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Deep learning is the subset of machine learning methods based on artificial neural networks with representation learning. The adjective "deep" refers to the use of multiple layers in the network. Methods used can be either supervised, semi-supervised or unsupervised.[2]

Deep-learning architectures such as deep neural networks, deep belief networks, recurrent neural networks, convolutional neural networks and transformers have been applied to fields including computer vision, speech recognition, natural language processing, machine translation, bioinformatics, drug design, medical image analysis, climate science, material inspection and board game programs, where they have produced results comparable to and in some cases surpassing human expert performance.[3][4][5]

From another angle to view deep learning, deep learning refers to "computer-simulate" or "automate" human learning processes from a source (e.g., an image of dogs) to a learned object (dogs). Therefore, a notion coined as "deeper" learning or "deepest" learning[10] makes sense. The deepest learning refers to the fully automatic learning from a source to a final learned object. A deeper learning thus refers to a mixed learning process: a human learning process from a source to a learned semi-object, followed by a computer learning process from the human learned semi-object to a final learned object.

Most modern deep learning models are based on multi-layered artificial neural networks such as convolutional neural networks and transformers, although they can also include propositional formulas or latent variables organized layer-wise in deep generative models such as the nodes in deep belief networks and deep Boltzmann machines.[11]

In deep learning, each level learns to transform its input data into a slightly more abstract and composite representation. In an image recognition application, the raw input may be a matrix of pixels; the first representational layer may abstract the pixels and encode edges; the second layer may compose and encode arrangements of edges; the third layer may encode a nose and eyes; and the fourth layer may recognize that the image contains a face. Importantly, a deep learning process can learn which features to optimally place in which level on its own. This does not eliminate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction.[12][13]

The word "deep" in "deep learning" refers to the number of layers through which the data is transformed. More precisely, deep learning systems have a substantial credit assignment path (CAP) depth. The CAP is the chain of transformations from input to output. CAPs describe potentially causal connections between input and output. For a feedforward neural network, the depth of the CAPs is that of the network and is the number of hidden layers plus one (as the output layer is also parameterized). For recurrent neural networks, in which a signal may propagate through a layer more than once, the CAP depth is potentially unlimited.[14] No universally agreed-upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth higher than 2. CAP of depth 2 has been shown to be a universal approximator in the sense that it can emulate any function.[15] Beyond that, more layers do not add to the function approximator ability of the network. Deep models (CAP > 2) are able to extract better features than shallow models and hence, extra layers help in learning the features effectively.

For supervised learning tasks, deep learning methods eliminate feature engineering, by translating the data into compact intermediate representations akin to principal components, and derive layered structures that remove redundancy in representation.

Deep learning algorithms can be applied to unsupervised learning tasks. This is an important benefit because unlabeled data are more abundant than the labeled data. Examples of deep structures that can be trained in an unsupervised manner are deep belief networks.[12][17]

Machine learning models are now adept at identifying complex patterns in financial market data. Due to the benefits of artificial intelligence, investors are increasingly utilizing deep learning techniques to forecast and analyze trends in stock and foreign exchange markets.[18]

The universal approximation theorem for deep neural networks concerns the capacity of networks with bounded width but the depth is allowed to grow. Lu et al.[23] proved that if the width of a deep neural network with ReLU activation is strictly larger than the input dimension, then the network can approximate any Lebesgue integrable function; if the width is smaller or equal to the input dimension, then a deep neural network is not a universal approximator.

Charles Tappert writes that Frank Rosenblatt developed and explored all of the basic ingredients of the deep learning systems of today,[33] referring to Rosenblatt's 1962 book[34] which introduced multilayer perceptron (MLP) with 3 layers: an input layer, a hidden layer with randomized weights that did not learn, and an output layer. It also introduced variants, including a version with four-layer perceptrons where the last two layers have learned weights (and thus a proper multilayer perceptron) (,[34] section 16). In addition, term deep learning was proposed in 1986 by Rina Dechter Dechter (1986) although the history of its appearance is apparently more complicated.[35]

The first general, working learning algorithm for supervised, deep, feedforward, multilayer perceptrons was published by Alexey Ivakhnenko and Lapa in 1967.[36] A 1971 paper described a deep network with eight layers trained by the group method of data handling.[37]

The first deep learning multilayer perceptron trained by stochastic gradient descent[38] was published in 1967 by Shun'ichi Amari.[39][31] In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned internal representations to classify non-linearily separable pattern classes.[31] In 1987 Matthew Brand reported that wide 12-layer nonlinear perceptrons could be fully end-to-end trained to reproduce logic functions of nontrivial circuit depth via gradient descent on small batches of random input/output samples, but concluded that training time on contemporary hardware (sub-megaflop computers) made the technique impractical, and proposed using fixed random early layers as an input hash for a single modifiable layer.[40] Instead, subsequent developments in hardware and hyperparameter tunings have made end-to-end stochastic gradient descent the currently dominant training technique.

Deep learning architectures for convolutional neural networks (CNNs) with convolutional layers and downsampling layers began with the Neocognitron introduced by Kunihiko Fukushima in 1980.[49] In 1969, he also introduced the ReLU (rectified linear unit) activation function.[26][31] The rectifier has become the most popular activation function for CNNs and deep learning in general.[50] CNNs have become an essential tool for computer vision.

In the 1980s, backpropagation did not work well for deep learning with long credit assignment paths. To overcome this problem, Jrgen Schmidhuber (1992) proposed a hierarchy of RNNs pre-trained one level at a time by self-supervised learning.[60] It uses predictive coding to learn internal representations at multiple self-organizing time scales. This can substantially facilitate downstream deep learning. The RNN hierarchy can be collapsed into a single RNN, by distilling a higher level chunker network into a lower level automatizer network.[60][31] In 1993, a chunker solved a deep learning task whose depth exceeded 1000.[61]

In 1991, Jrgen Schmidhuber also published adversarial neural networks that contest with each other in the form of a zero-sum game, where one network's gain is the other network's loss.[69][70][71] The first network is a generative model that models a probability distribution over output patterns. The second network learns by gradient descent to predict the reactions of the environment to these patterns. This was called "artificial curiosity". In 2014, this principle was used in a generative adversarial network (GAN) by Ian Goodfellow et al.[72] Here the environmental reaction is 1 or 0 depending on whether the first network's output is in a given set. This can be used to create realistic deepfakes.[73] Excellent image quality is achieved by Nvidia's StyleGAN (2018)[74] based on the Progressive GAN by Tero Karras et al.[75] Here the GAN generator is grown from small to large scale in a pyramidal fashion.

Sepp Hochreiter's diploma thesis (1991)[76] was called "one of the most important documents in the history of machine learning" by his supervisor Schmidhuber.[31] It not only tested the neural history compressor,[60] but also identified and analyzed the vanishing gradient problem.[76][77] Hochreiter proposed recurrent residual connections to solve this problem. This led to the deep learning method called long short-term memory (LSTM), published in 1997.[78] LSTM recurrent neural networks can learn "very deep learning" tasks[14] with long credit assignment paths that require memories of events that happened thousands of discrete time steps before. The "vanilla LSTM" with forget gate was introduced in 1999 by Felix Gers, Schmidhuber and Fred Cummins.[79] LSTM has become the most cited neural network of the 20th century.[31]In 2015, Rupesh Kumar Srivastava, Klaus Greff, and Schmidhuber used LSTM principles to create the Highway network, a feedforward neural network with hundreds of layers, much deeper than previous networks.[80][81] 7 months later, Kaiming He, Xiangyu Zhang; Shaoqing Ren, and Jian Sun won the ImageNet 2015 competition with an open-gated or gateless Highway network variant called Residual neural network.[82] This has become the most cited neural network of the 21st century.[31] 006ab0faaa

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