deep learning

Deep learning (also known as deep structured learning) is part of a broader family of machine learning methods based on artificial neural networks with representation learning. Learning can be supervised, semi-supervised or unsupervised.

Deep-learning architectures such as deep neural networks, deep belief networks, deep reinforcement learning, 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.

Artificial neural networks (ANNs) were inspired by information processing and distributed communication nodes in biological systems. ANNs have various differences from biological brains. Specifically, artificial neural networks tend to be static and symbolic, while the biological brain of most living organisms is dynamic (plastic) and analog.

The adjective "deep" in deep learning refers to the use of multiple layers in the network. Early work showed that a linear perceptron cannot be a universal classifier, but that a network with a nonpolynomial activation function with one hidden layer of unbounded width can. Deep learning is a modern variation which is concerned with an unbounded number of layers of bounded size, which permits practical application and optimized implementation, while retaining theoretical universality under mild conditions. In deep learning the layers are also permitted to be heterogeneous and to deviate widely from biologically informed connectionist models, for the sake of efficiency, trainability and understandability, hence the "structured" part.

Definition

Deep learning is a class of machine learning algorithms that uses multiple layers to progressively extract higher-level features from the raw input. For example, in image processing, lower layers may identify edges, while higher layers may identify the concepts relevant to a human such as digits or letters or faces.

Overview

Most modern deep learning models are based on artificial neural networks, specifically convolutional neural networks (CNN)s, 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.

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.

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. 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. 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.

Deep learning architectures can be constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance.

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.

Interpretations

Deep neural networks are generally interpreted in terms of the universal approximation theoremLu, Z., Pu, H., Wang, F., Hu, Z., & Wang, L. (2017)
The Expressive Power of Neural Networks: A View from the Width
. Neural Information Processing Systems, 6231-6239. or probabilistic inference.

The classic universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions. In 1989, the first proof was published by George Cybenko for sigmoid activation functions and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik. Recent work also showed that universal approximation also holds for non-bounded activation functions such as the rectified linear unit.

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. 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.

The probabilistic interpretation derives from the field of machine learning. It features inference, as well as the optimization concepts of training and testing, related to fitting and generalization, respectively. More specifically, the probabilistic interpretation considers the activation nonlinearity as a cumulative distribution function. The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks. The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop.

History

Some sources point out that Frank Rosenblatt developed and explored all of the basic ingredients of the deep learning systems of today. He described it in his book "Principles of Neurodynamics: Perceptrons and the Theory of Brain Mechanisms", published by Cornell Aeronautical Laboratory, Inc., Cornell University in 1962.

The first general, working learning algorithm for supervised, deep, feedforward, multilayer perceptrons was published by Alexey Ivakhnenko and Lapa in 1967. A 1971 paper described a deep network with eight layers trained by the group method of data handling. Other deep learning working architectures, specifically those built for computer vision, began with the Neocognitron introduced by Kunihiko Fukushima in 1980.

The term ''Deep Learning'' was introduced to the machine learning community by Rina Dechter in 1986, Rina Dechter (1986). Learning while searching in constraint-satisfaction problems. University of California, Computer Science Department, Cognitive Systems Laborator
Online
and to artificial neural networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons.Igor Aizenberg, Naum N. Aizenberg, Joos P.L. Vandewalle (2000). Multi-Valued and Universal Binary Neurons: Theory, Learning and Applications. Springer Science & Business Media.

In 1989, Yann LeCun et al. applied the standard backpropagation algorithm, which had been around as the reverse mode of automatic differentiation since 1970, Seppo Linnainmaa (1970). The representation of the cumulative rounding error of an algorithm as a Taylor expansion of the local rounding errors. Master's Thesis (in Finnish), Univ. Helsinki, 6-7. to a deep neural network with the purpose of recognizing handwritten ZIP codes on mail. While the algorithm worked, training required 3 days.LeCun ''et al.'', "Backpropagation Applied to Handwritten Zip Code Recognition," ''Neural Computation'', 1, pp. 541–551, 1989.

Independently in 1988, Wei Zhang et al. applied the backpropagation algorithm to a convolutional neural network (a simplified Neocognitron by keeping only the convolutional interconnections between the image feature layers and the last fully connected layer) for alphabets recognition and also proposed an implementation of the CNN with an optical computing system. Subsequently, Wei Zhang, et al. modified the model by removing the last fully connected layer and applied it for medical image object segmentation in 1991 and breast cancer detection in mammograms in 1994.

In 1994, André de Carvalho, together with Mike Fairhurst and David Bisset, published experimental results of a multi-layer boolean neural network, also known as a weightless neural network, composed of a 3-layers self-organising feature extraction neural network module (SOFT) followed by a multi-layer classification neural network module (GSN), which were independently trained. Each layer in the feature extraction module extracted features with growing complexity regarding the previous layer.

In 1995, Brendan Frey demonstrated that it was possible to train (over two days) a network containing six fully connected layers and several hundred hidden units using the wake-sleep algorithm, co-developed with Peter Dayan and Hinton. Many factors contribute to the slow speed, including the vanishing gradient problem analyzed in 1991 by Sepp Hochreiter.S. Hochreiter.,
Untersuchungen zu dynamischen neuronalen Netzen
," ''Diploma thesis. Institut f. Informatik, Technische Univ. Munich. Advisor: J. Schmidhuber'', 1991.

Since 1997, Sven Behnke extended the feed-forward hierarchical convolutional approach in the Neural Abstraction Pyramid by lateral and backward connections in order to flexibly incorporate context into decisions and iteratively resolve local ambiguities.

Simpler models that use task-specific handcrafted features such as Gabor filters and support vector machines (SVMs) were a popular choice in the 1990s and 2000s, because of artificial neural network's (ANN) computational cost and a lack of understanding of how the brain wires its biological networks.

Both shallow and deep learning (e.g., recurrent nets) of ANNs have been explored for many years. These methods never outperformed non-uniform internal-handcrafting Gaussian mixture model/Hidden Markov model (GMM-HMM) technology based on generative models of speech trained discriminatively. Key difficulties have been analyzed, including gradient diminishing and weak temporal correlation structure in neural predictive models. Additional difficulties were the lack of training data and limited computing power.

Most speech recognition researchers moved away from neural nets to pursue generative modeling. An exception was at SRI International in the late 1990s. Funded by the US government's NSA and DARPA, SRI studied deep neural networks in speech and speaker recognition. The speaker recognition team led by Larry Heck reported significant success with deep neural networks in speech processing in the 1998 National Institute of Standards and Technology Speaker Recognition evaluation. The SRI deep neural network was then deployed in the Nuance Verifier, representing the first major industrial application of deep learning.

The principle of elevating "raw" features over hand-crafted optimization was first explored successfully in the architecture of deep autoencoder on the "raw" spectrogram or linear filter-bank features in the late 1990s, showing its superiority over the Mel-Cepstral features that contain stages of fixed transformation from spectrograms. The raw features of speech, waveforms, later produced excellent larger-scale results.

Many aspects of speech recognition were taken over by a deep learning method called long short-term memory (LSTM), a recurrent neural network published by Hochreiter and Schmidhuber in 1997. LSTM RNNs avoid the vanishing gradient problem and can learn "Very Deep Learning" tasks that require memories of events that happened thousands of discrete time steps before, which is important for speech. In 2003, LSTM started to become competitive with traditional speech recognizers on certain tasks. Later it was combined with connectionist temporal classification (CTC) in stacks of LSTM RNNs.Santiago Fernandez, Alex Graves, and Jürgen Schmidhuber (2007)
An application of recurrent neural networks to discriminative keyword spotting
. Proceedings of ICANN (2), pp. 220–229. In 2015, Google's speech re