpretation, Verarbeitung und den Kommunikationsmustern innerhalb des Nervensystems, wie dem Neural-Coding, welches versucht eine Beziehung zwischen verschiedenen Stimuli und assoziierten Reaktionen der Neuronen im Hirn zu definieren. <!--Research in this area attempts to make better representations and create models to learn these representations from large-scale unlabeled data. Some of the representations are inspired by advances in [[neuroscience]] and are loosely based on interpretation of information processing and communication patterns in a [[nervous system]], such as [[neural coding]] which attempts to define a relationship between various stimuli and associated neuronal responses in the [[brain]].--><ref>{{cite journal |last1=Olshausen |first1=B. A. |year=1996 |title=Emergence of simple-cell receptive field properties by learning a sparse code for natural images |journal=Nature |volume=381 |issue=6583 |pages=607–609 |doi=10.1038/381607a0}}</ref>

Verschiedene Architekturen des Deep Learning (Deep neural networks, convolutional deep neural networks, deep belief networks und recurrent neural ) finden bereits Verwendung Anwendung in Gebieten wie Computer Vision, Automatische Spracherkennung, natürliche Sprachverarbeitung, Audioerkennung und Bioinformatik, bei welchen bereits Ergebnisse des derzeit höchsten Technologiestandes erzeugt werden. <!--Various deep learning architectures such as [[#Deep neural networks|deep neural network]]s, [[convolutional neural network|convolutional deep neural networks]], [[deep belief network]]s and [[recurrent neural network]]s have been applied to fields like [[computer vision]], [[automatic speech recognition]], [[natural language processing]], audio recognition and [[bioinformatics]] where they have been shown to produce state-of-the-art results on various tasks.-->

Deep learning wurde als neue Definition für neurale Netzwerke definiert.
<!--''Deep learning'' has been characterized as a [[buzzword]], or a rebranding of [[neural network]]s.--><ref>{{cite video |last=Collobert |first=R. |date=April 2011 |title=Deep Learning for Efficient Discriminative Parsing |url=http://videolectures.net/aistats2011_collobert_deep/ |website=VideoLectures.net |time=7min 45s}}</ref><ref>{{cite web |last=Gomes |first=L. |date=20 October 2014 |title=Machine-Learning Maestro Michael Jordan on the Delusions of Big Data and Other Huge Engineering Efforts |url=http://spectrum.ieee.org/robotics/artificial-intelligence/machinelearning-maestro-michael-jordan-on-the-delusions-of-big-data-and-other-huge-engineering-efforts |work=[[IEEE Spectrum]]}}</ref>

== Introduction ==

=== Definitions ===

There are a number of ways that the field of deep learning has been characterized. Deep learning is a class of [[machine learning]] [[algorithm]]s that<ref name="BOOK2014" />{{rp|pages=199–200}}
* use a cascade of many layers of [[Nonlinear filter|nonlinear processing]] units for [[feature extraction]] and transformation. Each successive layer uses the output from the previous layer as input. The algorithms may be [[Supervised learning|supervised]] or [[Unsupervised learning|unsupervised]] and applications include pattern analysis (unsupervised) and classification (supervised).
* are based on the (unsupervised) learning of multiple levels of features or representations of the data. Higher level features are derived from lower level features to form a hierarchical representation. 
* are part of the broader machine learning field of learning representations of data.
* learn multiple levels of representations that correspond to different levels of abstraction; the levels form a hierarchy of concepts.

These definitions have in common (1) multiple layers of nonlinear processing units and (2) the supervised or unsupervised learning of feature representations in each layer, with the layers forming a hierarchy from low-level to high-level features.<ref name="BOOK2014" />{{rp|page=200}} The composition of a layer of nonlinear processing units used in a deep learning algorithm depends on the problem to be solved. Layers that have been used in deep learning include hidden layers of an [[artificial neural network]] and sets of complicated [[propositional formula]]s.<ref name="BENGIODEEP" /> They may also include latent variables organized layer-wise in deep generative models such as the nodes in Deep Belief Networks and Deep Boltzmann Machines.

Deep learning algorithms transform their inputs through more layers than shallow learning algorithms. At each layer, the signal is transformed by a processing unit, like an artificial neuron, whose parameters are ‘learned’ through training.<ref name="SCHIDHUB" />{{rp|page=6}} A chain of transformations from input to output is a ''credit assignment path'' (CAP). CAPs describe potentially causal connections between input and output and may vary in length. For a feedforward neural network, the depth of the CAPs, and thus the depth of the network, is the number of hidden layers plus one (the output layer is also parameterized). For [[recurrent neural network]]s, in which a signal may propagate through a layer more than once, the CAP is potentially unlimited in length. There is no universally agreed upon threshold of depth dividing shallow learning from deep learning, but most researchers in the field agree that deep learning has multiple nonlinear layers (CAP > 2) and Schmidhuber considers CAP > 10 to be very deep learning.<ref name="SCHIDHUB" />{{rp|page=7}}

=== Fundamental concepts ===

Deep learning algorithms are based on distributed representations. The underlying assumption behind distributed representations is that observed data are generated by the interactions of factors organized in layers. Deep learning adds the assumption that these layers of factors correspond to levels of abstraction or composition. Varying numbers of layers and layer sizes can be used to provide different amounts of abstraction.<ref name="BENGIO2012"/>

Deep learning exploits this idea of hierarchical explanatory factors where higher level, more abstract concepts are learned from the lower level ones. These architectures are often constructed with a [[greedy algorithm|greedy]] layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features are useful for learning.<ref name="BENGIO2012"/>

For [[supervised learning]] tasks, deep learning methods obviate [[feature engineering]], by translating the data into compact intermediate representations akin to [[Principal Component Analysis|principal components]], and derive layered structures which remove redundancy in representation.<ref name="BOOK2014"/>

Many deep learning algorithms are applied to [[unsupervised learning]] tasks. This is an important benefit because unlabeled data are usually more abundant than labeled data. An example of a deep structure that can be trained in an unsupervised manner is a deep belief network.<ref name="BENGIO2012"/>

== Interpretations ==

Deep neural networks are generally interpreted in terms of: [[Universal approximation theorem]]<ref name="ReferenceB">Balázs Csanád Csáji. Approximation with Artificial Neural Networks; Faculty of Sciences; Eötvös Loránd University, Hungary</ref><ref name=cyb>{{cite journal | last1 = Cybenko | year = 1989 | title = Approximations by superpositions of sigmoidal functions | url = http://deeplearning.cs.cmu.edu/pdfs/Cybenko.pdf | format = PDF | journal = [[Mathematics of Control, Signals, and Systems]] | volume = 2 | issue = 4| pages = 303–314 | doi=10.1007/bf02551274}}</ref><ref name=horn>{{cite journal | last1 = Hornik | first1 = Kurt | year = 1991 | title = Approximation Capabilities of Multilayer Feedforward Networks | url = | journal = Neural Networks | volume = 4 | issue = 2| pages = 251–257 | doi=10.1016/0893-6080(91)90009-t}}</ref><ref name="Haykin, Simon 1998">Haykin, Simon (1998). ''Neural Networks: A Comprehensive Foundation'', Volume 2, Prentice Hall. ISBN 0-13-273350-1.</ref><ref name="Hassoun, M. 1995 p. 48">Hassoun, M. (1995) ''Fundamentals of Artificial Neural Networks'' MIT Press, p.&nbsp;48</ref> or [[Bayesian inference|Probabilistic inference]].<ref name="BOOK2014" /><ref name="BENGIODEEP" /><ref name="BENGIO2012" /><ref name="SCHIDHUB" /><ref name = MURPHY>Murphy, K.P. (2012) ''Machine learning: a probabilistic perspective'' MIT Press</ref><ref name="SCHOLARDBNS" />

=== Universal approximation theorem interpretation ===

The [[universal approximation theorem]] concerns the capacity of [[feedforward neural networks]] with a single hidden layer of finite size to approximate [[continuous functions]].<ref name="ReferenceB"/><ref name="cyb"/><ref name="horn"/><ref name="Haykin, Simon 1998"/><ref name="Hassoun, M. 1995 p. 48"/>

In 1989, the first proof was published by [[George Cybenko]] for [[sigmoid function|sigmoid]] activation functions<ref name=cyb /> and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik.<ref name=horn />

=== Probabilistic interpretation ===

The [[probabilistic]] interpretation<ref name="MURPHY" /> derives from the field of [[machine learning]]. It features inference,<ref name="BOOK2014" /><ref name="BENGIODEEP" /><ref name="BENGIO2012" /><ref name="SCHIDHUB" /><ref name="MURPHY" /><ref name="SCHOLARDBNS" /> as well as the [[optimization]] concepts of [[training]] and [[test (assessment)|testing]], related to fitting and [[generalization]] respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a [[cumulative distribution function]].<ref name="MURPHY" />  See [[Deep belief network]]. The probabilistic interpretation led to the introduction of [[dropout (neural networks)|dropout]] as [[Regularization (mathematics)|regularizer]] in neural networks.<ref name="DROPOUT">{{cite arXiv |last1=Hinton |first1=G. E. |last2=Srivastava| first2 =N.|last3=Krizhevsky| first3=A.| last4 =Sutskever| first4=I.| last5=Salakhutdinov| first5=R.R.|eprint=1207.0580 |class=math.LG |title=Improving neural networks by preventing co-adaptation of feature detectors |date=2012}}</ref>

The probabilistic interpretation was introduced and popularized by [[Geoff Hinton]], [[Yoshua Bengio]], [[Yann LeCun]] and [[Juergen Schmidhuber]].

==History==

Deep learning architectures, specifically those built from [[artificial neural networks]] (ANN), date back at least to the [[Neocognitron]] introduced by [[Kunihiko Fukushima]] in 1980.<ref name="FUKU1980">{{cite journal | last1 = Fukushima | first1 = K. | year = 1980 | title = Neocognitron: A self-organizing neural network model for a mechanism of pattern recognition unaffected by shift in position | url = | journal = Biol. Cybern. | volume = 36 | issue = | pages = 193–202 | doi=10.1007/bf00344251}}</ref> The ANNs themselves date back even further. The challenge was how to train networks with multiple layers. In 1989, [[Yann LeCun]] et al. were able to apply the standard [[backpropagation]] algorithm, which had been around since 1974,<ref name="WERBOS1974">P. Werbos., "Beyond Regression: New Tools for Prediction and Analysis in the Behavioral Sciences," ''PhD thesis, Harvard University'', 1974.</ref> to a deep neural network with the purpose of recognizing handwritten [[ZIP code]]s on mail. Despite the success of applying the algorithm, the time to train the network on this dataset was approximately 3 days, making it impractical for general use.<ref name="LECUN1989">LeCun ''et al.'', "Backpropagation Applied to Handwritten Zip Code Recognition," ''Neural Computation'', 1, pp. 541–551, 1989.</ref> In 1995, [[Brendan Frey]] demonstrated that it was possible to train a network containing six fully connected layers and several hundred hidden units using the [[wake-sleep algorithm]], which was co-developed with [[Peter Dayan]] and [[Geoffrey Hinton]].<ref>{{Cite journal|title = The wake-sleep algorithm for unsupervised neural networks |journal = Science|date = 1995-05-26|pages = 1158–1161|volume = 268|issue = 5214|doi = 10.1126/science.7761831|first = Geoffrey E.|last = Hinton|first2 = Peter|last2 = Dayan|first3 = Brendan J.|last3 = Frey|first4 = Radford|last4 = Neal}}</ref> However, training took two days.

Many factors contribute to the slow speed, one being the [[vanishing gradient problem]] analyzed in 1991 by [[Sepp Hochreiter]].<ref name="HOCH1991">S. Hochreiter., "[http://people.idsia.ch/~juergen/SeppHochreiter1991ThesisAdvisorSchmidhuber.pdf Untersuchungen zu dynamischen neuronalen Netzen]," ''Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber'', 1991.</ref><ref name="HOCH2001">S. Hochreiter ''et al.'', "Gradient flow in recurrent nets: the difficulty of learning long-term dependencies," ''In S. C. Kremer and J. F. Kolen, editors, A Field Guide to Dynamical Recurrent Neural Networks. IEEE Press'', 2001.</ref>

While by 1991 such neural networks were used for recognizing isolated 2-D hand-written digits, recognizing 3-D objects was done by matching 2-D images with a handcrafted 3-D object model. Juyang Weng ''et al.'' suggested that a human brain does not use a monolithic 3-D object model, and in 1992 they published Cresceptron,<ref name="Weng1992">J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronIJCNN1992.pdf Cresceptron: a self-organizing neural network which grows adaptively]," ''Proc. International Joint Conference on Neural Networks'', Baltimore, Maryland, vol I, pp. 576-581, June, 1992.</ref><ref name="Weng1993">J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronICCV1993.pdf Learning recognition and segmentation of 3-D objects from 2-D images]," ''Proc. 4th International Conf. Computer Vision'', Berlin, Germany, pp. 121-128, May, 1993.</ref><ref name="Weng1997">J. Weng, N. Ahuja and T. S. Huang, "[http://www.cse.msu.edu/~weng/research/CresceptronIJCV.pdf Learning recognition and segmentation using the Cresceptron]," ''International Journal of Computer Vision'', vol. 25, no. 2, pp. 105-139, Nov. 1997.</ref> a method for performing 3-D object recognition directly from cluttered scenes.  Cresceptron is a cascade of layers similar to [[Neocognitron]]. But while Neocognitron required a human programmer to hand-merge features, Cresceptron ''automatically'' learned an open number of unsupervised features in each layer, where each feature is represented by a convolution kernel.  Cresceptron also segmented each learned object from a cluttered scene through back-analysis through the network.  Max-pooling, now often adopted by deep neural networks (e.g., ImageNet tests), was first used in Cresceptron to reduce the position resolution by a factor of (2x2) to 1 through the cascade for better generalization.  Despite these advantages, simpler models that use task-specific handcrafted features such as [[Gabor filter]] and [[support vector machine]]s (SVMs) were of popular choice in the 1990s and 2000s, because of the computational cost by ANNs then and a great lack of understanding of how the brain autonomously wires its biological networks.

In the long history of speech recognition, both shallow and deep learning (e.g., recurrent nets) of artificial neural networks had been explored for many years.<ref name="Morgan1993">Morgan, Bourlard, Renals, Cohen, Franco (1993) "Hybrid neural network/hidden Markov model systems for continuous speech recognition. ICASSP/IJPRAI"</ref><ref name="Robinson1992">T. Robinson. (1992) A real-time recurrent error propagation network word recognition system, ICASSP.</ref><ref name="Waibel1989">Waibel, Hanazawa, Hinton, Shikano, Lang. (1989) "Phoneme recognition using time-delay neural networks. IEEE Transactions on Acoustics, Speech and Signal Processing."</ref>
But these methods never won over the non-uniform internal-handcrafting Gaussian [[mixture model]]/[[Hidden Markov model]] (GMM-HMM) technology based on generative models of speech trained discriminatively.<ref name="Baker2009">{{cite journal | last1 = Baker | first1 = J. | last2 = Deng | first2 = Li | last3 = Glass | first3 = Jim | last4 = Khudanpur | first4 = S. | last5 = Lee | first5 = C.-H. | last6 = Morgan | first6 = N. | last7 = O'Shaughnessy | first7 = D. | year = 2009 | title = Research Developments and Directions in Speech Recognition and Understanding, Part 1 | url = | journal = IEEE Signal Processing Magazine | volume = 26 | issue = 3| pages = 75–80 | doi=10.1109/msp.2009.932166}}</ref>
A number of key difficulties had been methodologically analyzed, including gradient diminishing and weak temporal correlation structure in the neural predictive models.<ref name="Bengio1991">Y. Bengio (1991). "Artificial Neural Networks and their Application to Speech/Sequence Recognition," Ph.D. thesis, McGill University, Canada.</ref><ref name="Deng1994">{{cite journal | last1 = Deng | first1 = L. | last2 = Hassanein | first2 = K. | last3 = Elmasry | first3 = M. | year = 1994 | title = Analysis of correlation structure for a neural predictive model with applications to speech recognition | url = | journal = Neural Networks | volume = 7 | issue = 2| pages = 331–339 | doi=10.1016/0893-6080(94)90027-2}}</ref>
Additional difficulties were the lack of big training data and weaker computing power in these early days. Thus, most speech recognition researchers who understood such barriers moved away from neural nets to pursue generative modeling, until a recent resurgence of deep learning overcame all these difficulties. Hinton et al. and Deng et al. reviewed part of this recent history about how their collaboration with each other and then with cross-group colleagues re-ignited neural networks research and initiated deep learning research and applications in speech recognition.<ref name=HintonDengYu2012/><ref name="ReferenceICASSP2013">{{cite journal|last1=Deng|first1=L.|last2=Hinton|first2=G.|last3=Kingsbury|first3=B.|title=New types of deep neural network learning for speech recognition and related applications: An overview (ICASSP)| date=2013}}</ref><ref name="HintonKeynoteICASSP2013">Keynote talk: Recent Developments in Deep Neural Networks. ICASSP, 2013 (by Geoff Hinton).</ref><ref name="interspeech2014Keynote">Keynote talk: "Achievements and Challenges of Deep Learning - From Speech Analysis and Recognition To Language and Multimodal Processing," Interspeech, September 2014.</ref>

The term "deep learning" gained traction in the mid-2000s after a publication by [[Geoffrey Hinton]] and Ruslan Salakhutdinov showed how a many-layered [[feedforward neural network]] could be effectively pre-trained one layer at a time, treating each layer in turn as an [[unsupervised learning|unsupervised]] [[restricted Boltzmann machine]], then fine-tuned using [[supervised learning|supervised]] [[backpropagation]].<ref name="HINTON2007">G. E. Hinton., "Learning multiple layers of representation," ''Trends in Cognitive Sciences'', 11, pp. 428–434, 2007.</ref> In 1992, Schmidhuber had already implemented a very similar idea for the more general case of unsupervised deep hierarchies of [[recurrent neural network]]s, and also experimentally shown its benefits for speeding up supervised learning.<ref name="SCHMID1992">J. Schmidhuber., "Learning complex, extended sequences using the principle of history compression," ''Neural Computation'', 4, pp. 234–242, 1992.</ref><ref name="SCHMID1991">J. Schmidhuber., "My First Deep Learning System of 1991 + Deep Learning Timeline 1962–2013."</ref>

Since its resurgence, deep learning has become part of many state-of-the-art systems in various disciplines, particularly computer vision and [[automatic speech recognition]] (ASR). Results on commonly used evaluation sets such as [[TIMIT]] (ASR) and [[MNIST database|MNIST]] ([[image classification]]), as well as a range of large-vocabulary speech recognition tasks are constantly being improved with new applications of deep learning.<ref name=HintonDengYu2012/><ref>http://research.microsoft.com/apps/pubs/default.aspx?id=189004</ref><ref name="MS2013">L. Deng et al. Recent Advances in Deep Learning for Speech Research at Microsoft, ICASSP, 2013.</ref> Recently, it was shown that deep learning architectures in the form of [[convolutional neural network]]s have been nearly best performing;<ref name="CNNspeech2013">L. Deng, O. Abdel-Hamid, and D. Yu, A deep convolutional neural network using heterogeneous pooling for trading acoustic invariance with phonetic confusion, ICASSP, 2013.</ref><ref name="SAIN2013"/> however, these are more widely used in computer vision than in ASR.

The real impact of deep learning in industry began in large-scale speech recognition around 2010. In late 2009, Li Deng invited Geoffrey Hinton to work with him and colleagues at Microsoft Research to apply deep learning to speech recognition. They co-organized the 2009 NIPS Workshop on Deep Learning for Speech Recognition. The workshop was motivated by the limitations of deep generative models of speech, and the possibility that the big-compute, big-data era warranted a serious try of deep neural nets (DNN). It was believed that pre-training DNNs using generative models of deep belief nets (DBN) would overcome the main difficulties of neural nets encountered in the 1990s.<ref name="HintonKeynoteICASSP2013"/> However, early into this research at Microsoft, it was discovered that without pre-training, but using large amounts of training data, and especially DNNs designed with corresponding large, context-dependent output layers, produced error rates dramatically lower than then-state-of-the-art GMM-HMM and also than more advanced generative model-based speech recognition systems. This finding was verified by several other major speech recognition research groups.<ref name="HintonDengYu2012">{{cite journal | last1 = Hinton | first1 = G. | last2 = Deng | first2 = L. | last3 = Yu | first3 = D. | last4 = Dahl | first4 = G. | last5 = Mohamed | first5 = A. | last6 = Jaitly | first6 = N. | last7 = Senior | first7 = A. | last8 = Vanhoucke | first8 = V. | last9 = Nguyen | first9 = P. | last10 = Sainath | first10 = T. | last11 = Kingsbury | first11 = B. | year = 2012 | title = Deep Neural Networks for Acoustic Modeling in Speech Recognition --- The shared views of four research groups | url = | journal = IEEE Signal Processing Magazine | volume = 29 | issue = 6| pages = 82–97 | doi=10.1109/msp.2012.2205597}}</ref><ref name="patent2011">D. Yu, L. Deng, G. Li, and F. Seide (2011). "Discriminative pretraining of deep neural networks," U.S. Patent Filing.</ref> Further, the nature of recognition errors produced by the two types of systems was found to be characteristically different,<ref name="ReferenceICASSP2013"/><ref name=NIPS2009/>
offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major players in speech recognition industry. The history of this significant development in deep learning has been described and analyzed in recent books and articles.<ref name=BOOK2014 /><ref name="ReferenceA">{{cite journal|last1=Yu|first1=D.|last2=Deng|first2=L.|title=Automatic Speech Recognition: A Deep Learning Approach (Publisher: Springer)| date=2014}}</ref><ref>IEEE (2015)http://blogs.technet.com/b/inside_microsoft_research/archive/2015/12/03/deng-receives-prestigious-ieee-technical-achievement-award.aspx</ref>

Advances in hardware have also been important in enabling the renewed interest of deep learning. In particular, powerful [[graphics processing unit]]s (GPUs) are well-suited for the kind of number crunching, matrix/vector math involved in machine learning. GPUs have been shown to speed up training algorithms by orders of magnitude, bringing running times of weeks back to days.<ref name="CIRESAN2010">D. C. Ciresan ''et al.'', "Deep Big Simple Neural Nets for Handwritten Digit Recognition," ''Neural Computation'', 22, pp. 3207–3220, 2010.</ref><ref name="RAINA2009">R. Raina, A. Madhavan, A. Ng., "Large-scale Deep Unsupervised Learning using Graphics Processors," ''Proc. 26th Int. Conf. on Machine Learning'', 2009.</ref>

== Artificial neural networks ==
Some of the most successful deep learning methods involve artificial [[neural network]]s. Artificial neural networks are inspired by the 1959 biological model proposed by [[Nobel laureate]]s [[David H. Hubel]] & [[Torsten Wiesel]], who found two types of cells in the [[primary visual cortex]]: [[simple cell]]s and [[complex cell]]s. Many artificial neural networks can be viewed as cascading models <ref name="Weng1992"/><ref name="Weng1993"/><ref name="Weng1997"/><ref>{{cite journal | last1 = Riesenhuber | first1 = M | last2 = Poggio | first2 = T | year = 1999 | title = Hierarchical models of object recognition in cortex | doi = 10.1038/14819 | journal = Nature Neuroscience | volume = 2 | issue = 11| pages = 1019–1025 }}</ref> of cell types inspired by these biological observations.

Fukushima's Neocognitron introduced [[convolution]]al neural networks partially trained by [[unsupervised learning]] with human-directed features in the neural plane. [[Yann LeCun]] et al. (1989) applied supervised [[backpropagation]] to such architectures.<ref name=LeCun1989>Y. LeCun, B. Boser, J. S. Denker, D. Henderson, R. E. Howard, W. Hubbard, L. D. Jackel. 1989 ''Backpropagation Applied to Handwritten Zip Code Recognition.'' Neural Computation, 1(4):541–551.</ref>  Weng et al. (1992) published convolutional neural networks Cresceptron<ref name="Weng1992"/><ref name="Weng1993"/><ref name="Weng1997"/>  for 3-D object recognition from images of cluttered scenes and segmentation of such objects from images.

An obvious need for recognizing general 3-D objects is least shift invariance and tolerance to deformation. Max-pooling appeared to be first proposed by Cresceptron<ref name="Weng1992"/><ref name="Weng1993"/> to enable the network to tolerate small-to-large deformation in a hierarchical way, while using convolution. Max-pooling helps, but does not guarantee, shift-invariance at the pixel level.<ref name="Weng1997"/>

With the advent of the [[back-propagation]] algorithm being discovered independently by several groups in the 1970s and 1980s,<ref name="WERBOS1974"/><ref name="ROMELNAT">Rumelhart, D. E., Hinton, G. E. & Williams, R. J. , "Learning representations by back-propagating errors" ''nature'', 1974.</ref> many researchers tried to train supervised deep [[artificial neural network]]s from scratch, initially with little success. [[Sepp Hochreiter]]'s diploma thesis of 1991<ref name="HOCH1991"/><ref name="HOCH2001"/> formally identified the reason for this failure as the [[vanishing gradient problem]], which affects many-layered feedforward networks and [[recurrent neural network]]s. Recurrent networks are trained by unfolding them into very deep feedforward networks, where a new layer is created for each time step of an input sequence processed by the network. As errors propagate from layer to layer, they shrink exponentially with the number of layers, impeding the tuning of neuron weights which is based on those errors.

To overcome this problem, several methods were proposed. One is [[Jürgen Schmidhuber]]'s multi-level hierarchy of networks (1992) pre-trained one level at a time by unsupervised learning, fine-tuned by [[backpropagation]].<ref name="SCHMID1992"/> Here each level learns a compressed representation of the observations that is fed to the next level.

Another method is the [[long short term memory]] (LSTM) network of [[Sepp Hochreiter|Hochreiter]] & [[Jürgen Schmidhuber|Schmidhuber]] (1997).<ref name=lstm>[[Sepp Hochreiter|Hochreiter, Sepp]]; and [[Jürgen Schmidhuber|Schmidhuber, Jürgen]]; ''Long Short-Term Memory'', Neural Computation, 9(8):1735–1780, 1997</ref> In 2009, deep multidimensional LSTM networks won three ICDAR 2009 competitions in connected handwriting recognition, without any prior knowledge about the three languages to be learned.<ref>Graves, Alex; and Schmidhuber, Jürgen; ''Offline Handwriting Recognition with Multidimensional Recurrent Neural Networks'', in Bengio, Yoshua; Schuurmans, Dale; Lafferty, John; Williams, Chris K. I.; and Culotta, Aron (eds.), ''Advances in Neural Information Processing Systems 22 (NIPS'22), December 7th–10th, 2009, Vancouver, BC'', Neural Information Processing Systems (NIPS) Foundation, 2009, pp. 545–552</ref><ref>{{cite journal | last1 = Graves | first1 = A. | last2 = Liwicki | first2 = M. | last3 = Fernandez | first3 = S. | last4 = Bertolami | first4 = R. | last5 = Bunke | first5 = H. | last6 = Schmidhuber | first6 = J. | year = 2009 | title = A Novel Connectionist System for Improved Unconstrained Handwriting Recognition | doi = 10.1109/tpami.2008.137 | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence | volume = 31 | issue = 5| pages =  855–868}}</ref>

Sven Behnke in 2003 relied only on the sign of the gradient ([[Rprop]]) when training his Neural Abstraction Pyramid<ref>
{{cite book
 |author=Sven Behnke
 |year=2003
 |title=Hierarchical Neural Networks for Image Interpretation.
 |series=Lecture Notes in Computer Science     |volume=2766
 |publisher=Springer
 |url=http://www.ais.uni-bonn.de/books/LNCS2766.pdf 
}}</ref> to solve problems like image reconstruction and face localization.

Other methods also use unsupervised pre-training to structure a neural network, making it first learn generally useful [[feature detection (computer vision)|feature detectors]]. Then the network is trained further by supervised [[back-propagation]] to classify labeled data. The deep model of Hinton et al. (2006) involves learning the distribution of a high-level representation using successive layers of binary or real-valued  [[latent variable]]s.  It uses a [[restricted Boltzmann machine]] (Smolensky, 1986<ref name="smolensky1986">
{{cite book
 |last1=Smolensky |first1=P. |authorlink1=Paul Smolensky
 |year=1986
 |chapter=Information processing in dynamical systems: Foundations of harmony theory.
 |title=Parallel Distributed Processing: Explorations in the Microstructure of Cognition
 |editors=D. E. Rumelhart, J. L. McClelland, & the PDP Research Group
 |volume=1
 |pages=194–281
 |url=http://portal.acm.org/citation.cfm?id=104290 
}}</ref>) to model each new layer of higher level features.  Each new layer guarantees an increase on the [[Lower bound|lower-bound]] of the [[log likelihood]] of the data, thus improving the model, if trained properly.  Once sufficiently many layers have been learned, the deep architecture may be used as a [[generative model]] by reproducing the data when sampling down the model (an "ancestral pass") from the top level feature activations.<ref name="hinton2006">{{cite journal
 |doi=10.1162/neco.2006.18.7.1527
 |last1=Hinton |first1=G. E. |authorlink1=Geoffrey Hinton
 |last2=Osindero |first2=S.
 |last3=Teh |first3=Y. 
 |year=2006
 |title=A fast learning algorithm for deep belief nets
 |journal=[[Neural Computation]]
 |volume=18 
 |issue=7 |pages=1527–1554 
 |url=http://www.cs.toronto.edu/~hinton/absps/fastnc.pdf 
 |pmid=16764513
}}</ref>
Hinton reports that his models are effective feature extractors over high-dimensional, structured data.<ref>{{Cite journal | last1 = Hinton | first1 = G. | title = Deep belief networks | doi = 10.4249/scholarpedia.5947 | journal = Scholarpedia | volume = 4 | issue = 5 | pages = 5947 | year = 2009 | pmid =  | pmc = | url = http://www.scholarpedia.org/article/Deep_belief_networks}}</ref>

The [[Google Brain]] team led by [[Andrew Ng]] and [[Jeff Dean (computer scientist)|Jeff Dean]] created a neural network that learned to recognize higher-level concepts, such as cats, only from watching unlabeled images taken from [[YouTube]] videos.<ref name="markoff2012">{{cite news
|title= How Many Computers to Identify a Cat? 16,000.
|newspaper = New York Times
|author=John Markoff
|url=http://www.nytimes.com/2012/06/26/technology/in-a-big-network-of-computers-evidence-of-machine-learning.html
|date=25 June 2012
}}</ref><ref name="ng2012">
{{cite arxiv
|title= Building High-level Features Using Large Scale Unsupervised Learning
|last1=Ng |first1=Andrew
|last2=Dean |first2=Jeff
|arxiv=1112.6209
|year=2012
}}</ref>

Other methods rely on the sheer processing power of modern computers, in particular, [[GPU]]s. In 2010, Dan Ciresan and colleagues<ref name="CIRESAN2010"/> in [[Jürgen Schmidhuber]]'s group at the Swiss AI Lab [[IDSIA]] showed that despite the above-mentioned "vanishing gradient problem," the superior processing power of GPUs makes plain [[back-propagation]] feasible for deep feedforward neural networks with many layers. The method outperformed all other machine learning techniques on the old, famous MNIST handwritten digits problem of [[Yann LeCun]] and colleagues at [[NYU]].

At about the same time, in late 2009, deep learning made inroads into speech recognition, as marked by the NIPS Workshop on Deep Learning for Speech Recognition. Intensive collaborative work between Microsoft Research and University of Toronto researchers demonstrated by mid-2010 in Redmond that deep neural networks interfaced with a hidden Markov model with context-dependent states that define the neural network output layer can drastically reduce errors in large-vocabulary speech recognition tasks such as voice search. The same deep neural net model was shown to scale up to Switchboard tasks about one year later at Microsoft Research Asia.

As of 2011, the state of the art in deep learning feedforward networks alternates convolutional layers and max-pooling layers,<ref name="ciresan2011">D. C. Ciresan, U. Meier, J. Masci, L. M. Gambardella, J. Schmidhuber. Flexible, High Performance Convolutional Neural Networks for Image Classification. International Joint Conference on Artificial Intelligence (IJCAI-2011, Barcelona), 2011.</ref><ref name="martines2013">{{cite journal | last1 = Martines | first1 = H. | last2 = Bengio | first2 = Y. | last3 = Yannakakis | first3 = G. N. | year = 2013 | title = Learning Deep Physiological Models of Affect | url = | journal = IEEE Computational Intelligence | volume = 8 | issue = 2| pages = 20–33 | doi=10.1109/mci.2013.2247823}}</ref> topped by several fully connected or sparsely connected layer followed by a final classification layer. Training is usually done without any unsupervised pre-training. Since 2011, GPU-based implementations<ref name="ciresan2011"/> of this approach won many pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,<ref name="ciresan2011NN">D. C. Ciresan, U. Meier, J. Masci, J. Schmidhuber. Multi-Column Deep Neural Network for Traffic Sign Classification. Neural Networks, 2012.</ref> the ISBI 2012 Segmentation of neuronal structures in EM stacks challenge,<ref name="ciresan2012NIPS">D. Ciresan, A. Giusti, L. Gambardella, J. Schmidhuber. Deep Neural Networks Segment Neuronal Membranes in Electron Microscopy Images. In Advances in Neural Information Processing Systems (NIPS 2012), Lake Tahoe, 2012.</ref> and others.

Such supervised deep learning methods also were the first artificial pattern recognizers to achieve human-competitive performance on certain tasks.<ref name="ciresan2011CVPR">D. C. Ciresan, U. Meier, J. Schmidhuber. Multi-column Deep Neural Networks for Image Classification. IEEE Conf. on Computer Vision and Pattern Recognition CVPR 2012.
</ref>

To overcome the barriers of weak AI represented by deep learning, it is necessary to go beyond deep learning architectures, because biological brains use both shallow and deep circuits as reported by brain anatomy<ref name="VanEssen1991">D. J. Felleman and D. C. Van Essen, "[http://cercor.oxfordjournals.org/content/1/1/1.1.full.pdf+html Distributed hierarchical processing in the primate cerebral cortex]," ''Cerebral Cortex'', 1, pp. 1-47, 1991.</ref> displaying a wide variety of invariance. Weng<ref name="Weng2012">J. Weng, "[http://www.amazon.com/Natural-Artificial-Intelligence-Introduction-Computational/dp/0985875720 Natural and Artificial Intelligence: Introduction to Computational Brain-Mind]," BMI Press, ISBN  978-0985875725, 2012.</ref> argued that the brain self-wires largely according to signal statistics and, therefore, a serial cascade cannot catch all major statistical dependencies.  ANNs were able to guarantee shift invariance to deal with small and large natural objects in large cluttered scenes, only when invariance extended beyond shift, to all ANN-learned concepts, such as location, type (object class label), scale, lighting. This was realized in Developmental Networks (DNs)<ref name="Weng2011">J. Weng, "[http://www.cse.msu.edu/~weng/research/WhyPass-Weng-NI-2011.pdf Why Have We Passed `Neural Networks Do not Abstract Well'?]," ''Natural Intelligence: the INNS Magazine'', vol. 1, no.1, pp. 13-22, 2011.</ref> whose embodiments are Where-What Networks, WWN-1 (2008)<ref name="Weng08">Z. Ji, J. Weng, and D. Prokhorov, "[http://www.cse.msu.edu/~weng/research/ICDL08_0077.pdf Where-What Network 1: Where and What Assist Each Other Through Top-down Connections]," ''Proc. 7th International Conference on Development and Learning (ICDL'08)'', Monterey, CA, Aug. 9-12, pp. 1-6, 2008.</ref> through WWN-7 (2013).<ref name="Weng13">X. Wu, G. Guo, and J. Weng, "[http://www.cse.msu.edu/~weng/research/WWN7-Wu-ICBM-2013.pdf Skull-closed Autonomous Development: WWN-7 Dealing with Scales]," ''Proc. International Conference on Brain-Mind'', July 27–28, East Lansing, Michigan, pp. +1-9, 2013.</ref>

== Architectures ==

There are huge number of variants of deep architectures. Most of them are branched from some original parent architectures. It is not always possible to compare the performance of multiple architectures all together, because they are not all evaluated on the same data sets. Deep learning is a fast-growing field, and new architectures, variants, or algorithms appear every few weeks.

=== Deep neural networks ===

A deep neural network (DNN) is an [[artificial neural network]] (ANN) with multiple hidden layers of units between the input and output layers.<ref name="BENGIODEEP" /><ref name="SCHIDHUB" /> Similar to shallow ANNs, DNNs can model complex non-linear relationships. DNN architectures, e.g., for [[object detection]] and [[Natural language processing|parsing]] generate compositional models where the object is expressed as a layered composition of image primitives.<ref>Szegedy, Christian, Alexander Toshev, and Dumitru Erhan. "Deep neural networks for object detection." Advances in Neural Information Processing Systems. 2013.</ref> The extra layers enable composition of features from lower layers, giving the potential of modeling complex data with fewer units than a similarly performing shallow network.<ref name="BENGIODEEP" />

DNNs are typically designed as [[feedforward neural network|feedforward]] networks, but recent research has successfully applied the deep learning architecture to [[recurrent neural network]]s for applications such as [[language model]]ing.<ref name="MIKO2010">T. Mikolov ''et al.'', "Recurrent neural network based language model," ''Interspeech'', 2010.</ref> [[convolutional neural network|Convolutional deep neural networks]] (CNNs) are used in computer vision where their success is well-documented.<ref name="LECUN86">{{cite journal |last1=LeCun |first1=Y. |display-authors=etal |year= |title=Gradient-based learning applied to document recognition |url= |journal=Proceedings of the IEEE |volume=86 |issue=11 |pages=2278–2324 |doi=10.1109/5.726791}}</ref> More recently, CNNs have been applied to [[acoustic model]]ing for automatic speech recognition (ASR), where they have shown success over previous models.<ref name="SAIN2013">T. Sainath ''et al.'', "Convolutional neural networks for LVCSR," ''ICASSP'', 2013.</ref> For simplicity, a look at training DNNs is given here.

A DNN can be [[discriminative model|discriminatively]] trained with the standard [[backpropagation]] algorithm. The weight updates can be done via [[stochastic gradient descent]] using the following equation:

:<math> w_{ij}(t + 1) = w_{ij}(t) + \eta\frac{\partial C}{\partial w_{ij}} </math>

Here, <math> \eta </math> is the learning rate, and <math> C </math> is the [[loss function|cost function]]. The choice of the cost function depends on factors such as the learning type (supervised, unsupervised, [[Reinforcement learning|reinforcement]], etc.) and the [[activation function]]. For example, when performing supervised learning on a [[multiclass classification]] problem, common choices for the activation function and cost function are the [[softmax activation function|softmax]] function and [[cross entropy]] function, respectively. The softmax function is defined as <math> p_j = \frac{\exp(x_j)}{\sum_k \exp(x_k)} </math> where <math> p_j </math> represents the class probability (output of the unit <math> j </math>) and <math> x_j </math> and <math> x_k </math> represent the total input to units <math> j </math> and <math> k </math> of the same level respectively. Cross entropy is defined as <math> C = -\sum_j d_j \log(p_j) </math> where <math> d_j </math> represents the target probability for output unit <math> j </math> and <math> p_j </math> is the probability output for <math> j </math> after applying the activation function.<ref name="HINTON2012">G. E. Hinton ''et al.''., "Deep Neural Networks for Acoustic Modeling in Speech Recognition: The shared views of four research groups," ''IEEE Signal Processing Magazine'', pp. 82–97, November 2012.</ref>

These can be used to output object bounding boxes in form of a binary mask. They are also used for multi-scale regression to increase localization precision. DNN-based regression can learn features that capture geometric information in addition to being a good classifier. They remove the limitation of designing a model which will capture parts and their relations explicitly. This helps to learn a wide variety of objects. The model consists of multiple layers, each of which has a [[rectified linear unit]] for non-linear transformation. Some layers are convolutional, while others are fully connected. Every convolutional layer has an additional max pooling. The network is trained to minimize L2 error for predicting the mask ranging over the entire training set containing bounding boxes represented as masks.

==== Problems with deep neural networks ====
As with ANNs, many issues can arise with DNNs if they are naively trained. Two common issues are [[overfitting]] and computation time.

DNNs are prone to overfitting because of the added layers of abstraction, which allow them to model rare dependencies in the training data. [[Regularization (mathematics)|Regularization]] methods such as [[weight decay]] (<math> \ell_2 </math>-regularization) or [[sparse matrix|sparsity]] (<math> \ell_1 </math>-regularization) can be applied during training to help combat overfitting.<ref name="BENGIO2013">Y. Bengio ''et al.''., "Advances in optimizing recurrent networks," ''ICASSP'', 2013.</ref> A more recent regularization method applied to DNNs is [[Dropout (neural networks)|dropout]] regularization. In dropout, some number of units are randomly omitted from the hidden layers during training. This helps to break the rare dependencies that can occur in the training data.<ref name="DAHL2013">G. Dahl ''et al.''., "Improving DNNs for LVCSR using rectified linear units and dropout," ''ICASSP'', 2013.</ref>

The dominant method for training these structures has been error-correction training (such as [[backpropagation]] with [[gradient descent]]) due to its ease of implementation and its tendency to converge to better [[Local optimum|local optima]] than other training methods. However, these methods can be computationally expensive, especially for DNNs. There are many training parameters to be considered with a DNN, such as the size (number of layers and number of units per layer), the learning rate and initial weights. [[Hyperparameter optimization#Grid search|Sweeping through the parameter space]] for optimal parameters may not be feasible due to the cost in time and computational resources. Various 'tricks' such as using mini-batching (computing the gradient on several training examples at once rather than individual examples) <ref name="RBMTRAIN">G. E. Hinton., "A Practical Guide to Training Restricted Boltzmann Machines," ''Tech. Rep. UTML TR 2010-003, Dept. CS., Univ. of Toronto'', 2010.</ref> have been shown to speed up computation. The large processing throughput of GPUs has produced significant speedups in training, due to the matrix and vector computations required being well suited for GPUs.<ref name="SCHIDHUB" /> Radical alternatives to backprop such as [[Extreme Learning Machines]],<ref>{{cite journal | last1 = Huang | first1 = Guang-Bin | last2 = Zhu | first2 = Qin-Yu | last3 = Siew | first3 = Chee-Kheong | year = 2006 | title = Extreme learning machine: theory and applications | url = | journal = Neurocomputing | volume = 70 | issue = 1| pages = 489–501 | doi=10.1016/j.neucom.2005.12.126}}</ref> "No-prop" networks,<ref>{{cite journal | last1 = Widrow | first1 = Bernard | display-authors = etal   | year = 2013 | title = The no-prop algorithm: A new learning algorithm for multilayer neural networks | url = | journal = Neural Networks | volume = 37 | issue = | pages = 182–188 | doi=10.1016/j.neunet.2012.09.020}}</ref> training without backtracking,<ref>{{cite arxiv |last=Ollivier |first=Yann |last2=Charpiat |first2=Guillaume |year=2015 |title=Training recurrent networks without backtracking |arxiv=1507.07680}}</ref> "weightless" networks,<ref>Aleksander, Igor, et al. "A brief introduction to Weightless Neural Systems." ESANN. 2009.</ref> and [[holographic associative memory|non-connectionist neural networks]] are gaining attention.

=== Deep belief networks ===
{{main|Deep belief network}}

[[File:Restricted Boltzmann machine.svg|thumb| A [[restricted Boltzmann machine]] (RBM) with fully connected visible and hidden units. Note there are no hidden-hidden or visible-visible connections.]]

A deep belief network (DBN) is a probabilistic, [[generative model]] made up of multiple layers of hidden units. It can be considered a [[Function composition|composition]] of simple learning modules that make up each layer.<ref name="SCHOLARDBNS">{{cite journal | last1 = Hinton | first1 = G.E. | year = | title = Deep belief networks | url = | journal = Scholarpedia | volume = 4 | issue = 5| page = 5947 | doi=10.4249/scholarpedia.5947}}</ref>

A DBN can be used to generatively pre-train a DNN by using the learned DBN weights as the initial DNN weights. Back-propagation or other discriminative algorithms can then be applied for fine-tuning of these weights. This is particularly helpful when limited training data are available, because poorly initialized weights can significantly hinder the learned model's performance. These pre-trained weights are in a region of the weight space that is closer to the optimal weights than are randomly chosen initial weights. This allows for both improved modeling and faster convergence of the fine-tuning phase.<ref name="LAROCH2007">{{cite journal | last1 = Larochelle | first1 = H. | display-authors = etal   | year = | title = An empirical evaluation of deep architectures on problems with many factors of variation | url = | journal = Proc. 24th Int. Conf. Machine Learning | volume = 2007 | issue = | pages = 473–480 }}</ref>

A DBN can be efficiently trained in an unsupervised, layer-by-layer manner, where the layers are typically made of [[restricted Boltzmann machine]]s (RBM). An RBM is an [[undirected graph|undirected]], generative energy-based model with a "visible" input layer and a hidden layer, and connections between the layers but not within layers. The training method for RBMs proposed by Geoffrey Hinton for use with training "Product of Expert" models is called [[contrastive divergence]] (CD).<ref name="POE">G. E. Hinton., [http://www.cs.toronto.edu/~fritz/absps/nccd.pdf "Training Product of Experts by Minimizing Contrastive Divergence,"] ''Neural Computation'', 14, pp. 1771–1800, 2002.</ref> CD provides an approximation to the [[maximum likelihood]] method that would ideally be applied for learning the weights of the RBM.<ref name="RBMTRAIN" /><ref name="RBMTutorial">{{cite journal | last1 = Fischer | first1 = A. | last2 = Igel | first2 = C. | year = 2014 | title = Training Restricted Boltzmann Machines: An Introduction | url = http://image.diku.dk/igel/paper/TRBMAI.pdf | format = PDF | journal = Pattern Recognition | volume = 47 | issue = | pages = 25–39 | doi=10.1016/j.patcog.2013.05.025}}</ref> In training a single RBM, weight updates are performed with [[gradient descent|gradient ascent]] via the following equation:  <math> \Delta w_{ij}(t+1) = w_{ij}(t) + \eta\frac{\partial \log(p(v))}{\partial w_{ij}} </math>. Here, <math>p(v)</math> is the probability of a visible vector, which is given by <math>p(v) = \frac{1}{Z}\sum_he^{-E(v,h)}</math>. <math> Z </math> is the partition function (used for normalizing) and <math>E(v,h)</math> is the energy function assigned to the state of the network. A lower energy indicates the network is in a more "desirable" configuration. The gradient <math>\frac{\partial \log(p(v))}{\partial w_{ij}}</math> has the simple form <math>\langle v_ih_j\rangle_\text{data} - \langle v_ih_j\rangle_\text{model}</math> where <math>\langle\cdots\rangle_p</math> represent averages with respect to distribution <math>p</math>. The issue arises in sampling <math>\langle v_ih_j\rangle_\text{model}</math> because this requires running alternating [[Gibbs sampling]] for a long time. CD replaces this step by running alternating Gibbs sampling for <math>n</math> steps (values of <math>n = 1</math> have empirically been shown to perform well). After <math>n</math> steps, the data are sampled and that sample is used in place of <math>\langle v_ih_j\rangle_\text{model}</math>. The CD procedure works as follows:<ref name="RBMTRAIN" />

# Initialize the visible units to a training vector.
# Update the hidden units in parallel given the visible units: <math>p(h_j = 1 \mid \textbf{V}) = \sigma(b_j + \sum_i v_iw_{ij})</math>. <math>\sigma</math> is the [[sigmoid function]] and <math>b_j</math> is the bias of <math>h_j</math>.
# Update the visible units in parallel given the hidden units: <math>p(v_i = 1 \mid \textbf{H}) = \sigma(a_i + \sum_j h_jw_{ij})</math>. <math>a_i</math> is the bias of <math>v_i</math>. This is called the "reconstruction" step.
# Re-update the hidden units in parallel given the reconstructed visible units using the same equation as in step 2.
# Perform the weight update: <math>\Delta w_{ij} \propto \langle v_ih_j\rangle_\text{data} - \langle v_ih_j\rangle_\text{reconstruction}</math>.

Once an RBM is trained, another RBM is "stacked" atop it, taking its input from the final already-trained layer.  The new visible layer is initialized to a training vector, and values for the units in the already-trained layers are assigned using the current weights and biases. The new RBM is then trained with the procedure above. This whole process is repeated until some desired stopping criterion is met.<ref name="BENGIODEEP"/>

Although the approximation of CD to maximum likelihood is very crude (CD has been shown to not follow the gradient of any function), it has been empirically shown to be effective in training deep architectures.<ref name="RBMTRAIN"/>

=== Convolutional neural networks ===
{{main|Convolutional neural network}}

A CNN is composed of one or more [[convolution]]al layers with fully connected layers (matching those in typical artificial neural networks) on top. It also uses tied weights and pooling layers. This architecture allows CNNs to take advantage of the 2D structure of input data. In comparison with other deep architectures, convolutional neural networks are starting to show superior results in both image and speech applications. They can also be trained with standard backpropagation. CNNs are easier to train than other regular, deep, feed-forward neural networks and have many fewer parameters to estimate, making them a highly attractive architecture to use.<ref name="STANCNN">http://ufldl.stanford.edu/tutorial/supervised/ConvolutionalNeuralNetwork/</ref> Examples of applications in Computer Vision include [[DeepDream]].<ref name=deepdream>{{cite journal|first1=Christian |last1=Szegedy  |first2=Wei |last2=Liu |first3=Yangqing |last3=Jia|first4=Pierre |last4=Sermanet|first5=Scott |last5=Reed|first6=Dragomir |last6=Anguelov|first7=Dumitru |last7=Erhan|first8=Vincent |last8=Vanhoucke|first9=Andrew |last9=Rabinovich|title = Going Deeper with Convolutions|journal= Computing Research Repository|arxiv= 1409.4842|year=2014 }}</ref>

=== Convolutional deep belief networks ===
A recent achievement in deep learning is the use of convolutional deep belief networks (CDBN). CDBNs have structure very similar to a [[convolutional neural network]]s and are trained similar to deep belief networks. Therefore, they exploit the 2D structure of images, like CNNs do, and make use of pre-training like [[deep belief network]]s. They provide a generic structure which can be used in many image and signal processing tasks. Recently, many benchmark results on standard image datasets like CIFAR <ref name="CDBN-CIFAR">[http://www.cs.toronto.edu/~kriz/conv-cifar10-aug2010.pdf Convolutional Deep Belief Networks on CIFAR-10]</ref> have been obtained using CDBNs.<ref name="CDBN">[http://dl.acm.org/citation.cfm?id=1553453 Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations]</ref>

=== Large memory storage and retrieval neural networks ===

Large memory storage and retrieval neural networks (LAMSTAR)<ref name=book2013>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013.</ref><ref name=GrPatent>D. Graupe," Large memory storage and retrieval (LAMSTAR) network, US Patent 5920852 A", April 1996.</ref> are fast deep learning neural networks of many layers which can use many filters simultaneously.  These filters may be nonlinear, stochastic, logic, [[non-stationary]], or even non-analytical. They are biologically motivated and continuously learning.
 
A LAMSTAR neural network may serve as a dynamic neural network in spatial or time domain or both.  Its speed is provided by [[Hebbian]] link-weights (Chapter 9 of in D. Graupe, 2013<ref name=book2013a>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013, pp.203-274.</ref>), which serve to integrate the various and usually different filters (preprocessing functions) into its many layers and to dynamically rank the significance of the various layers and functions relative to a given task for deep learning. This grossly imitates biological learning which integrates outputs various preprocessors ([[cochlea]], [[retina]], ''etc.'') and cortexes ([[Auditory cortex|auditory]], [[Visual cortex|visual]], ''etc.'') and their various regions.  Its deep learning capability is further enhanced by using inhibition, correlation and by its ability to cope with incomplete data, or "lost" neurons or layers even at the midst of a task.  Furthermore, it is fully transparent due to its link weights. The link-weights also allow dynamic determination of innovation and redundancy, and facilitate the ranking of layers, of filters or of individual neurons relative to a task.

LAMSTAR has been applied to many medical<ref name=Nigam>V. P. Nigam, D. Graupe, (2004),"A neural-network-based detection of epilepsy", ''Neurological Research'', 26(1): 55-60.</ref><ref name=Waxman>{{cite journal | last1 = Waxman | first1 = J. | last2 = Graupe | first2 = D. | last3 = Carley | first3 = C W. | year = 2010 | title = Automated prediction of apnea and hypopnea, using a LAMSTAR artificial neural network | url = | journal = American Journal of Respiratory and Critical Care Medicine | volume = 171 | issue = 7| pages = 727–733 }}</ref><ref name=GrGrZh>{{cite journal | last1 = Graupe | first1 = D. | last2 = Graupe | first2 = M. H. | last3 = Zhong | first3 = Y. | last4 = Jackson | first4 = R. K. | year = 2008 | title = Blind adaptive filtering for non-invasive extraction of the fetal electrocardiogram and its non-stationarities | url = | journal = Proc. Inst. Mech Eng., UK, Part H:  Journal of Engineering in Medicine | volume = 222 | issue = 8| pages = 1221–1234 | doi=10.1243/09544119jeim417}}</ref> and financial predictions (see Graupe, 2013<ref name=book2013b>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013, pp.240-253.</ref> Section 9C), adaptive filtering of noisy speech in unknown noise,<ref name=GrAbon>{{cite journal | last1 = Graupe | first1 = D. | last2 = Abon | first2 = J. | year = 2002 | title = A Neural Network for Blind Adaptive Filtering of Unknown Noise from Speech | url = | journal = Intelligent Engineering Systems Through Artificial Neural Networks | volume = 12 | issue = | pages = 683–688 }}</ref> still-image recognition<ref name=Homayon>{{cite journal | last1 = Homayon | first1 = S. | year = 2015 | title = Iris Recognition for Personal Identification Using LAMSTAR Neural Network | url = | journal = International Journal of Computer Science and Information Technology | volume = 7 | issue = 1 }}</ref> (Graupe, 2013<ref name=book2013c>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers", 2013, pp.253-274.</ref> Section 9D), video image recognition,<ref name=Girado>{{cite journal | last1 = Girado | first1 = J. I. | last2 = Sandin | first2 = D. J. | last3 = DeFanti | first3 = T. A. | year = 2003 | title = Real-time camera-based face detection using amodified LAMSTAR neural network system | url = | journal = Proc. SPIE 5015, Applications of Artificial Neural Networks in Image Processing VIII | volume =  | issue = | page =  | doi = 10.1117/12.477405 }}</ref> software security,<ref name=VenkSel>{{cite journal | last1 = Venkatachalam | first1 = V | last2 = Selvan | first2 = S. | year = 2007 | title = Intrusion Detection using an Improved Competitive Learning Lamstar Network | url = | journal = International Journal of Computer Science and Network Security | volume = 7 | issue = 2| pages = 255–263 }}</ref> adaptive control of non-linear systems,<ref name=GrSmol>D. Graupe, M. Smollack, (2007), "Control of unstable nonlinear and nonstationary systems using LAMSTAR neural networks", Proceedings of 10th IASTED on Intelligent Control, Sect.592, 141-144.</ref> and others. LAMSTAR had a much faster computing speed and somewhat lower error than a convolutional neural network based on [[ReLU]]-function filters and max pooling, in a comparative character recognition study.<ref name=GrConSat>D. Graupe, C. Contaldi, A. Sattiraju, (2015) [https://www.academia.edu/18095724/Comparison_of_Lamstar_NN_and_Convolutional_NN_Character_Recognition "Comparison of  Lamstar NN & Convolutional NN  – Character Recognition"].</ref>

These applications demonstrate delving into aspects of the data that are hidden from shallow learning networks or even from the human senses (eye, ear), such as in the cases of predicting onset of [[sleep apnea]] events,<ref name="Waxman"/> of an electrocardiogram of a fetus as recorded from skin-surface electrodes placed on the mother's abdomen early in pregnancy,<ref name="GrGrZh"/> of financial prediction (Section 9C in Graupe, 2013),<ref name="book2013"/>  or in blind filtering of noisy speech.<ref name="GrAbon"/>

LAMSTAR was proposed in 1996 ({{US Patent|5920852 A}}) and was further developed by D Graupe and H Kordylewski 1997-2002.<ref name="GKmidwet">{{cite journal | last1 = Graupe | first1 = H. Kordylewski | year = 1996 | title = Network based on SOM (self-organizing-map) modules combined with statistical decision tools | url = | journal = Proc. IEEE 39th Midwest Conf. on Circuits and Systems | volume = 1 | issue = | pages = 471–475 }}</ref><ref name="GKsoftware">D, Graupe, H. Kordylewski, (1998), "A large memory storage and retrieval neural network for adaptive retrieval and diagnosis", International Journal of Software Engineering and Knowledge Engineering, 1998.</ref><ref name=Kordylew>{{cite journal | last1 = Kordylewski | first1 = H. | last2 = Graupe | first2 = D | last3 = Liu | first3 = K. | year = | title = A novel large-memory neural network as an aid in medical diagnosis applications | url = | journal = IEEE Transactions on Information Technology in Biomedicine | volume = 5 | issue = 3| pages = 202–209 | doi=10.1109/4233.945291}}</ref>   A modified version, known as LAMSTAR 2, was developed by N C Schneider and D Graupe in 2008.<ref name="Schn">{{cite journal | last1 = Schneider | first1 = N.C. | last2 = Graupe | year = 2008 | title = A modified LAMSTAR neural network and its applications | url = | journal = International journal of neural systems | volume = 18 | issue = 4| pages = 331–337 | doi=10.1142/s0129065708001634}}</ref><ref name=book2013d>D. Graupe, "Principles of Artificial Neural Networks.3rd Edition", World Scientific Publishers, 2013, p.217.</ref>

=== Deep Boltzmann machines ===

A deep Boltzmann machine (DBM) is a type of binary pairwise [[Markov random field]] ([[Graph (discrete mathematics)#Undirected graph|undirected]] probabilistic [[graphical model]]) with multiple layers of [[Latent variable|hidden]] [[random variables]]. It is a network of symmetrically coupled stochastic [[Binary variable|binary units]]. It comprises a set of visible units <math>\boldsymbol{\nu} \in \{0,1\}^D</math>, and a series of layers of hidden units <math>\boldsymbol{h}^{(1)} \in \{0,1\}^{F_1}, \boldsymbol{h}^{(2)} \in \{0,1\}^{F_2}, \ldots, \boldsymbol{h}^{(L)} \in \{0,1\}^{F_L}</math>. There is no connection between units of the same layer (like [[Restricted Boltzmann machine|RBM]]). For the {{H:title|Deep Boltzmann machine|DBM}}, the probability assigned to vector <math>\nu</math> is

<math>p(\boldsymbol{\nu}) = \frac{1}{Z}\sum_h e^{\sum_{ij}W_{ij}^{(1)}\nu_i h_j^{(1)} + \sum_{jl}W_{jl}^{(2)}h_j^{(1)}h_l^{(2)}+\sum_{lm}W_{lm}^{(3)}h_l^{(2)}h_m^{(3)}},</math>

where <math>\boldsymbol{h} = \{\boldsymbol{h}^{(1)}, \boldsymbol{h}^{(2)}, \boldsymbol{h}^{(3)} \}</math> are the set of hidden units, and <math>\theta = \{\boldsymbol{W}^{(1)}, \boldsymbol{W}^{(2)}, \boldsymbol{W}^{(3)} \} </math> are the model parameters, representing visible-hidden and hidden-hidden interactions. If <math>\boldsymbol{W}^{(2)} = 0</math> and <math>\boldsymbol{W}^{(3)} = 0</math> the network is the well-known [[restricted Boltzmann machine]].<ref name="ref1">{{cite journal
 | last1 = Hinton 
 | first1 = Geoffrey
 | last2 = Salakhutdinov
 | first2 = Ruslan
 | title = A better way to pretrain deep Boltzmann machines
 | journal = Advances in Neural
 | volume = 3
 | pages = 1–9
 | date = 2012
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2012_1178.pdf}}</ref> Interactions are symmetric because links are undirected. By contrast, in a [[deep belief network]] (DBN) only the top two layers form a restricted Boltzmann machine (which is an undirected [[graphical model]]), but lower layers form a directed generative model.

Like DBNs, DBMs can learn complex and abstract internal representations of the input in tasks such as [[Object recognition|object]] or [[speech recognition]], using limited labeled data to fine-tune the representations built using a large supply of unlabeled sensory input data. However, unlike {{H:title|Deep belief network|DBNs}} and deep convolutional neural networks, they adopt the [[inference]] and training procedure in both directions, bottom-up and top-down pass, which allow the {{H:title|Deep Boltzmann machine|DBMs}} to better unveil the representations of the ambiguous and complex input structures.<ref name="ref3">{{cite journal
 | last1 = Hinton 
 | first1 = Geoffrey
 | last2 = Salakhutdinov
 | first2 = Ruslan
 | title = Efficient Learning of Deep Boltzmann Machines
 | volume = 3
 | pages = 448–455
 | date = 2009
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS09_SalakhutdinovH.pdf
}}</ref><ref name="ref4">{{cite journal
 | last1 = Bengio 
 | first1 = Yoshua 
 | last2 = LeCun
 | first2 = Yann 
 | title = Scaling Learning Algorithms towards AI
 | volume = 1
 | pages = 1–41
 | date = 2007
 | url = http://www.iro.umontreal.ca/~lisa/bib/pub_subject/language/pointeurs/bengio+lecun-chapter2007.pdf}}</ref>

However, the speed of DBMs limits their performance and functionality. Because exact maximum likelihood learning is intractable for DBMs, we may perform approximate maximum likelihood learning. Another option is to use mean-field inference to estimate data-dependent expectations, and approximation the expected sufficient statistics of the model by using ''[[Markov chain Monte Carlo]]'' ''(MCMC)''.<ref name="ref1" /> This approximate inference, which must be done for each test input, is about 25 to 50 times slower than a single bottom-up pass in DBMs. This makes the joint optimization impractical for large data sets, and seriously restricts the use of DBMs for tasks such as feature representation.<ref name="ref2">{{cite journal
 | last1 =  Larochelle
 | first1 = Hugo
 | last2 = Salakhutdinov
 | first2 = Ruslan
 | title = Efficient Learning of Deep Boltzmann Machines
 | pages = 693–700
 | date = 2010
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2010_SalakhutdinovL10.pdf}}</ref>

=== Stacked (de-noising) auto-encoders ===

The [[auto encoder]] idea is motivated by the concept of a ''good'' representation. For example, for a [[Linear classifier|classifier]], a good representation can be defined as one that will yield a better performing classifier.

An ''encoder'' is a deterministic mapping <math>f_\theta</math> that transforms an input vector''''' x''''' into hidden representation '''''y''''', where <math>\theta = \{\boldsymbol{W}, b\}</math>, <math>\boldsymbol{W}</math> is the weight matrix and '''b''' is an offset vector (bias). A ''decoder'' maps back the hidden representation '''y''' to the reconstructed input '''''z ''''' via <math>g_\theta</math>. The whole process of auto encoding is to compare this reconstructed input to the original and try to minimize this error to make the reconstructed value as close as possible to the original.

In ''stacked denoising auto encoders'', the partially corrupted output is cleaned (de-noised). This idea was introduced in 2010 by Vincent et al.<ref name="ref9">{{cite journal
 | last1 = Vincent 
 | first1 = Pascal
 | last2 = Larochelle
 | first2 = Hugo
 | last3 = Lajoie 
 | first3 = Isabelle
 | last4 = Bengio
 | first4 = Yoshua
 | last5 = Manzagol
 | first5 = Pierre-Antoine
 | title = Stacked Denoising Autoencoders: Learning Useful Representations in a Deep Network with a Local Denoising Criterion
 | journal = The Journal of Machine Learning Research
 | volume = 11
 | pages = 3371–3408
 | date = 2010
 | url = http://dl.acm.org/citation.cfm?id=1953039}}</ref> with a specific approach to ''good'' representation, a ''good representation is one that can be obtained [[Robustness (computer science)|robustly]] from a corrupted input and that will be useful for recovering the corresponding clean input.'' Implicit in this definition are the following ideas:

* The higher level representations are relatively stable and robust to input corruption; 
* It is necessary to extract features that are useful for representation of the input distribution.

The algorithm consists of multiple steps; starts by a [[stochastic mapping]] of <math>\boldsymbol{x}</math> to <math>\tilde{\boldsymbol{x}}</math> through <math>q_D(\tilde{\boldsymbol{x}}|\boldsymbol{x})</math>, this is the corrupting step. Then the corrupted input <math>\tilde{\boldsymbol{x}}</math> passes through a basic auto encoder process and is mapped to a hidden representation <math>\boldsymbol{y} = f_\theta(\tilde{\boldsymbol{x}}) = s(\boldsymbol{W}\tilde{\boldsymbol{x}}+b)</math>. From this hidden representation, we can reconstruct <math>\boldsymbol{z} = g_\theta(\boldsymbol{y})</math>. In the last stage, a [[minimization algorithm]] runs in order to have '''''z''''' as close as possible to uncorrupted input <math>\boldsymbol{x}</math>. The reconstruction error <math>L_H(\boldsymbol{x},\boldsymbol{z})</math> might be either the [[cross-entropy]] loss with an affine-sigmoid decoder, or the squared error loss with an affine decoder.<ref name="ref9" />

In order to make a deep architecture, auto encoders stack one on top of another. Once the encoding function <math>f_\theta</math> of the first denoising auto encoder is learned and used to uncorrupt the input (corrupted input), we can train the second level.<ref name="ref9" />

Once the stacked auto encoder is trained, its output can be used as the input to a [[supervised learning]] algorithm such as [[support vector machine]] classifier or a multi-class [[logistic regression]].<ref name="ref9" />

=== Deep stacking networks ===

One deep architecture based on a hierarchy of blocks of simplified [[neural network]] modules is a deep convex network, introduced in 2011.<ref name="ref16">{{cite journal
 | last1 = Deng 
 | first1 = Li
 | last2 = Yu 
 | first2 = Dong 
 | title = Deep Convex Net: A Scalable Architecture for Speech Pattern Classification
 | journal = Proceedings of the Interspeech
 | pages = 2285–2288
 | date = 2011
 | url = http://www.truebluenegotiations.com/files/deepconvexnetwork-interspeech2011-pub.pdf}}</ref> Here, the weights learning problem is formulated as a [[convex optimization problem]] with a [[Closed-form expression|closed-form solution]]. This architecture is also called a deep stacking network (DSN),<ref name="ref17">{{cite journal
 | last1 = Deng 
 | first1 = Li
 | last2 = Yu
 | first2 = Dong
 | last3 = Platt
 | first3 = John
 | title = Scalable stacking and learning for building deep architectures
 | journal = 2012 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
 | pages = 2133–2136
 | date = 2012
 | url = http://research-srv.microsoft.com/pubs/157586/DSN-ICASSP2012.pdf}}</ref> emphasizing the mechanism's similarity to ''stacked generalization''.<ref name="ref18">{{cite journal
 | last1 = David 
 | first1 = Wolpert
 | title = Stacked generalization
 | journal = Neural Networks
 | volume = 5 | issue = 2 
 | pages = 241–259
 | date = 1992
 | doi=10.1016/S0893-6080(05)80023-1}}</ref> Each DSN block is a simple module that is easy to train by itself in a [[Supervised learning|supervised]] fashion without [[back-propagation]] for the entire blocks.<ref name="ref12">{{cite journal
 | last1 = Bengio 
 | first1 = Yoshua
 | title = Learning deep architectures for AI
 | journal = Foundations and Trends in Machine Learning
 | volume = 2 | issue = 1 
 | pages = 1–127
 | date = 2009
 | url = http://www.nowpublishers.com/product.aspx?product=MAL&doi=2200000006
 | doi=10.1561/2200000006}}</ref>

As designed by Deng and Dong,<ref name="ref16" /> each block consists of a simplified [[multi-layer perceptron]] (MLP) with a single hidden layer. The hidden layer '''''h''''' has logistic [[Sigmoid function|sigmoidal]] [[Artificial neuron|units]], and the output layer has linear units. Connections between these layers are represented by weight matrix '''''U;''''' input-to-hidden-layer connections have weight matrix '''''W'''''. Target vectors '''''t''''' form the columns of matrix '''''T''''', and the input data vectors '''''x''''' form the columns of matrix '''''X.''''' The matrix of hidden units is <math>\boldsymbol{H} = \sigma(\boldsymbol{W}^T\boldsymbol{X})</math>. Modules are trained in order, so lower-layer weights '''''W''''' are known at each stage. The function performs the element-wise logistic sigmoid operation. Each block estimates the same final label class ''y'', and its estimate is concatenated with original input '''''X''''' to form the ''expanded input'' for the next block.  Thus, the input to the first block contains the original data only, while downstream blocks' input also has the output of preceding blocks. Then learning the upper-layer weight matrix '''''U''''' given other weights in the network can be formulated as a convex optimization problem:

:<math>\min_{U^T} f = ||\boldsymbol{U}^T \boldsymbol{H} - \boldsymbol{T}||^2_F,</math>

which has a closed-form solution.

Unlike other deep architectures, such as [[Deep belief network|DBNs]], the goal is not to discover the transformed [[Feature (machine learning)|feature]] representation. The structure of the hierarchy of this kind of architecture makes parallel learning straightforward, as a batch-mode optimization problem. In purely [[Discriminative model|discriminative tasks]], DSNs perform better than conventional [[Deep belief network|DBN]].<ref name="ref17" />

=== Tensor deep stacking networks ===

This architecture is an extension of deep stacking networks (DSN). It improves on {{H:title|Deep stacking network|DSN}} in two important ways: it uses higher-order information from [[covariance]] statistics, and it transforms the [[Convex optimization|non-convex problem]] of a lower-layer to a convex sub-problem of an upper-layer.<ref name="ref19">{{cite journal
 | last1 = Hutchinson 
 | first1 = Brian
 | last2 = Deng
 | first2 = Li 
 | last3 = Yu
 | first3 = Dong
 | title = Tensor deep stacking networks
 | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
 | volume = 1-15
 | date = 2012
 | doi=10.1109/tpami.2012.268
 | pages=1944–1957}}</ref> TDSNs use covariance statistics of the data by using a [[bilinear map]]ping from each of two distinct sets of hidden units in the same layer to predictions, via a third-order [[tensor]].

While parallelization and scalability are not considered seriously in conventional {{H:title|Deep neural networks|DNNs}},<ref name="ref26">{{cite journal
 | last1 = Hinton 
 | first1 = Geoffrey
 | last2 = Salakhutdinov
 | first2 = Ruslan 
 | title = Reducing the Dimensionality of Data with Neural Networks
 | journal = Science
 | volume = 313
 | pages = 504–507
 | date = 2006
 | doi=10.1126/science.1127647
 | pmid=16873662}}</ref><ref name="ref27">{{cite journal
 | last1 = Dahl 
 | first1 = G.
 | last2 = Yu
 | first2 = D.
 | last3 = Deng 
 | first3 = L.
 | last4 = Acero
 | first4 = A.
 | title = Context-Dependent Pre-Trained Deep Neural Networks for Large-Vocabulary Speech Recognition
 | journal = IEEE Transactions on Audio, Speech, and Language Processing
 | volume = 20 | issue = 1 
 | pages = 30–42
 | date = 2012
 | doi=10.1109/tasl.2011.2134090}}</ref><ref name="ref28">{{cite journal
 | last1 = Mohamed 
 | first1 = Abdel-rahman 
 | last2 = Dahl
 | first2 = George
 | last3 = Hinton
 | first3 = Geoffrey
 | title = Acoustic Modeling Using Deep Belief Networks
 | journal = IEEE Transactions on Audio, Speech, and Language Processing
 | volume = 20 | issue = 1 
 | pages = 14–22
 | date = 2012
 | doi=10.1109/tasl.2011.2109382}}</ref> all learning for {{H:title|Deep stacking network|DSN}}s and {{H:title|Tensor deep stacking network|TDSN}}s is done in batch mode, to allow parallelization on a [[Computer cluster|cluster]] of [[CPU]] or [[GPU]] nodes.<ref name="ref16" /><ref name="ref17" /> Parallelization allows scaling the design to larger (deeper) architectures and data sets.

The basic architecture is suitable for diverse tasks such as [[Statistical classification|classification]] and [[regression analysis|regression]].

=== Spike-and-slab RBMs ===

The need for deep learning with [[Real number|real-valued]] inputs, as in Gaussian restricted Boltzmann machines, motivates the ''spike-and-slab'' [[Restricted Boltzmann machine|RBM]] (''ss''[[Restricted Boltzmann machine|RBMs]]), which models continuous-valued inputs with strictly [[Binary variable|binary]] [[latent variable]]s.<ref name="ref30">{{cite journal
 | last1 = Courville 
 | first1 = Aaron
 | last2 = Bergstra
 | first2 = James
 | last3 =  Bengio | first3 = Yoshua
 | title = A Spike and Slab Restricted Boltzmann Machine
 | journal = JMLR: Workshop and Conference Proceeding
 | volume = 15
 | pages = 233–241
 | date = 2011
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/AISTATS2011_CourvilleBB11.pdf}}</ref> Similar to basic [[Restricted Boltzmann machine|RBMs]] and its variants, a spike-and-slab [[Restricted Boltzmann machine|RBM]] is a [[bipartite graph]], while like [[Restricted Boltzmann machine|GRBM]]s, the visible units (input) are real-valued. The difference is in the hidden layer, where each hidden unit has a binary spike variable and a real-valued slab variable. A spike is a discrete [[probability mass]] at zero, while a slab is a [[Probability density|density]] over continuous domain;<ref name="ref32">{{cite conference
 | last1 = Courville 
 | first1 = Aaron
 | last2 = Bergstra
 | first2 = James
 | last3 = Bengio
 | first3 = Yoshua
 | chapter= Unsupervised Models of Images by Spike-and-Slab RBMs
 | title = Proceedings of the 28th International Conference on Machine Learning
 | volume = 10
 | pages = 1–8
 | date = 2011
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/ICML2011Courville_591.pdf}}</ref><ref name="ref32" /> their mixture forms a [[Prior probability|prior]]. The terms come from the statistics literature.<ref name="ref31">{{cite journal
 | last1 = Mitchell 
 | first1 = T
 | last2 = Beauchamp
 | first2 = J
 | title = Bayesian Variable Selection in Linear Regression
 | journal = Journal of the American Statistical Association
 | volume = 83 | issue = 404 
 | pages = 1023–1032
 | date = 1988
 | doi=10.1080/01621459.1988.10478694}}</ref>

An extension of ss[[Restricted Boltzmann machine|RBM]] called µ-ss[[Restricted Boltzmann machine|RBM]] provides extra modeling capacity using additional terms in the [[energy function]]. One of these terms enables the model to form a [[Conditional probability distribution|conditional distribution]] of the spike variables by [[marginalizing out]] the slab variables given an observation.

=== Compound hierarchical-deep models ===

Compound hierarchical-deep models compose deep networks with non-parametric [[Bayesian network|Bayesian models]]. [[Feature (machine learning)|Features]] can be learned using deep architectures such as [[Deep belief network|DBNs]],<ref name="hinton2006" /> [[Deep Boltzmann Machines|DBMs]],<ref name="ref3" /> deep auto encoders,<ref name="ref15">{{cite journal
 | last1 = Larochelle 
 | first1 = Hugo 
 | last2 = Bengio
 | first2 = Yoshua
 | last3 = Louradour 
 | first3 = Jerdme 
 | last4 = Lamblin
 | first4 = Pascal
 | title = Exploring Strategies for Training Deep Neural Networks
 | journal = The Journal of Machine Learning Research
 | volume = 10
 | pages = 1–40
 | date = 2009
 | url = http://dl.acm.org/citation.cfm?id=1577070}}</ref> convolutional variants,<ref name="ref39">{{cite journal
 | last1 = Coates 
 | first1 = Adam
 | last2 = Carpenter
 | first2 = Blake
 | title = Text Detection and Character Recognition in Scene Images with Unsupervised Feature Learning
 | pages = 440–445
 | date = 2011
 | url = }}</ref><ref name="ref40">{{cite journal
 | last1 = Lee 
 | first1 = Honglak 
 | last2 = Grosse
 | first2 = Roger 
 | title = Convolutional deep belief networks for scalable unsupervised learning of hierarchical representations
 | journal = Proceedings of the 26th Annual International Conference on Machine Learning
 | pages = 1–8
 | date = 2009
 | url = http://portal.acm.org/citation.cfm?doid=1553374.1553453}}</ref> ssRBMs,<ref name="ref32" /> deep coding networks,<ref name="ref41">{{cite journal
 | last1 = Lin 
 | first1 = Yuanqing 
 | last2 = Zhang
 | first2 = Tong
 | title = Deep Coding Network | journal = Advances in Neural . . . 
 | pages = 1–9
 | date = 2010
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2010_1077.pdf}}</ref> DBNs with sparse feature learning,<ref name="ref42">{{cite journal
 | last1 = Ranzato 
 | first1 = Marc Aurelio 
 | last2 = Boureau
 | first2 = Y-Lan
 | title = Sparse Feature Learning for Deep Belief Networks
 | journal = Advances in Neural Information Processing Systems
 | volume=23 | pages = 1–8
 | date = 2007
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2007_1118.pdf}}</ref> recursive neural networks,<ref name="ref43">{{cite journal
 | last1 =  Socher  
 | first1 = Richard
 | last2 = Lin
 | first2 = Clif
 | title = Parsing Natural Scenes and Natural Language with Recursive Neural Networks
 | journal = Proceedings of the 26th International Conference on Machine Learning
 | date = 2011
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/ICML2011Socher_125.pdf}}</ref> conditional DBNs,<ref name="ref44">{{cite journal
 | last1 = Taylor 
 | first1 = Graham
 | last2 = Hinton
 | first2 = Geoffrey
 | title = Modeling Human Motion Using Binary Latent Variables
 | journal = Advances in Neural Information Processing Systems
 | date = 2006
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/NIPS2006_693.pdf}}</ref> de-noising auto encoders.<ref name="ref45">{{cite journal
 | last1 = Vincent 
 | first1 = Pascal
 | last2 = Larochelle
 | first2 = Hugo
 | title = Extracting and composing robust features with denoising autoencoders
 | journal = Proceedings of the 25th international conference on Machine learning - ICML '08 
 | pages = 1096–1103
 | date = 2008
 | url = http://portal.acm.org/citation.cfm?doid=1390156.1390294}}</ref> This provides a better representation, allowing faster learning and more accurate classification with high-dimensional data. However, these architectures are poor at learning novel classes with few examples, because all network units are involved in representing the input (a ''distributed representation'') and must be adjusted together (high [[degree of freedom]]). Limiting the degree of freedom reduces the number of parameters to learn, facilitating learning of new classes from few examples. [[Hierarchical Bayesian model|''Hierarchical Bayesian (HB)'' models]] allow learning from few examples, for example <ref name="ref34">{{cite journal
 | last1 = Kemp 
 | first1 = Charles
 | last2 = Perfors
 | first2 = Amy
 | last3 = Tenenbaum
 | first3 = Joshua
 | title = Learning overhypotheses with hierarchical Bayesian models
 | journal = Developmental Science
 | volume = 10 | issue = 3 
 | pages = 307–21
 | date = 2007
 | pmid=17444972
 | doi=10.1111/j.1467-7687.2007.00585.x}}</ref><ref name="ref37">{{cite journal
 | last1 = Xu 
 | first1 = Fei
 | last2 = Tenenbaum
 | first2 = Joshua
 | title = Word learning as Bayesian inference
 | journal = Psychol. Rev.
 | volume = 114 | issue = 2 
 | pages = 245–72
 | date = 2007
 | pmid=17500627
 | doi=10.1037/0033-295X.114.2.245}}</ref><ref name="ref46">{{cite journal
 | last1 =  Chen
 | first1 = Bo
 | last2 = Polatkan
 | first2 = Gungor
 | title = The Hierarchical Beta Process for Convolutional Factor Analysis and Deep Learning
 | journal = Machine Learning . . . 
 | date = 2011
 | url = http://machinelearning.wustl.edu/mlpapers/paper_files/ICML2011Chen_251.pdf}}</ref><ref name="ref47">{{cite journal
 | last1 = Fei-Fei 
 | first1 = Li
 | last2 = Fergus
 | first2 = Rob
 | title = One-shot learning of object categories
 | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
 | volume = 28 | issue = 4 
 | pages = 594–611
 | date = 2006
 | pmid=16566508
 | doi=10.1109/TPAMI.2006.79}}</ref><ref name="ref48">{{cite journal
 | last1 = Rodriguez 
 | first1 = Abel
 | last2 = Dunson
 | first2 = David
 | title = The Nested Dirichlet Process
 | journal = Journal of the American Statistical Association
 | volume = 103 | issue = 483 
 | pages = 1131–1154
 | date = 2008
 | url = http://amstat.tandfonline.com/doi/full/10.1198/016214508000000553
 | doi=10.1198/016214508000000553}}</ref> for [[computer vision]], [[statistics]], and [[cognitive science]].

Compound HD architectures aim to integrate characteristics of both HB and deep networks. The compound HDP-DBM architecture, a ''[[hierarchical Dirichlet process]] (HDP)'' as a hierarchical model, incorporated with DBM architecture. It is a full [[generative model]], generalized from abstract concepts flowing through the layers of the model, which is able to synthesize new examples in novel classes that look ''reasonably natural''. All the levels are learned jointly by maximizing a joint [[Log probability|log-probability]] score.<ref name="ref38">{{cite journal
 | last1 = Ruslan 
 | first1 = Salakhutdinov
 | last2 = Joshua
 | first2 = Tenenbaum
 | title = Learning with Hierarchical-Deep Models
 | journal = IEEE Transactions on Pattern Analysis and Machine Intelligence
 | pages = 1958–71
 | date = 2012
 | doi=10.1109/TPAMI.2012.269
 | volume=35}}</ref>

In a DBM with three hidden layers, the probability of a visible input <math>\boldsymbol{\nu}</math> is:

<math>p(\boldsymbol{\nu}, \psi) = \frac{1}{Z}\sum_h e^{\sum_{ij}W_{ij}^{(1)}\nu_i h_j^1 + \sum_{jl}W_{jl}^{(2)}h_j^{1}h_l^{2}+\sum_{lm}W_{lm}^{(3)}h_l^{2}h_m^{3}},</math>

where <math>\boldsymbol{h} = \{\boldsymbol{h}^{(1)}, \boldsymbol{h}^{(2)}, \boldsymbol{h}^{(3)} \}</math> is the set of hidden units, and <math>\psi = \{\boldsymbol{W}^{(1)}, \boldsymbol{W}^{(2)}, \boldsymbol{W}^{(3)} \} </math> are the model parameters, representing visible-hidden and hidden-hidden symmetric interaction terms.

After a DBM model is learned, we have an undirected model that defines the joint distribution <math>P(\nu, h^1, h^2, h^3)</math>. One way to express what has been learned is the [[Discriminative model|conditional model]] <math>P(\nu, h^1, h^2|h^3)</math> and a prior term <math>P(h^3)</math>.

Here <math>P(\nu, h^1, h^2|h^3)</math> represents a ''conditional'' DBM model, which can be viewed as a two-layer DBM but with bias terms given by the states of <math>h^3</math>:

<math>P(\nu, h^1, h^2|h^3) = \frac{1}{Z(\psi, h^3)}e^{\sum_{ij}W_{ij}^{(1)}\nu_i h_j^1 + \sum_{jl}W_{jl}^{(2)}h_j^{1}h_l^{2}+\sum_{lm}W_{lm}^{(3)}h_l^{2}h_m^{3}}.</math>

=== Deep coding networks ===

There are advantages of a model which can ''actively'' update itself from the context in data. Deep coding network (DPCN) is a [[Predictive modelling|predictive]] coding scheme where top-down information is used to empirically adjust the priors needed for a bottom-up [[inference]] procedure by means of a deep locally connected [[generative model]]. This works by extracting sparse [[Feature (machine learning)|features]] from time-varying observations using a linear dynamical model. Then, a pooling strategy is used to learn invariant feature representations. These units compose to form a deep architecture, and are trained by [[Greedy algorithm|greedy]] layer-wise [[unsupervised learning]]. The layers constitute a kind of [[Markov chain]] such that the states at any layer only depend on the preceding and succeeding layers.

Deep predictive coding network (DPCN)<ref name="ref56">{{cite journal
 | last1 = Chalasani 
 | first1 = Rakesh
 | last2 = Principe
 | first2 = Jose 
 | title = Deep Predictive Coding Networks
 | journal =
 | pages = 1–13
 | date = 2013
 | arxiv=1301.3541
}}</ref> predicts the representation of the layer, by using a top-down approach using the information in upper layer and temporal dependencies from the previous states.

DPCNs can be extended to form a [[Convolutional neural network|convolutional network]].<ref name="ref56" />

=== Multilayer kernel machine ===

Multilayer kernel machines (MKM) as introduced in <ref name="ref59">{{cite journal
 | last1 = Cho 
 | first1 = Youngmin
 | title = Kernel Methods for Deep Learning
 | pages = 1–9
 | date = 2012
 | url = http://cseweb.ucsd.edu/~yoc002/paper/thesis_youngmincho.pdf}}</ref> are a way of learning highly nonlinear functions by iterative application of weakly nonlinear kernels. They use the [[kernel principal component analysis]] (KPCA), in<ref name="ref60">{{cite journal
 | last1 = Scholkopf  
 | first1 = B
 | last2 = Smola
 | first2 = Alexander 
 | title = Nonlinear component analysis as a kernel eigenvalue problem
 | journal = Neural computation
 | volume = (44)
 | date = 1998
 | doi=10.1162/089976698300017467
 | pages=1299–1319}}</ref> as method for [[Unsupervised learning|unsupervised]] greedy layer-wise pre-training step of the deep learning architecture.

Layer <math>l+1</math>-th learns the representation of the previous layer <math>l</math>, extracting the <math>n_l</math> [[Principal component analysis|principal component]] (PC) of the projection layer <math>l</math> output in the feature domain induced by the kernel. For the sake of [[dimensionality reduction]] of the updated representation in each layer, a [[Supervised learning|supervised strategy]] is proposed to select the best informative features among features extracted by KPCA. The process is:

* rank the <math>n_l</math> features according to their [[mutual information]] with the class labels;
* for different values of ''K'' and <math>m_l \in\{1, \ldots, n_l\}</math>, compute the classification error rate of a ''[[K-nearest neighbor]] (K-NN)'' classifier using only the <math>m_l</math> most informative features on a [[validation set]];
* the value of <math>m_l</math> with which the classifier has reached the lowest error rate determines the number of features to retain.

There are some drawbacks in using the KPCA method as the building cells of an MKM.

A more straightforward way to use kernel machines for deep learning was developed by Microsoft researchers for spoken language understanding.<ref name="KDCN">L. Deng, G. Tur, X. He, and D. Hakkani-Tur. "Use of Kernel Deep Convex Networks and End-To-End Learning for Spoken Language Understanding," ''Proc. IEEE Workshop on Spoken Language Technologies'', 2012</ref> The main idea is to use a kernel machine to approximate a shallow neural net with an infinite number of hidden units, then use [[#Deep stacking networks|stacking]] to splice the output of the kernel machine and the raw input in building the next, higher level of the kernel machine. The number of levels in the deep convex network is a hyper-parameter of the overall system, to be determined by cross validation.

=== Deep q-networks ===

This is the latest class of deep learning models, using [[Q-learning]], a form of [[reinforcement learning]], from [[Google DeepMind]]. Preliminary results were presented in 2014, with a paper published in February 2015 in Nature<ref name="DQN">{{cite journal
 | last1 = Mnih 
 | first1 = Volodymyr
 | title = Human-level control through deep reinforcement learning
 | pages = 529–533
 | date = 2015
 | volume=518|display-authors=etal
 | doi=10.1038/nature14236
 | journal=Nature}}</ref> The application discussed in this paper is limited to [[Atari 2600]] gaming, but the implications for other applications are profound.

===Memory networks ===
Integrating external memory with [[artificial neural networks]] dates to early research in [[distributed representations]] <ref name="Hinton, Geoffrey E 1984">Hinton, Geoffrey E. "Distributed representations." (1984)</ref> and [[self-organizing map]]s. For example, in [[sparse distributed memory]] or [[hierarchical temporal memory]], the patterns encoded by neural networks are used as addresses for [[content-addressable memory]], with "neurons" essentially serving as address [[encoder]]s and [[Binary decoder|decoder]]s.

====Long short-term memory==== 
In the 1990s and 2000s, there was much related work with [[long short-term memory]] (LSTM - adding differentiable memory to recurrent functions). For example:
*Differentiable push and pop actions for alternative memory networks called ''neural stack machines''<ref name="S. Das, C.L. Giles p. 79">S. Das, C.L. Giles, G.Z. Sun, "Learning Context Free Grammars: Limitations of a Recurrent Neural Network with an External Stack Memory," Proc. 14th Annual Conf. of the Cog. Sci. Soc., p. 79, 1992.</ref><ref name="Mozer, M. C. 1993 pp. 863-870">Mozer, M. C., & Das, S. (1993). A connectionist symbol manipulator that discovers the structure of context-free languages. NIPS 5 (pp. 863-870).</ref>
*Memory networks where the control network's external differentiable storage is in the fast weights of another network <ref name="ReferenceC">{{cite journal | last1 = Schmidhuber | first1 = J. | year = 1992 | title = Learning to control fast-weight memories: An alternative to recurrent nets | url = | journal = Neural Computation | volume = 4 | issue = 1| pages = 131–139 | doi=10.1162/neco.1992.4.1.131}}</ref>
*LSTM ''"forget gates"'' <ref name="F. Gers, N. Schraudolph 2002">{{cite journal | last1 = Gers | first1 = F. | last2 = Schraudolph | first2 = N. | last3 = Schmidhuber | first3 = J. | year = 2002 | title = Learning precise timing with LSTM recurrent networks | url = | journal = JMLR | volume = 3 | issue = | pages = 115–143 }}</ref>
*Self-referential [[recurrent neural networks]] (RNNs) with special output units for addressing and rapidly manipulating each of the RNN's own weights in differentiable fashion (internal storage) <ref name="J. Schmidhuber pages 191-195">{{Cite conference | author = [[Jürgen Schmidhuber]] | title = An introspective network that can learn to run its own weight change algorithm | booktitle= In Proc. of the Intl. Conf. on Artificial Neural Networks, Brighton | pages = 191–195 | publisher = IEE | year = 1993 | url = ftp://ftp.idsia.ch/pub/juergen/iee93self.ps.gz }}</ref><ref name="Hochreiter, Sepp 2001">{{cite journal | last1 = Hochreiter | first1 = Sepp | last2 = Younger | first2 = A. Steven | last3 = Conwell | first3 = Peter R. | year = 2001 | title = Learning to Learn Using Gradient Descent | url = | journal = ICANN | volume = 2130 | issue = | pages = 87–94 }}</ref>
*Learning to transduce with unbounded memory<ref name="Grefenstette, Edward 1506">Grefenstette, Edward, et al. [http://arxiv.org/pdf/1506.02516.pdf "Learning to Transduce with Unbounded Memory."]  {{arXiv|1506.02516}} (2015).</ref>

====Semantic hashing====
Approaches which represent previous experiences directly and [[Instance-based learning|use a similar experience to form a local model]] are often called [[nearest neighbour]] or [[k-nearest neighbors algorithm|k-nearest neighbors]] methods.<ref>Atkeson, Christopher G., and Stefan Schaal. "Memory-based neural networks for robot learning." Neurocomputing 9.3 (1995): 243-269.</ref> More recently, deep learning was shown to be useful in semantic hashing<ref>Salakhutdinov, Ruslan, and Geoffrey Hinton. [http://www.utstat.toronto.edu/~rsalakhu/papers/sdarticle.pdf "Semantic hashing."] International Journal of Approximate Reasoning 50.7 (2009): 969-978.</ref> where a deep [[graphical model]] the word-count vectors<ref>{{Cite arxiv|last=Le |first=Quoc V. |last2=Mikolov |first2=Tomas |title=Distributed representations of sentences and documents |arxiv=1405.4053 |year=2014}}</ref> obtained from a large set of documents. Documents are mapped to memory addresses in such a way that semantically similar documents are located at nearby addresses. Documents similar to a query document can then be found by simply accessing all the addresses that differ by only a few bits from the address of the query document. Unlike [[sparse distributed memory]] which operates on 1000-bit addresses, semantic hashing works on 32 or 64-bit addresses found in a conventional computer architecture.

====Neural Turing machines====
[[Neural Turing machines]],<ref name="Graves, Alex 1410">Graves, Alex, Greg Wayne, and Ivo Danihelka. "Neural Turing Machines." {{arXiv|1410.5401}} (2014).</ref> developed by [[Google DeepMind]], couple deep neural networks to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a [[Turing machine]] but is differentiable end-to-end, allowing it to be efficiently trained by [[gradient descent]]. Preliminary results demonstrate that neural Turing machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.

====Memory networks====
Memory networks <ref name="Weston, Jason 1410">Weston, Jason, Sumit Chopra, and Antoine Bordes. "Memory networks." {{arXiv|1410.3916}} (2014).</ref><ref>Sukhbaatar, Sainbayar, et al. "End-To-End Memory Networks."  {{arXiv|1503.08895}} (2015).</ref> is another extension to neural networks incorporating [[long-term memory]], which was developed by the [[Facebook]] research team. The long-term memory can be read and written to, with the goal of using it for prediction. These models have been applied in the context of [[question answering]] (QA) where the long-term memory effectively acts as a (dynamic) knowledge base, and the output is a textual response.<ref>Bordes, Antoine, et al. "Large-scale Simple Question Answering with Memory Networks."  {{arXiv|1506.02075}} (2015).</ref>

====Pointer networks====
Deep neural networks can be potentially improved if they get deeper and have fewer parameters, while maintaining trainability. While training extremely deep (e.g. 1-million-layer-deep) neural networks might not be practically feasible, [[CPU]]-like architectures such as pointer networks <ref>Vinyals, Oriol, Meire Fortunato, and Navdeep Jaitly. "Pointer networks." {{arXiv|1506.03134}} (2015).</ref> and neural random-access machines <ref>Kurach,Karol, Andrychowicz, Marcin and  Sutskever,Ilya. "Neural Random-Access Machines." {{arXiv|1511.06392}} (2015).</ref> developed by [[Google Brain]] researchers overcome this limitation by using external [[random-access memory]] as well as adding other components that typically belong to a [[computer architecture]] such as [[Processor register|registers]], [[Arithmetic logic unit|ALU]] and [[Pointer (computer programming)|pointers]]. Such systems operate on [[probability distribution]] vectors stored in memory cells and registers. Thus, the model is fully differentiable and trains end-to-end. The key characteristic of these models is that their depth, the size of their short-term memory, and the number of parameters can be altered independently — unlike models like [[LSTM]], whose number of parameters grows quadratically with memory size.

====Encoder–decoder networks====
An encoder–decoder framework is a framework based on neural networks that aims to map highly [[Structured prediction|structured]] input to highly structured output. It was proposed recently in the context of [[machine translation]],<ref>N. Kalchbrenner and P. Blunsom, "Recurrent continuous translation models," in EMNLP’2013, 2013.</ref><ref>I. Sutskever, O. Vinyals, and Q. V. Le, "Sequence to sequence learning with neural networks," in NIPS’2014, 2014.</ref><ref>K. Cho, B. van Merrienboer, C. Gulcehre, F. Bougares, H. Schwenk, and Y. Bengio, "Learning phrase representations using RNN encoder-decoder for statistical machine translation," in Proceedings of the Empiricial Methods in Natural Language Processing (EMNLP 2014), Oct. 2014</ref> where the input and output are written sentences in two natural languages. In that work, an [[recurrent neural network]] (RNN) or [[convolutional neural network]] (CNN) was used as an encoder to summarize a source sentence, and the summary was decoded using a conditional recurrent neural network [[language model]] to produce the translation.<ref>Cho, Kyunghyun, Aaron Courville, and Yoshua Bengio. "Describing Multimedia Content using Attention-based Encoder--Decoder Networks."  {{arXiv|1507.01053}} (2015).</ref> All these systems have the same building blocks: gated RNNs and CNNs, and trained attention mechanisms.

== Applications ==

=== Automatic speech recognition ===
The results shown in the table below are for automatic speech recognition on the popular [[TIMIT]] data set. This is a common data set used for initial evaluations of deep learning architectures. The entire set contains 630 speakers from eight major [[dialect]]s of [[American English]], where each speaker reads 10 sentences.<ref name="LDCTIMIT">''TIMIT Acoustic-Phonetic Continuous Speech Corpus'' Linguistic Data Consortium, Philadelphia.</ref> Its small size allows many configurations to be tried effectively. More importantly, the TIMIT task concerns phone-sequence recognition, which, unlike word-sequence recognition, allows very weak "language models" and thus the weaknesses in acoustic modeling aspects of speech recognition can be more easily analyzed. Such analysis on TIMIT by Li Deng and collaborators around 2009-2010, contrasting the GMM (and other generative models of speech) vs. DNN models, stimulated early industrial investment in deep learning for speech recognition from small to large scales,<ref name=ReferenceICASSP2013 /><ref name="NIPS2009">NIPS Workshop: Deep Learning for Speech Recognition and Related Applications, Whistler, BC, Canada, Dec. 2009 (Organizers: Li Deng, Geoff Hinton, D. Yu).</ref> eventually leading to pervasive and dominant use in that industry. That analysis was done with comparable performance (less than 1.5% in error rate) between discriminative DNNs and generative models. The error rates listed below, including these early results and measured as percent phone error rates (PER), have been summarized over a time span of the past 20 years:

{| class="wikitable"
|-
! Method !! PER (%)
|-
| Randomly Initialized RNN || 26.1
|-
| Bayesian Triphone GMM-HMM || 25.6
|-
| Hidden Trajectory (Generative) Model|| 24.8
|-
| Monophone Randomly Initialized DNN|| 23.4
|-
| Monophone DBN-DNN|| 22.4
|-
| Triphone GMM-HMM with BMMI Training|| 21.7
|-
| Monophone DBN-DNN on fbank || 20.7
|-
| Convolutional DNN<ref name=CNN-2014>{{cite journal|last1=Abdel-Hamid|first1=O.|title=Convolutional Neural Networks for Speech Recognition|journal=IEEE/ACM Transactions on Audio, Speech, and Language Processing|date=2014|volume=22|issue=10|pages=1533–1545|doi=10.1109/taslp.2014.2339736|display-authors=etal}}</ref>|| 20.0
|-
| Convolutional DNN w. Heterogeneous Pooling|| 18.7
|-
| Ensemble DNN/CNN/RNN <ref name=EnsembleDL>{{cite journal|last1=Deng|first1=L.|last2=Platt|first2=J.|title=Ensemble Deep Learning for Speech Recognition|journal=Proc. Interspeech|date=2014}}</ref>|| 18.2
|-
| Bidirectional LSTM|| 17.9
|}

In 2010, industrial researchers extended deep learning from TIMIT to large vocabulary speech recognition, by adopting large output layers of the DNN based on context-dependent HMM states constructed by [[decision tree]]s.<ref name="Roles2010">{{cite journal|last1=Yu|first1=D.|last2=Deng|first2=L.|title=Roles of Pre-Training and Fine-Tuning in Context-Dependent DBN-HMMs for Real-World Speech Recognition|journal=NIPS Workshop on Deep Learning and Unsupervised Feature Learning|date=2010}}</ref><ref name="ICASSP2013">Deng L., Li, J., Huang, J., Yao, K., Yu, D., Seide, F. et al. Recent Advances in Deep Learning for Speech Research at Microsoft. ICASSP, 2013.</ref> Comprehensive reviews of this development and of the state of the art as of October 2014 are provided in the recent Springer book from Microsoft Research.<ref name="ReferenceA"/> An earlier article<ref>{{cite journal|last1=Deng|first1=L.|last2=Li|first2=Xiao|title=Machine Learning Paradigms for Speech Recognition: An Overview|journal=IEEE Transactions on Audio, Speech, and Language Processing|date=2013|doi=10.1109/tasl.2013.2244083|volume=21|pages=1060–1089}}</ref> reviewed the background of automatic speech recognition and the impact of various machine learning paradigms, including deep learning.

One fundamental principle of deep learning is to do away with hand-crafted [[feature engineering]] and to use raw features. This principle was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear filter-bank features,<ref name="interspeech2010">L. Deng, M. Seltzer, D. Yu, A. Acero, A. Mohamed, and G. Hinton (2010) Binary Coding of Speech Spectrograms Using a Deep Auto-encoder. Interspeech.</ref> showing its superiority over the Mel-Cepstral features which contain a few stages of fixed transformation from spectrograms. The true "raw" features of speech, [[waveform]]s, have more recently been shown to produce excellent larger-scale speech recognition results.<ref name="interspeech2014">Z. Tuske, P. Golik, R. Schlüter and H. Ney (2014). Acoustic Modeling with Deep Neural Networks Using Raw Time Signal for LVCSR. Interspeech.</ref>

Since the initial successful debut of DNNs for speech recognition around 2009-2011, progress (and future directions) can be summarized into eight major areas:<ref name=BOOK2014 /><ref name="interspeech2014Keynote"/><ref name=ReferenceA /> 
* Scaling up/out and speedup DNN training and decoding; 
* Sequence discriminative training of DNNs; 
* Feature processing by deep models with solid understanding of the underlying mechanisms; 
* Adaptation of DNNs and of related deep models; 
* [[Multi-task learning|Multi-task]] and [[Inductive transfer|transfer learning]] by DNNs and related deep models; 
* Convolution neural networks and how to design them to best exploit domain knowledge of speech; 
* Recurrent neural network and its rich LSTM variants; 
* Other types of deep models including tensor-based models and integrated deep generative/discriminative models.

Large-scale automatic speech recognition is the first and most convincing successful case of deep learning in the recent history, embraced by both industry and academia across the board. Between 2010 and 2014, the two major conferences on signal processing and speech recognition, IEEE-ICASSP and Interspeech, have seen a large increase in the numbers of accepted papers in their respective annual conference papers on the topic of deep learning for speech recognition.  More importantly, all major commercial speech recognition systems (e.g., Microsoft Cortana, Xbox, Skype Translator, Google Now, Apple Siri, Baidu and iFlyTek voice search, and a range of Nuance speech products, etc.) are based on deep learning methods.<ref name=BOOK2014 /><ref name="Wire">McMillan, R. "How Skype Used AI to Build Its Amazing New Language Translator", Wire, Dec. 2014.</ref><ref name="Baidu">Hannun et al. (2014) "Deep Speech: Scaling up end-to-end speech recognition", {{arXiv|1412.5567}}.</ref> See also the recent media interview with the CTO of Nuance Communications.<ref name="SPM2015">Ron Schneiderman (2015) "Accuracy, Apps Advance Speech Recognition --- Interviews with Vlad Sejnoha and Li Deng", IEEE Signal Processing Magazine, Jan, 2015.</ref>

The wide-spreading success in speech recognition achieved by 2011 was followed shortly in large-scale image recognition.

=== Image recognition ===
A common evaluation set for image classification is the [[MNIST database]] data set. MNIST is composed of handwritten digits and includes 60000 training examples and 10000 test examples. As with TIMIT, its small size allows multiple configurations to be tested. A comprehensive list of results on this set can be found in.<ref name="YANNMNIST">http://yann.lecun.com/exdb/mnist/.</ref> The current best result on MNIST is an error rate of 0.23%, achieved by Ciresan ''et al.'' in 2012.<ref name="CIRESAN2012">D. Ciresan, U. Meier, J. Schmidhuber., "Multi-column Deep Neural Networks for Image Classification," ''Technical Report No. IDSIA-04-12', 2012.</ref>

The real impact of deep learning in image or object recognition, a major branch of computer vision, was felt in the fall of 2012 after the team of Geoff Hinton and his students won the large-scale ImageNet competition by a significant margin over the then-state-of-the-art shallow machine learning methods. The technology is based on 20-year-old deep convolutional nets, but with much larger scale on a much larger task, since it had been learned that deep learning works well for large-scale speech recognition. In 2013 and 2014, the error rate on the ImageNet task using deep learning was further reduced quickly, following a similar trend in large-scale speech recognition.

As in the ambitious moves from automatic speech recognition toward automatic speech translation and understanding, image classification has recently been extended to the more challenging task of automatic image captioning, in which deep learning is the essential underlying technology.<ref name="1411.4555">Vinyals et al. (2014)."Show and Tell: A Neural Image Caption Generator,"  {{arXiv|1411.4555}}.</ref><ref name="1411.4952">Fang et al. (2014)."From Captions to Visual Concepts and Back," {{arXiv|1411.4952}}.</ref><ref name="1411.2539">Kiros et al. (2014). "Unifying Visual-Semantic Embeddings with Multimodal Neural Language Models," {{arXiv|1411.2539}}.</ref><ref>{{cite journal|last1=Zhong|first1=S.|last2=Liu|first2=Y.|last3=Liu|first3=Y.|title=Bilinear Deep Learning for Image Classification|journal=Proceedings of the 19th ACM International Conference on Multimedia|volume=11|pages=343–352|accessdate=5 April 2015}}</ref>

One example application is a car computer said to be trained with deep learning, which may enable cars to interpret 360° camera views.<ref>[http://www.technologyreview.com/news/533936/nvidia-demos-a-car-computer-trained-with-deep-learning/ Nvidia Demos a Car Computer Trained with "Deep Learning"] (2015-01-06), David Talbot, ''[[MIT Technology Review]]''</ref> Another example is the technology known as [[Facial Dysmorphology Novel Analysis|Facial Dysmorphology Novel Analysis (FDNA)]] used to analyze cases of human malformation connected to a large database of genetic syndromes.

=== Natural language processing ===

Neural networks have been used for implementing [[language model]]s since the early 2000s.<ref name="BENGIO2003">Y. Bengio, R. Ducharme, P. Vincent, C. Jauvin., "A Neural Probabilistic Language Model," ''Journal of Machine Learning Research 3 (2003) 1137–1155', 2003.</ref> Key techniques in this field are [[negative sampling]]<ref name=GoldbergLevy2014>{{cite web|last1=Goldberg|first1=Yoav|last2=Levy|first2=Omar|title=word2vec Explained: Deriving Mikolov et al.’s Negative-Sampling Word-Embedding Method|url=http://arxiv.org/pdf/1402.3722v1.pdf|website=Arxiv|accessdate=26 October 2014}}</ref> and [[word embedding]]. Word embedding, such as ''word2vec'', can be thought of as a representational layer in a deep learning architecture, that transforms an atomic word into a positional representation of the word relative to other words in the dataset; the position is represented as a point in a [[vector space]]. Using a word embedding as an input layer to a recursive neural network (RNN) allows to train the network to parse sentences and phrases using an effective ''compositional vector grammar''. A compositional vector grammar can be thought of as [[probabilistic context free grammar]] (PCFG) implemented by a recursive neural network.<ref name=SocherManning2014>{{cite web|last1=Socher|first1=Richard|last2=Manning|first2=Christopher|title=Deep Learning for NLP|url=http://nlp.stanford.edu/courses/NAACL2013/NAACL2013-Socher-Manning-DeepLearning.pdf|accessdate=26 October 2014}}</ref> Recursive auto-encoders built atop word embeddings have been trained to assess sentence similarity and detect paraphrasing.<ref name=SocherManning2014 /> Deep neural architectures have achieved state-of-the-art results in many natural language processing tasks such as [[Statistical parsing|constituency parsing]],<ref>{{Cite journal|url = http://aclweb.org/anthology/P/P13/P13-1045.pdf|title = Parsing With Compositional Vector Grammars|last = Socher|first = Richard|date = 2013|journal = Proceedings of the ACL 2013 conference|accessdate = |doi = |pmid = |last2 = Bauer|first2 = John|last3 = Manning|first3 = Christopher|last4 = Ng|first4 = Andrew}}</ref> [[sentiment analysis]],<ref>{{Cite journal|url = http://nlp.stanford.edu/~socherr/EMNLP2013_RNTN.pdf|title = Recursive Deep Models for Semantic Compositionality Over a Sentiment Treebank|last = Socher|first = Richard|date = 2013|journal = EMNLP 2013|accessdate = |doi = |pmid = }}</ref> information retrieval,<ref name="CIKM2014">Y. Shen, X. He, J. Gao, L. Deng, and G. Mesnil (2014) " A Latent Semantic Model with Convolutional-Pooling Structure for Information Retrieval," Proc. CIKM.</ref><ref name="CIKM2013">P. Huang, X. He, J. Gao, L. Deng, A. Acero, and L. Heck (2013) "Learning Deep Structured Semantic Models for Web Search using Clickthrough Data," Proc. CIKM.</ref> machine translation,<ref name="NIPS2014">I. Sutskever, O. Vinyals, Q. Le (2014) "Sequence to Sequence Learning with Neural Networks," Proc. NIPS.</ref><ref name="ACL2014">J. Gao, X. He, W. Yih, and L. Deng(2014) "Learning Continuous Phrase Representations for Translation Modeling," Proc. ACL.</ref> contextual entity linking,<ref name="EMNLP2014">J. Gao, P. Pantel, M. Gamon, X. He, L. Deng (2014) "Modeling Interestingness with Deep Neural Networks," Proc. EMNLP.</ref> and others.<ref name="Tutorial2014">J. Gao, X. He, L. Deng (2014) "Deep Learning for Natural Language Processing: Theory and Practice (Tutorial)," CIKM.</ref>

=== Drug discovery and toxicology ===
The [[pharmaceutical industry]] faces the problem that a large percentage of candidate drugs fail to reach the market. These failures of [[chemical compounds]] are caused by insufficient efficacy on the [[Biological target|biomolecular target]] (on-target effect), undetected and undesired interactions with other [[biomolecules]] (off-target effects), or unanticipated [[cytotoxicity|toxic effects]].<ref name="ARROWSMITH2013">{{Cite journal
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}}</ref> In 2012, a team led by George Dahl won the "Merck Molecular Activity Challenge" using multi-task deep neural networks to predict the biomolecular target of a compound.<ref name="MERCK2012">"Announcement of the winners of the Merck Molecular Activity Challenge" https://www.kaggle.com/c/MerckActivity/details/winners.</ref><ref name="DAHL2014">Dahl, G. E.; Jaitly, N.; & Salakhutdinov, R. (2014) "Multi-task Neural Networks for QSAR Predictions," ArXiv, 2014.</ref>  In 2014, Sepp Hochreiter's group used Deep Learning to detect off-target and [[cytotoxicity|toxic effects]] of environmental chemicals in nutrients, household products and drugs and won the "Tox21 Data Challenge" of [[NIH]], [[FDA]] and [[National Center for Advancing Translational Sciences|NCATS]].<ref name="TOX21">"Toxicology in the 21st century Data Challenge" https://tripod.nih.gov/tox21/challenge/leaderboard.jsp</ref><ref name="TOX21Data">"NCATS Announces Tox21 Data Challenge Winners" http://www.ncats.nih.gov/news-and-events/features/tox21-challenge-winners.html</ref> These impressive successes show that deep learning may be superior to other [[virtual screening]] methods.<ref name="Unterthiner2014">Unterthiner, T.; Mayr, A.; Klambauer, G.; Steijaert, M.; Ceulemans, H.; Wegner, J. K.; & Hochreiter, S. (2014) [http://www.bioinf.jku.at/publications/2014/NIPS2014a.pdf "Deep Learning as an Opportunity in Virtual Screening"]. Workshop on Deep Learning and Representation Learning (NIPS2014).</ref><ref name="Unterthiner2015">Unterthiner, T.; Mayr, A.; Klambauer, G.; & Hochreiter, S. (2015) [http://arxiv.org/pdf/1503.01445v1 "Toxicity Prediction using Deep Learning"]. ArXiv, 2015.</ref> Researchers from [[Google]] and [[Stanford University|Stanford]] enhanced deep learning for drug discovery by combining data from a variety of sources.<ref name="Ramsudar2015">Ramsundar, B.; Kearnes, S.; Riley, P.; Webster, D.; Konerding, D.;& Pande, V. (2015) "Massively Multitask Networks for Drug Discovery". ArXiv, 2015.</ref> In 2015, Atomwise introduced AtomNet, the first deep learning neural networks for structure-based rational drug design.<ref>{{cite arXiv|title = AtomNet: A Deep Convolutional Neural Network for Bioactivity Prediction in Structure-based Drug Discovery|arxiv= 1510.02855|date = 2015-10-09|first = Izhar|last = Wallach|first2 = Michael|last2 = Dzamba|first3 = Abraham|last3 = Heifets}}</ref> Subsequently, AtomNet was used to predict novel candidate biomolecules for several disease targets, most notably treatments for the Ebola virus<ref>{{Cite web|title = Toronto startup has a faster way to discover effective medicines|url = http://www.theglobeandmail.com/report-on-business/small-business/starting-out/toronto-startup-has-a-faster-way-to-discover-effective-medicines/article25660419/|website = The Globe and Mail|accessdate = 2015-11-09}}</ref> and multiple sclerosis.<ref>{{Cite web|title = Startup Harnesses Supercomputers to Seek Cures|url = http://ww2.kqed.org/futureofyou/2015/05/27/startup-harnesses-supercomputers-to-seek-cures/|website = KQED Future of You|accessdate = 2015-11-09|language = en-us}}</ref><ref>http://www.theglobeandmail.com/report-on-business/small-business/starting-out/toronto-startup-has-a-faster-way-to-discover-effective-medicines/article25660419/%5d%20and%20multiple%20sclerosis%20%5b/</ref>

=== Customer relationship management ===
Recently success has been reported with application of deep reinforcement learning in direct marketing settings, illustrating suitability of the method for [[Customer relationship management|CRM]] automation. A neural network was used to approximate the value of possible direct marketing actions over the customer state space, defined in terms of [[RFM (customer value)|RFM]] variables. The estimated value function was shown to have a natural interpretation as [[customer lifetime value]].<ref>Tkachenko, Yegor. Autonomous CRM Control via CLV Approximation with Deep Reinforcement Learning in Discrete and Continuous Action Space. (April 8, 2015). arXiv.org: http://arxiv.org/abs/1504.01840</ref>

=== Recommendation systems ===
[[Recommendation systems]] have used deep learning to extract meaningful deep features for latent factor model for content-based recommendation for music.<ref>Van den Oord, Aaron, Sander Dieleman, and Benjamin Schrauwen. "Deep content-based music recommendation." Advances in Neural Information Processing Systems. 2013.</ref> Recently, a more general approach for learning user preferences from multiple domains using mulitview deep learning has been introduced.<ref>Elkahky, Ali Mamdouh, Yang Song, and Xiaodong He. "A Multi-View Deep Learning Approach for Cross Domain User Modeling in Recommendation Systems." Proceedings of the 24th International Conference on World Wide Web. International World Wide Web Conferences Steering Committee, 2015.</ref> The model uses a hybrid collaborative and content-based approach and enhances recommendations in multiple tasks.

=== Bioinformatics === 
Recently, a deep-learning approach based on an [[autoencoder]] [[artificial neural network]] has been used in [[bioinformatics]], to predict [[Gene Ontology]] annotations and gene-function relationships.<ref>[http://dl.acm.org/citation.cfm?id=2649442 Davide Chicco, Peter Sadowski, and Pierre Baldi, "Deep autoencoder neural networks for gene ontology annotation predictions". Proceedings of the 5th ACM Conference on Bioinformatics, Computational Biology, and Health Informatics. ACM, 2014.]</ref>

== Theories of the human brain ==

Computational deep learning is closely related to a class of theories of [[brain development]] (specifically, neocortical development) proposed by [[cognitive neuroscientist]]s in the early 1990s.<ref name="UTGOFF">{{cite journal | last1 = Utgoff | first1 = P. E. | last2 = Stracuzzi | first2 = D. J. | year = 2002 | title = Many-layered learning | url = | journal = Neural Computation | volume = 14 | issue = | pages = 2497–2529 | doi=10.1162/08997660260293319}}</ref> An approachable summary of this work is Elman, et al.'s 1996 book "Rethinking Innateness" <ref name="ELMAN">J. Elman, ''et al.'', "Rethinking Innateness," 1996.</ref> (see also: Shrager and Johnson;<ref name="SHRAGER">{{cite journal | last1 = Shrager | first1 = J. | last2 = Johnson | first2 = MH | year = 1996 | title = Dynamic plasticity influences the emergence of function in a simple cortical array | url = | journal = Neural Networks | volume = 9 | issue = 7| pages = 1119–1129 | doi=10.1016/0893-6080(96)00033-0}}</ref> Quartz and Sejnowski <ref name="QUARTZ">{{cite journal | last1 = Quartz | first1 = SR | last2 = Sejnowski | first2 = TJ | year = 1997 | title = The neural basis of cognitive development: A constructivist manifesto | url = | journal = Behavioral and Brain Sciences | volume = 20 | issue = 4| pages = 537–556 | doi=10.1017/s0140525x97001581}}</ref>). As these developmental theories were also instantiated in computational models, they are technical predecessors of purely computationally motivated deep learning models. These developmental models share the interesting property that various proposed learning dynamics in the brain (e.g., a wave of [[nerve growth factor]]) conspire to support the [[self-organization]] of just the sort of inter-related neural networks utilized in the later, purely computational deep learning models; and such computational neural networks seem analogous to a view of the brain's neocortex as a hierarchy of filters in which each layer captures some of the information in the operating environment, and then passes the remainder, as well as modified base signal, to other layers further up the hierarchy. This process yields a self-organizing stack of [[transducer]]s, well-tuned to their operating environment. As described in The [[New York Times]] in 1995: "...the infant's brain seems to organize itself under the influence of waves of so-called trophic-factors ... different regions of the brain become connected sequentially, with one layer of tissue maturing before another and so on until the whole brain is mature."<ref name="BLAKESLEE">S. Blakeslee., "In brain's early growth, timetable may be critical," ''The New York Times, Science Section'', pp. B5–B6, 1995.</ref>

The importance of deep learning with respect to the evolution and development of human [[cognition]] did not escape the attention of these researchers. One aspect of human development that distinguishes us from our nearest primate neighbors may be changes in the timing of development.<ref name="BUFILL">{BUFILL} E. Bufill, J. Agusti, R. Blesa., "Human neoteny revisited: The case of synaptic plasticity," ''American Journal of Human Biology'', 23 (6), pp. 729–739, 2011.</ref> Among [[primate]]s, the human brain remains relatively plastic until late in the post-natal period, whereas the brains of our closest relatives are more completely formed by birth. Thus, humans have greater access to the complex experiences afforded by being out in the world during the most formative period of brain development. This may enable us to "tune in" to rapidly changing features of the environment that other animals, more constrained by evolutionary structuring of their brains, are unable to take account of. To the extent that these changes are reflected in similar timing changes in hypothesized wave of cortical development, they may also lead to changes in the extraction of information from the stimulus environment during the early self-organization of the brain. Of course, along with this flexibility comes an extended period of immaturity, during which we are dependent upon our caretakers and our community for both support and training. The theory of deep learning therefore sees the coevolution of culture and cognition as a fundamental condition of human evolution.<ref name="SHRAGER2">J. Shrager and M. H. Johnson., "Timing in the development of cortical function: A computational approach," ''In B. Julesz and I. Kovacs (Eds.), Maturational windows and adult cortical plasticity'', 1995.</ref>

== Commercial activities ==
Deep learning is often presented as a step towards realising [[Artificial general intelligence|strong AI]]<ref name="HERN2013">D. Hernandez., "The Man Behind the Google Brain: Andrew Ng and the Quest for the New AI," ''http://www.wired.com/wiredenterprise/2013/05/neuro-artificial-intelligence/all/. Wired'', 10 May 2013.</ref> and thus many organizations have become interested in its use for particular applications. In December 2013, [[Facebook]] hired [[Yann LeCun]] to head its new [[artificial intelligence]] (AI) lab that was to have operations in California, London, and New York. The AI lab will develop deep learning techniques to help Facebook do tasks such as [[Automatic image annotation|automatically tagging uploaded pictures]] with the names of the people in them.<ref name="METZ2013">C. Metz., "Facebook's 'Deep Learning' Guru Reveals the Future of AI," ''http://www.wired.com/wiredenterprise/2013/12/facebook-yann-lecun-qa/. Wired'', 12 December 2013.</ref> Late in 2014, Facebook also hired [[Vladimir Vapnik]], a main developer of the Vapnik–Chervonenkis theory of statistical learning, and co-inventor of the [[support vector machine]] method.<ref name="Vapnik2014">V. Vapnik., "research.facebook.com" ''https://research.facebook.com/researchers/1566384816909948/vladimir-vapnik/'',</ref>

In March 2013, [[Google]] hired [[Geoffrey Hinton]] and two of his graduate students, Alex Krizhevsky and Ilya Sutskever. Their work was to focus on both improving existing machine learning products at Google and help deal with the growing amount of data Google has. Google also bought Hinton's company, DNNresearch.

In 2014, Google also bought [[DeepMind Technologies]], a British start-up that developed a system capable of learning how to play [[Atari]] video games using only raw pixels as data input.  In 2015 they demonstrated [[AlphaGo]] system which achieved one of the long-standing "grand challenges" of AI by learning the game of [[Go (game)|Go]] well enough to beat a human professional Go player.<ref>{{Cite web|title = Google AI algorithm masters ancient game of Go|url = http://www.nature.com/news/google-ai-algorithm-masters-ancient-game-of-go-1.19234|website = Nature News & Comment|access-date = 2016-01-30}}</ref><ref>{{Cite journal|title = Mastering the game of Go with deep neural networks and tree search|url = http://www.nature.com/nature/journal/v529/n7587/full/nature16961.html|journal = Nature|date = 2016-01-28|issn = 0028-0836|pages = 484–489|volume = 529|issue = 7587|doi = 10.1038/nature16961|language = en|first = David|last = Silver|first2 = Aja|last2 = Huang|first3 = Chris J.|last3 = Maddison|first4 = Arthur|last4 = Guez|first5 = Laurent|last5 = Sifre|first6 = George|last6 = van den Driessche|first7 = Julian|last7 = Schrittwieser|first8 = Ioannis|last8 = Antonoglou|first9 = Veda|last9 = Panneershelvam}}</ref><ref>{{Cite web|title = A Google DeepMind Algorithm Uses Deep Learning and More to Master the Game of Go {{!}} MIT Technology Review|url = http://www.technologyreview.com/news/546066/googles-ai-masters-the-game-of-go-a-decade-earlier-than-expected/|website = MIT Technology Review|access-date = 2016-01-30}}</ref>

Also in 2014, Microsoft established The Deep Learning Technology Center in its MSR division, amassing deep learning experts for application-focused activities.

[[Baidu]] hired [[Andrew Ng]] to head its new Silicon Valley-based research lab focusing on deep learning.

In 2015, [[Blippar]] demonstrated a new mobile [[augmented reality]] application that makes use of deep learning to recognize objects in real time.<ref>{{Cite web|title=Blippar Demonstrates New Real-Time Augmented Reality App|url=http://techcrunch.com/2015/12/08/blippar-demonstrates-new-real-time-augmented-reality-app/|website=TechCrunch}}</ref>

== Criticism and comment ==

Given the far-reaching implications of artificial intelligence coupled with the realization that deep learning is emerging as one of its most powerful techniques, the subject is understandably attracting both criticism and comment, and in some cases from outside the field of computer science itself.

A main criticism of deep learning concerns the lack of theory surrounding many of the methods. Most of the learning in deep architectures is just some form of [[gradient descent]]. While gradient descent has been understood for a while now, the theory surrounding other algorithms, such as contrastive divergence is less clear (i.e., Does it converge? If so, how fast? What is it approximating?). Deep learning methods are often looked at as a black box, with most confirmations done empirically, rather than theoretically.

Others point out that deep learning should be looked at as a step towards realizing strong AI, not as an all-encompassing solution. Despite the power of deep learning methods, they still lack much of the functionality needed for realizing this goal entirely. Research psychologist [[Gary Marcus]] has noted that:<blockquote>"Realistically, deep learning is only part of the larger challenge of building intelligent machines. Such techniques lack ways of representing [[causality|causal relationships]] (...) have no obvious ways of performing [[inference|logical inferences]], and they are also still a long way from integrating abstract knowledge, such as information about what objects are, what they are for, and how they are typically used. The most powerful A.I. systems, like [[Watson (computer)|Watson]] (...) use techniques like deep learning as just one element in a very complicated ensemble of techniques, ranging from the statistical technique of [[Bayesian inference]] to [[deductive reasoning]]." <ref name="MARCUS">G. Marcus., "Is "Deep Learning" a Revolution in Artificial Intelligence?" ''The New Yorker'', 25 November 2012.</ref></blockquote>To the extent that such a viewpoint implies, without intending to, that deep learning will ultimately constitute nothing more than the primitive discriminatory levels of a comprehensive future machine intelligence, a recent pair of speculations regarding art and artificial intelligence<ref>{{cite web |url=http://artent.net/2015/03/27/art-and-artificial-intelligence-by-g-w-smith/|author=Smith, G. W.|date=March 27, 2015|title=Art and Artificial Intelligence|publisher=ArtEnt|accessdate=March 27, 2015}}</ref> offers an alternative and more expansive outlook.  The first such speculation is that it might be possible to train a machine vision stack to perform the sophisticated task of discriminating between "old master" and amateur figure drawings; and the second is that such a sensitivity might in fact represent the rudiments of a non-trivial machine empathy.  It is suggested, moreover, that such an eventuality would be in line with anthropology, which identifies a concern with aesthetics as a key element of [[behavioral modernity]] (eg, in <ref>{{cite web |url=https://www.newscientist.com/article/dn1528-tools-point-to-african-origin-for-human-behaviour/ |author=Knight, Will |date=November 7, 2001 |title=Tools point to African origin for human behaviour |publisher=New Scientist |accessdate=October 7, 2015 }}</ref>).

In further reference to the idea that a significant degree of artistic sensitivity might inhere within relatively low levels, whether biological or digital, of the cognitive hierarchy, a published series of graphic representations of the internal states of deep (20-30 layers) neural networks attempting to discern within essentially random data the images on which they were trained<ref>{{cite web |url=http://googleresearch.blogspot.co.uk/2015/06/inceptionism-going-deeper-into-neural.html|author=Alexander Mordvintsev, Christopher Olah, and Mike Tyka|date=June 17, 2015|title=Inceptionism: Going Deeper into Neural Networks|publisher=Google Research Blog|accessdate=June 20, 2015}}</ref> seem to demonstrate a striking visual appeal in light of the remarkable level of public attention which this work captured: the original research notice received well over 1,000 comments, and the [[The Guardian]] coverage<ref>{{cite web |url=http://www.theguardian.com/technology/2015/jun/18/google-image-recognition-neural-network-androids-dream-electric-sheep|author=Alex Hern|date=June 18, 2015|title=Yes, androids do dream of electric sheep|publisher=The Guardian|accessdate=June 20, 2015}}</ref> was for a time the most frequently accessed article on that newspaper's web site.

Some currently popular and successful deep learning architectures display certain problematic behaviors,<ref name=goertzel>Ben Goertzel. Are there Deep Reasons Underlying the Pathologies of Today's Deep Learning Algorithms? (2015) Url: http://goertzel.org/DeepLearning_v1.pdf</ref> such as confidently classifying random data as belonging to a familiar category of nonrandom images<ref>Nguyen, Anh, Jason Yosinski, and Jeff Clune. "Deep Neural Networks are Easily Fooled: High Confidence Predictions for Unrecognizable Images."  {{arXiv|1412.1897}} (2014).</ref> and misclassifying minuscule perturbations of correctly classified images.<ref>Szegedy, Christian, et al. "Intriguing properties of neural networks."  {{arXiv|1312.6199}} (2013).</ref> The creator of [[OpenCog]], [[Ben Goertzel]], hypothesized<ref name="goertzel"/> that these behaviors are due to limitations in the internal representations learned by these architectures, and that these limitations would inhibit integration of these architectures into heterogeneous multi-component [[Artificial general intelligence|AGI]] architectures. It is suggested that these issues can be worked around by developing deep learning architectures that internally form states homologous to image-grammar<ref>{{cite journal | last1 = Zhu | first1 = S.C. | last2 = Mumford | first2 = D. | year = | title = A stochastic grammar of images | url = | journal = Found. Trends Comput. Graph. Vis. | volume = 2 | issue = 4| pages = 259–362 | doi = 10.1561/0600000018 }}</ref> decompositions of observed entities and events.<ref name="goertzel"/> Learning a [[grammar]] (visual or linguistic) from training data would be equivalent to restricting the system to [[commonsense reasoning]] which operates on concepts in terms of [[Production (computer science)|production rules]] of the grammar, and is a basic goal of both human language acquisition <ref>Miller, G. A., and N. Chomsky. "Pattern conception." Paper for Conference on pattern detection, University of Michigan. 1957.</ref> and AI. (See also [[Grammar induction]].<ref>Jason Eisner, Deep Learning of Recursive Structure: Grammar Induction, http://techtalks.tv/talks/deep-learning-of-recursive-structure-grammar-induction/58089/</ref>)

== Software libraries ==

* Caffe — A deep learning framework specializing in image recognition.
* CNTK — open source<ref>[http://blogs.microsoft.com/next/2016/01/25/microsoft-releases-cntk-its-open-source-deep-learning-toolkit-on-github/ CNTK on Github]</ref> deep-learning Computational Network Toolkit by Microsoft Research.
* ConvNetJS — A [[Javascript]] library for training deep learning models. It contains online demos.
* [[Deeplearning4j]] — An open-source<ref>[https://github.com/deeplearning4j/deeplearning4j Deeplearning4j on Github]</ref> deep-learning library written for Java with LSTMs and convolutional networks. It provides parallelization with CPUs and GPUs.
* [[Gensim]] — A toolkit for natural language processing implemented in the Python programming language.
* Keras — deep learning framework capable of running on top of either TensorFlow or Theano.
* NVIDIA cuDNN — A GPU-accelerated library of primitives for deep neural networks.
* [[OpenNN]] — An open source C++ library which implements deep neural networks and provides parallelization with CPUs.
* [[TensorFlow]]  — Google's open source machine learning library in C++ and Python with APIs for both. It provides parallelization with CPUs and GPUs.<ref name="DeanMonga2015">{{cite web|last1=Dean|first1=Jeff|last2=Monga|first2=Rajat|authorlink1=Jeff Dean (computer scientist)|title=TensorFlow: Large-scale machine learning on heterogeneous systems|url=http://download.tensorflow.org/paper/whitepaper2015.pdf|website=TensorFlow.org|publisher=Google Research|accessdate=10 November 2015|date=November 9, 2015|display-authors=etal}}</ref>
* [[Theano (software)|Theano]] — An open source machine learning library for Python. 
* [[Torch (machine learning)|Torch]] — An open source software library for machine learning based on the Lua programming language.

==See also==
* [[Sparse coding]]
* [[Compressed Sensing]]
* [[Connectionism]]
* [[Applications of artificial intelligence]]
* [[List of artificial intelligence projects]]
* [[Reservoir computing]]
* [[Liquid state machine]]
* [[Echo state network]]
* [[Comparison of deep learning software]]
* [[List of datasets for machine learning research]]

==References==
{{Reflist|30em}}

==External links==
* [http://www.teglor.com/b/deep-learning-libraries-language-cm569/ Deep Learning Libraries by Language]
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