Deep learning

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Deep learning (also known as deep structured learning or hierarchical learning) is part of a broader family of machine learning methods based on learning data representations, as opposed to task-specific algorithms. Learning can be supervised, semi-supervised or unsupervised.

Deep learning architectures such as deep neural networks, deep belief networks and recurrent neural networks have been applied to fields including computer vision, speech recognition, natural language processing, audio recognition, social network filtering, machine translation, bioinformatics, drug design and board game programs, where they have produced results comparable to and in some cases superior to human experts.

Deep learning models are vaguely inspired by information processing and communication patterns in biological nervous systems yet have various differences from the structural and functional properties of biological brains, which make them incompatible with neuroscience evidences.^[7][8][9]

Definition

Deep learning is a class of machine learning algorithms that:^{[10](pp199–200)}

• use a cascade of multiple layers of nonlinear processing units for feature extraction and transformation. Each successive layer uses the output from the previous layer as input.
• learn in supervised (e.g., classification) and/or unsupervised (e.g., pattern analysis) manners.
• learn multiple levels of representations that correspond to different levels of abstraction; the levels form a hierarchy of concepts.

Overview

Most modern deep learning models are based on an artificial neural network, 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. (Of course, this does not completely obviate the need for hand-tuning; for example, varying numbers of layers and layer sizes can provide different degrees of abstraction.)^[1][12]

The "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.^[2] No universally agreed upon threshold of depth divides shallow learning from deep learning, but most researchers agree that deep learning involves CAP depth > 2. CAP of depth 2 has been shown to be a universal approximator in the sense that it can emulate any function.^{[citation needed]} Beyond that more layers do not add to the function approximator ability of the network. The extra layers help in learning features.

Deep learning architectures are often constructed with a greedy layer-by-layer method. Deep learning helps to disentangle these abstractions and pick out which features improve performance.^[1]

For supervised learning tasks, deep learning methods obviate 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 labeled data. Examples of deep structures that can be trained in an unsupervised manner are neural history compressors^[13] and deep belief networks.^[1][14]

Interpretations

Deep neural networks are generally interpreted in terms of the universal approximation theorem^{[15][16][17][18][19]} or probabilistic inference.

The universal approximation theorem concerns the capacity of feedforward neural networks with a single hidden layer of finite size to approximate continuous functions.^{[15][16][17][18][19]} In 1989, the first proof was published by George Cybenko for sigmoid activation functions^[16] and was generalised to feed-forward multi-layer architectures in 1991 by Kurt Hornik.^[17]

The probabilistic interpretation^[20] derives from the field of machine learning. It features inference,^{[10][11][1][2][14][20]} 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.^[20] The probabilistic interpretation led to the introduction of dropout as regularizer in neural networks.^[22] The probabilistic interpretation was introduced by researchers including Hopfield, Widrow and Narendra and popularized in surveys such as the one by Bishop.^[23]

History

The term Deep Learning was introduced to the machine learning community by Rina Dechter in 1986,^[24][13] and to Artificial Neural Networks by Igor Aizenberg and colleagues in 2000, in the context of Boolean threshold neurons.^[25][26]

The first general, working learning algorithm for supervised, deep, feedforward, multilayer perceptrons was published by Alexey Ivakhnenko and Lapa in 1965.^[27] A 1971 paper described a deep network with 8 layers trained by the group method of data handling algorithm.^[28]

Other deep learning working architectures, specifically those built for computer vision, began with the Neocognitron introduced by Kunihiko Fukushima in 1980.^[29] In 1989, Yann LeCun et al. applied the standard backpropagation algorithm, which had been around as the reverse mode of automatic differentiation since 1970,^{[30][31][32][33]} to a deep neural network with the purpose of recognizing handwritten ZIP codes on mail. While the algorithm worked, training required 3 days.^[34]

By 1991 such systems were used for recognizing isolated 2-D hand-written digits, while recognizing 3-D objects was done by matching 2-D images with a handcrafted 3-D object model. Weng et al. suggested that a human brain does not use a monolithic 3-D object model and in 1992 they published Cresceptron,^[35][36][37] a method for performing 3-D object recognition in cluttered scenes. Cresceptron is a cascade of layers similar to Neocognitron. But while Neocognitron required a human programmer to hand-merge features, Cresceptron learned an open number of features in each layer without supervision, where each feature is represented by a convolution kernel. Cresceptron 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.

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.^[38]

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.^[39] Many factors contribute to the slow speed, including the vanishing gradient problem analyzed in 1991 by Sepp Hochreiter.^[40][41]

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 ANNs' 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.^[42][43][44] 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.^[45] Key difficulties have been analyzed, including gradient diminishing^[40] and weak temporal correlation structure in neural predictive models.^[46][47] 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. Heck's speaker recognition team achieved the first significant success with deep neural networks in speech processing in the 1998 National Institute of Standards and Technology Speaker Recognition evaluation.^[48] While SRI experienced success with deep neural networks in speaker recognition, they were unsuccessful in demonstrating similar success in speech recognition. 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,^[48] 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.^[49]

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.^[50] LSTM RNNs avoid the vanishing gradient problem and can learn "Very Deep Learning" tasks^[2] 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.^[51] Later it was combined with connectionist temporal classification (CTC)^[52] in stacks of LSTM RNNs.^[53] In 2015, Google's speech recognition reportedly experienced a dramatic performance jump of 49% through CTC-trained LSTM, which they made available through Google Voice Search.^[54]

In 2006, publications by Geoff Hinton, Ruslan Salakhutdinov, Osindero and Teh^{[55] [56][57]} 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 restricted Boltzmann machine, then fine-tuning it using supervised backpropagation.^[58] The papers referred to learning for deep belief nets.

Deep learning is part of 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 (image classification), as well as a range of large-vocabulary speech recognition tasks have steadily improved.^[59][60][61] Convolutional neural networks (CNNs) were superseded for ASR by CTC^[52] for LSTM.^{[50][54][62][63][64][65][66]} but are more successful in computer vision.

The impact of deep learning in industry began in the early 2000s, when CNNs already processed an estimated 10% to 20% of all the checks written in the US, according to Yann LeCun.^[67] Industrial applications of deep learning to large-scale speech recognition started around 2010.

The 2009 NIPS Workshop on Deep Learning for Speech Recognition^[68] was motivated by the limitations of deep generative models of speech, and the possibility that given more capable hardware and large-scale data sets that deep neural nets (DNN) might become practical. It was believed that pre-training DNNs using generative models of deep belief nets (DBN) would overcome the main difficulties of neural nets.^[69] However, it was discovered that replacing pre-training with large amounts of training data for straightforward backpropagation when using DNNs with large, context-dependent output layers produced error rates dramatically lower than then-state-of-the-art Gaussian mixture model (GMM)/Hidden Markov Model (HMM) and also than more-advanced generative model-based systems.^[59][70] The nature of the recognition errors produced by the two types of systems was characteristically different,^[71][68] offering technical insights into how to integrate deep learning into the existing highly efficient, run-time speech decoding system deployed by all major speech recognition systems.^[10][72][73] Analysis around 2009-2010, contrasted the GMM (and other generative speech models) vs. DNN models, stimulated early industrial investment in deep learning for speech recognition,^[71][68] 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.^{[59][71][69][74]}

In 2010, 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 trees.^{[75][76][77][72]}

Advances in hardware enabled the renewed interest. In 2009, Nvidia was involved in what was called the “big bang” of deep learning, “as deep-learning neural networks were trained with Nvidia graphics processing units (GPUs).”^[78] That year, Google Brain used Nvidia GPUs to create capable DNNs. While there, Ng determined that GPUs could increase the speed of deep-learning systems by about 100 times.^[79] In particular, GPUs are well-suited for the matrix/vector math involved in machine learning.^[80][81] GPUs speed up training algorithms by orders of magnitude, reducing running times from weeks to days.^[82][83] Specialized hardware and algorithm optimizations can be used for efficient processing.^[84]

Deep learning revolution

In 2012, a team led by Dahl won the "Merck Molecular Activity Challenge" using multi-task deep neural networks to predict the biomolecular target of one drug.^[85][86] In 2014, Hochreiter's group used deep learning to detect off-target and toxic effects of environmental chemicals in nutrients, household products and drugs and won the "Tox21 Data Challenge" of NIH, FDA and NCATS.

Significant additional impacts in image or object recognition were felt from 2011 to 2012. Although CNNs trained by backpropagation had been around for decades, and GPU implementations of NNs for years, including CNNs, fast implementations of CNNs with max-pooling on GPUs in the style of Ciresan and colleagues were needed to progress on computer vision.^{[80][81][34][90][2]} In 2011, this approach achieved for the first time superhuman performance in a visual pattern recognition contest. Also in 2011, it won the ICDAR Chinese handwriting contest, and in May 2012, it won the ISBI image segmentation contest.^[91] Until 2011, CNNs did not play a major role at computer vision conferences, but in June 2012, a paper by Ciresan et al. at the leading conference CVPR^[4] showed how max-pooling CNNs on GPU can dramatically improve many vision benchmark records. In October 2012, a similar system by Krizhevsky et al.^[5] won the large-scale ImageNet competition by a significant margin over shallow machine learning methods. In November 2012, Ciresan et al.'s system also won the ICPR contest on analysis of large medical images for cancer detection, and in the following year also the MICCAI Grand Challenge on the same topic.^[92] In 2013 and 2014, the error rate on the ImageNet task using deep learning was further reduced, following a similar trend in large-scale speech recognition. The Wolfram Image Identification project publicized these improvements.^[93]

Image classification was then extended to the more challenging task of generating descriptions (captions) for images, often as a combination of CNNs and LSTMs.^{[94][95][96][97]}

Some researchers assess that the October 2012 ImageNet victory anchored the start of a "deep learning revolution" that has transformed the AI industry.^[98]

Artificial neural networks

Artificial neural networks (ANNs) or connectionist systems are computing systems inspired by the biological neural networks that constitute animal brains. Such systems learn (progressively improve their ability) to do tasks by considering examples, generally without task-specific programming. For example, in image recognition, they might learn to identify images that contain cats by analyzing example images that have been manually labeled as "cat" or "no cat" and using the analytic results to identify cats in other images. They have found most use in applications difficult to express with a traditional computer algorithm using rule-based programming.

An ANN is based on a collection of connected units called artificial neurons, (analogous to biological neurons in a biological brain). Each connection (synapse) between neurons can transmit a signal to another neuron. The receiving (postsynaptic) neuron can process the signal(s) and then signal downstream neurons connected to it. Neurons may have state, generally represented by real numbers, typically between 0 and 1. Neurons and synapses may also have a weight that varies as learning proceeds, which can increase or decrease the strength of the signal that it sends downstream.

Typically, neurons are organized in layers. Different layers may perform different kinds of transformations on their inputs. Signals travel from the first (input), to the last (output) layer, possibly after traversing the layers multiple times.

The original goal of the neural network approach was to solve problems in the same way that a human brain would. Over time, attention focused on matching specific mental abilities, leading to deviations from biology such as backpropagation, or passing information in the reverse direction and adjusting the network to reflect that information.

Neural networks have been used on a variety of tasks, including computer vision, speech recognition, machine translation, social network filtering, playing board and video games and medical diagnosis.

As of 2017, neural networks typically have a few thousand to a few million units and millions of connections. Despite this number being several order of magnitude less than the number of neurons on a human brain, these networks can perform many tasks at a level beyond that of humans (e.g., recognizing faces, playing "Go"^[99] ).

Deep neural networks

A deep neural network (DNN) is an artificial neural network (ANN) with multiple layers between the input and output layers.^[11][2] The DNN finds the correct mathematical manipulation to turn the input into the output, whether it be a linear relationship or a non-linear relationship. The network moves through the layers calculating the probability of each output. For example, a DNN that is trained to recognize dog breeds will go over the given image and calculate the probability that the dog in the image is a certain breed. The user can review the results and select which probabilities the network should display (above a certain threshold, etc.) and return the proposed label. Each mathematical manipulation as such is considered a layer, and complex DNN have many layers, hence the name "deep" networks.

DNNs can model complex non-linear relationships. DNN architectures generate compositional models where the object is expressed as a layered composition of primitives.^[100] The extra layers enable composition of features from lower layers, potentially modeling complex data with fewer units than a similarly performing shallow network.^[11]

Deep architectures include many variants of a few basic approaches. Each architecture has found success in specific domains. It is not always possible to compare the performance of multiple architectures, unless they have been evaluated on the same data sets.

DNNs are typically feedforward networks in which data flows from the input layer to the output layer without looping back. At first, the DNN creates a map of virtual neurons and assigns random numerical values, or "weights", to connections between them. The weights and inputs are multiplied and return an output between 0 and 1. If the network didn’t accurately recognize a particular pattern, an algorithm would adjust the weights.^[101] That way the algorithm can make certain parameters more influential, until it determines the correct mathematical manipulation to fully process the data.

Recurrent neural networks (RNNs), in which data can flow in any direction, are used for applications such as language modeling.^{[102][103][104][105][106]} Long short-term memory is particularly effective for this use.^[50][107]

Convolutional deep neural networks (CNNs) are used in computer vision.^[108] CNNs also have been applied to acoustic modeling for automatic speech recognition (ASR).^[66]

Challenges

As with ANNs, many issues can arise with naively trained DNNs. 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 methods such as Ivakhnenko's unit pruning^[28] or weight decay (${\displaystyle \ell _{2}}$-regularization) or sparsity (${\displaystyle \ell _{1}}$-regularization) can be applied during training to combat overfitting.^[109] Alternatively dropout regularization randomly omits units from the hidden layers during training. This helps to exclude rare dependencies.^[110] Finally, data can be augmented via methods such as cropping and rotating such that smaller training sets can be increased in size to reduce the chances of overfitting.^[111]

DNNs must consider many training parameters, such as the size (number of layers and number of units per layer), the learning rate, and initial weights. 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 batching (computing the gradient on several training examples at once rather than individual examples)^[112] speed up computation. Large processing capabilities of many-core architectures (such as, GPUs or the Intel Xeon Phi) have produced significant speedups in training, because of the suitability of such processing architectures for the matrix and vector computations.^[113][114]

Alternatively, engineers may look for other types of neural networks with more straightforward and convergent training algorithms. CMAC (cerebellar model articulation controller) is one such kind of neural network. It doesn't require learning rates or randomized initial weights for CMAC. The training process can be guaranteed to converge in one step with a new batch of data, and the computational complexity of the training algorithm is linear with respect to the number of neurons involved.^[115][116]

Deep decision trees

Directed acyclic graph of decision rules - decision stream.^[117]

A deep directed acyclic graph of decision rules is generated for the tasks of classification and regression by statistic-based supervised learning technique - decision stream. It builds a graph with strong connectivity by fusion statistically similar nodes, reducing in such way the predictive model width and increasing classification/regression precision on the basis of representative data quantity in leaf nodes. Decision stream splits and merges the data multiple times by different features. Due to partition of data only into statistically different groups it decreases the overfitting and reduces complexity on every level of predictive model. The merging of leaves and reduction of model width enforce the generation of extremely deep graphs, that can consist of hundreds of levels.^[117]

Applications

Automatic speech recognition

Large-scale automatic speech recognition is the first and most convincing successful case of deep learning. LSTM RNNs can learn "Very Deep Learning" tasks^[2] that involve multi-second intervals containing speech events separated by thousands of discrete time steps, where one time step corresponds to about 10 ms. LSTM with forget gates^[107] is competitive with traditional speech recognizers on certain tasks.^[51]

The initial success in speech recognition was based on small-scale recognition tasks based on TIMIT. The data set contains 630 speakers from eight major dialects of American English, where each speaker reads 10 sentences.^[118] Its small size lets many configurations be tried. More importantly, the TIMIT task concerns phone-sequence recognition, which, unlike word-sequence recognition, allows weak phone bigram language models. This lets the strength of the acoustic modeling aspects of speech recognition be more easily analyzed. The error rates listed below, including these early results and measured as percent phone error rates (PER), have been summarized since 1991.

Method	PER (%)
Randomly Initialized RNN[119]	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[120]	20.0
Convolutional DNN w. Heterogeneous Pooling	18.7
Ensemble DNN/CNN/RNN[121]	18.3
Bidirectional LSTM	17.9
Hierarchical Convolutional Deep Maxout Network[122]	16.5

The debut of DNNs for speaker recognition in the late 1990s and speech recognition around 2009-2011 and of LSTM around 2003-2007, accelerated progress in eight major areas:^[10][74][72]

• Scale-up/out and acclerated DNN training and decoding
• Sequence discriminative training
• Feature processing by deep models with solid understanding of the underlying mechanisms
• Adaptation of DNNs and related deep models
• Multi-task and transfer learning by DNNs and related deep models
• CNNs and how to design them to best exploit domain knowledge of speech
• RNN and its rich LSTM variants
• Other types of deep models including tensor-based models and integrated deep generative/discriminative models.

All major commercial speech recognition systems (e.g., Microsoft Cortana, Xbox, Skype Translator, Amazon Alexa, Google Now, Apple Siri, Baidu and iFlyTek voice search, and a range of Nuance speech products, etc.) are based on deep learning.^{[10][123][124][125]}

Image recognition

A common evaluation set for image classification is the MNIST database data set. MNIST is composed of handwritten digits and includes 60,000 training examples and 10,000 test examples. As with TIMIT, its small size lets users test multiple configurations. A comprehensive list of results on this set is available.^[126]

Deep learning-based image recognition has become "superhuman", producing more accurate results than human contestants. This first occurred in 2011.^[127]

Deep learning-trained vehicles now interpret 360° camera views.^[128] Another example is Facial Dysmorphology Novel Analysis (FDNA) used to analyze cases of human malformation connected to a large database of genetic syndromes.

Visual art processing

Closely related to the progress that has been made in image recognition is the increasing application of deep learning techniques to various visual art tasks. DNNs have proven themselves capable, for example, of a) identifying the style period of a given painting, b) "capturing" the style of a given painting and applying it in a visually pleasing manner to an arbitrary photograph, and c) generating striking imagery based on random visual input fields.^[129][130]

Natural language processing

Neural networks have been used for implementing language models since the early 2000s.^[102][131] LSTM helped to improve machine translation and language modeling.^{[103][104][105]}

Other key techniques in this field are negative sampling^[132] 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 word embedding as an RNN input layer allows 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 an RNN.^[133] Recursive auto-encoders built atop word embeddings can assess sentence similarity and detect paraphrasing.^[133] Deep neural architectures provide the best results for constituency parsing,^[134] sentiment analysis,^[135] information retrieval,^[136][137] spoken language understanding,^[138] machine translation,^[103][139] contextual entity linking,^[139] writing style recognition,^[140] Text classifcation and others.^[141]

Google Translate (GT) uses a large end-to-end long short-term memory network.^{[142][143][144][145][146][147]} Google Neural Machine Translation (GNMT) uses an example-based machine translation method in which the system "learns from millions of examples."^[143] It translates "whole sentences at a time, rather than pieces. Google Translate supports over one hundred languages.^[143] The network encodes the "semantics of the sentence rather than simply memorizing phrase-to-phrase translations".^[143][148] GT uses English as an intermediate between most language pairs.^[148]

Drug discovery and toxicology

A large percentage of candidate drugs fail to win regulatory approval. These failures are caused by insufficient efficacy (on-target effect), undesired interactions (off-target effects), or unanticipated toxic effects.^[149][150] Research has explored use of deep learning to predict biomolecular target,^[85][86] off-target and toxic effects of environmental chemicals in nutrients, household products and drugs.^[87][88][89]

AtomNet is a deep learning system for structure-based rational drug design.^[151] AtomNet was used to predict novel candidate biomolecules for disease targets such as the Ebola virus^[152] and multiple sclerosis.^[153][154]

Customer relationship management

Deep reinforcement learning has been used to approximate the value of possible direct marketing actions, defined in terms of RFM variables. The estimated value function was shown to have a natural interpretation as customer lifetime value.^[155]

Recommendation systems

Recommendation systems have used deep learning to extract meaningful features for a latent factor model for content-based music recommendations.^[156] Multiview deep learning has been applied for learning user preferences from multiple domains.^[157] The model uses a hybrid collaborative and content-based approach and enhances recommendations in multiple tasks.

Bioinformatics

An autoencoder ANN was used in bioinformatics, to predict gene ontology annotations and gene-function relationships.^[158]

In medical informatics, deep learning was used to predict sleep quality based on data from wearables^[159][160] and predictions of health complications from electronic health record data.^[161] Deep learning has also showed efficacy in healthcare.^[162][163]

Mobile advertising

Finding the appropriate mobile audience for mobile advertising is always challenging, since many data points must be considered and assimilated before a target segment can be created and used in ad serving by any ad server.^[164][165] Deep learning has been used to interpret large, many-dimensioned advertising datasets. Many data points are collected during the request/serve/click internet advertising cycle. This information can form the basis of machine learning to improve ad selection.

Image restoration

Deep learning has been successfully applied to inverse problems such as denoising, super-resolution, and inpainting. These applications include learning methods such "Shrinkage Fields for Effective Image Restoration"^[166] which trains on an image dataset, and Deep Image Prior, which trains on the image that needs restoration.

Relation to human cognitive and brain development

Deep learning is closely related to a class of theories of brain development (specifically, neocortical development) proposed by cognitive neuroscientists in the early 1990s.^{[167][168][169][170]} These developmental theories were instantiated in computational models, making them predecessors of deep learning systems. These developmental models share the property that various proposed learning dynamics in the brain (e.g., a wave of nerve growth factor) support the self-organization somewhat analogous to the neural networks utilized in deep learning models. Like the neocortex, neural networks employ a hierarchy of layered filters in which each layer considers information from a prior layer (or the operating environment), and then passes its output (and possibly the original input), to other layers. This process yields a self-organizing stack of transducers, well-tuned to their operating environment. A 1995 description stated, "...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."^[171]

A variety of approaches have been used to investigate the plausibility of deep learning models from a neurobiological perspective. On the one hand, several variants of the backpropagation algorithm have been proposed in order to increase its processing realism.^[172][173] Other researchers have argued that unsupervised forms of deep learning, such as those based on hierarchical generative models and deep belief networks, may be closer to biological reality.^[174][175] In this respect, generative neural network models have been related to neurobiological evidence about sampling-based processing in the cerebral cortex.^[176]

Although a systematic comparison between the human brain organization and the neuronal encoding in deep networks has not yet been established, several analogies have been reported. For example, the computations performed by deep learning units could be similar to those of actual neurons^[177][178] and neural populations.^[179] Similarly, the representations developed by deep learning models are similar to those measured in the primate visual system^[180] both at the single-unit^[181] and at the population^[182] levels.

Commercial activity

Many organizations employ deep learning for particular applications. Facebook's AI lab performs tasks such as automatically tagging uploaded pictures with the names of the people in them.^[183]

Google's DeepMind Technologies developed a system capable of learning how to play Atari video games using only pixels as data input. In 2015 they demonstrated their AlphaGo system, which learned the game of Go well enough to beat a professional Go player.^{[184][185][186]} Google Translate uses an LSTM to translate between more than 100 languages.

In 2015, Blippar demonstrated a mobile augmented reality application that uses deep learning to recognize objects in real time.^[187]

Criticism and comment

Deep learning has attracted both criticism and comment, in some cases from outside the field of computer science.

Theory

A main criticism concerns the lack of theory surrounding the methods.^{[citation needed]} Learning in the most common deep architectures is implemented using well-understood gradient descent. However, the theory surrounding other algorithms, such as contrastive divergence is less clear.^{[citation needed]} (e.g., 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.^[188]
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 noted:

"Realistically, deep learning is only part of the larger challenge of building intelligent machines. Such techniques lack ways of representing causal relationships (...) have no obvious ways of performing 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 (...) 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."^[189]

As an alternative to this emphasis on the limits of deep learning, one author speculated 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 hypothesized that such a sensitivity might represent the rudiments of a non-trivial machine empathy.^[190] This same author proposed that this would be in line with anthropology, which identifies a concern with aesthetics as a key element of behavioral modernity.^[191]

In further reference to the idea that artistic sensitivity might inhere within relatively low levels 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^[192] demonstrate a visual appeal: the original research notice received well over 1,000 comments, and was the subject of what was for a time the most frequently accessed article on The Guardian's^[193] web site.

Errors

Some deep learning architectures display problematic behaviors,^[194] such as confidently classifying unrecognizable images as belonging to a familiar category of ordinary images^[195] and misclassifying minuscule perturbations of correctly classified images.^[196] Goertzel hypothesized that these behaviors are due to limitations in their internal representations and that these limitations would inhibit integration into heterogeneous multi-component AGI architectures.^[194] These issues may possibly be addressed by deep learning architectures that internally form states homologous to image-grammar^[197] decompositions of observed entities and events.^[194] Learning a grammar (visual or linguistic) from training data would be equivalent to restricting the system to commonsense reasoning that operates on concepts in terms of grammatical production rules and is a basic goal of both human language acquisition^[198] and AI.^[199]

Cyberthreat

As deep learning moves from the lab into the world, research and experience shows that artificial neural networks are vulnerable to hacks and deception. By identifying patterns that these systems use to function, attackers can modify inputs to ANNs in such a way that the ANN finds a match that human observers would not recognize. For example, an attacker can make subtle changes to an image such that the ANN finds a match even though the image looks to a human nothing like the search target. Such a manipulation is termed an “adversarial attack.” In 2016 researchers used one ANN to doctor images in trial and error fashion, identify another's focal points and thereby generate images that deceived it. The modified images looked no different to human eyes. Another group showed that printouts of doctored images then photographed successfully tricked an image classification system.^[200] One defense is reverse image search, in which a possible fake image is submitted to a site such as TinEye that can then find other instances of it. A refinement is to search using only parts of the image, to identify images from which that piece may have been taken.^[201]

Another group showed that certain psychedelic spectacles could fool a facial recognition system into thinking ordinary people were celebrities, potentially allowing one person to impersonate another. In 2017 researchers added stickers to stop signs and caused an ANN to misclassify them.^[200]

ANNs can however be further trained to detect attempts at deception, potentially leading attackers and defenders into an arms race similar to the kind that already defines the malware defense industry. ANNs have been trained to defeat ANN-based anti-malware software by repeatedly attacking a defense with malware that was continually altered by a genetic algorithm until it tricked the anti-malware while retaining its ability to damage the target.^[200]

Another group demonstrated that certain sounds could make the Google Now voice command system open a particular web address that would download malware.^[200]

In “data poisoning”, false data is continually smuggled into a machine learning system’s training set to prevent it from achieving mastery.

Self-organizing map

From Wikipedia, the free encyclopedia

A self-organizing map (SOM) or self-organizing feature map (SOFM) is a type of artificial neural network (ANN) that is trained using unsupervised learning to produce a low-dimensional (typically two-dimensional), discretized representation of the input space of the training samples, called a map, and is therefore a method to do dimensionality reduction. Self-organizing maps differ from other artificial neural networks as they apply competitive learning as opposed to error-correction learning (such as backpropagation with gradient descent), and in the sense that they use a neighborhood function to preserve the topological properties of the input space.

A self-organizing map showing U.S. Congress voting patterns. The input data was a table with a row for each member of Congress, and columns for certain votes containing each member's yes/no/abstain vote. The SOM algorithm arranged these members in a two-dimensional grid placing similar members closer together. The first plot shows the grouping when the data are split into two clusters. The second plot shows average distance to neighbours: larger distances are darker. The third plot predicts Republican (red) or Democratic (blue) party membership. The other plots each overlay the resulting map with predicted values on an input dimension: red means a predicted 'yes' vote on that bill, blue means a 'no' vote. The plot was created in Synapse.

This makes SOMs useful for visualization by creating low-dimensional views of high-dimensional data, akin to multidimensional scaling. The artificial neural network introduced by the Finnish professor Teuvo Kohonen in the 1980s is sometimes called a Kohonen map or network.^[1][2] The Kohonen net is a computationally convenient abstraction building on biological models of neural systems from the 1970s^[3] and morphogenesis models dating back to Alan Turing in the 1950s.^[4]

While it is typical to consider this type of network structure as related to feedforward networks where the nodes are visualized as being attached, this type of architecture is fundamentally different in arrangement and motivation.

Useful extensions include using toroidal grids where opposite edges are connected and using large numbers of nodes.

It has been shown that while self-organizing maps with a small number of nodes behave in a way that is similar to K-means, larger self-organizing maps rearrange data in a way that is fundamentally topological in character.

It is also common to use the U-Matrix.^[5] The U-Matrix value of a particular node is the average distance between the node's weight vector and that of its closest neighbors.^[6] In a square grid, for instance, we might consider the closest 4 or 8 nodes (the Von Neumann and Moore neighborhoods, respectively), or six nodes in a hexagonal grid.

Large SOMs display emergent properties. In maps consisting of thousands of nodes, it is possible to perform cluster operations on the map itself.^[7]

Structure and operations

Like most artificial neural networks, SOMs operate in two modes: training and mapping. "Training" builds the map using input examples (a competitive process, also called vector quantization), while "mapping" automatically classifies a new input vector.

The visible part of a self-organizing map is the map space, it consists of components called nodes or neurons. The map space is defined beforehand, usually as a finite two-dimensional region where nodes are arranged in a regular hexagonal or rectangular grid.^[8] Each node is associated with a "weight" vector, which is a position in the input space; that is, it has the same dimension as each input vector. While nodes in the map space stay fixed, training consists in moving weight vectors toward the input data, without spoiling the topology induced from the map space. Thus, the self-organizing map describes a mapping from a higher-dimensional input space to a lower-dimensional map space. Once trained, the map can classify a vector from the data space by finding the node with the closest (smallest distance metric) weight vector to the data space vector.

Learning algorithm

The goal of learning in the self-organizing map is to cause different parts of the network to respond similarly to certain input patterns. This is partly motivated by how visual, auditory or other sensory information is handled in separate parts of the cerebral cortex in the human brain.^[9]

An illustration of the training of a self-organizing map. The

blue blob is the distribution of the training data, and the

small white disc is the current training datum drawn from

that distribution. At first (left) the SOM nodes are arbitrarily

positioned in the data space. The node (highlighted in yellow)

which is nearest to the training datum is selected. It is moved

towards the training datum, as (to a lesser extent) are its

neighbors on the grid. After many iterations the grid tends to

approximate the data distribution (right).

The weights of the neurons are initialized either to small random values or sampled evenly from the subspace spanned by the two largest principal component eigenvectors. With the latter alternative, learning is much faster because the initial weights already give a good approximation of SOM weights.^[10]

The network must be fed a large number of example vectors that represent, as close as possible, the kinds of vectors expected during mapping. The examples are usually administered several times as iterations.

The training utilizes competitive learning. When a training example is fed to the network, its Euclidean distance to all weight vectors is computed. The neuron whose weight vector is most similar to the input is called the best matching unit (BMU). The weights of the BMU and neurons close to it in the SOM grid are adjusted towards the input vector. The magnitude of the change decreases with time and with the grid-distance from the BMU. The update formula for a neuron v with weight vector W_v(s) is

${\displaystyle W_{v}(s+1)=W_{v}(s)+\theta (u,v,s)\cdot \alpha (s)\cdot (D(t)-W_{v}(s))}$,

where s is the step index, t an index into the training sample, u is the index of the BMU for D(t), α(s) is a monotonically decreasing learning coefficient and D(t) is the input vector; Θ(u, v, s) is the neighborhood function which gives the distance between the neuron u and the neuron v in step s.^[11] Depending on the implementations, t can scan the training data set systematically (t is 0, 1, 2...T-1, then repeat, T being the training sample's size), be randomly drawn from the data set (bootstrap sampling), or implement some other sampling method (such as jackknifing).

The neighborhood function Θ(u, v, s) depends on the grid-distance between the BMU (neuron u) and neuron v. In the simplest form it is 1 for all neurons close enough to BMU and 0 for others, but a Gaussian function is a common choice, too. Regardless of the functional form, the neighborhood function shrinks with time.^[9] At the beginning when the neighborhood is broad, the self-organizing takes place on the global scale. When the neighborhood has shrunk to just a couple of neurons, the weights are converging to local estimates. In some implementations the learning coefficient α and the neighborhood function Θ decrease steadily with increasing s, in others (in particular those where t scans the training data set) they decrease in step-wise fashion, once every T steps.

This process is repeated for each input vector for a (usually large) number of cycles λ. The network winds up associating output nodes with groups or patterns in the input data set. If these patterns can be named, the names can be attached to the associated nodes in the trained net.

During mapping, there will be one single winning neuron: the neuron whose weight vector lies closest to the input vector. This can be simply determined by calculating the Euclidean distance between input vector and weight vector.

While representing input data as vectors has been emphasized in this article, it should be noted that any kind of object which can be represented digitally, which has an appropriate distance measure associated with it, and in which the necessary operations for training are possible can be used to construct a self-organizing map. This includes matrices, continuous functions or even other self-organizing maps.

Variables

These are the variables needed, with vectors in bold,

• ${\displaystyle s}$ is the current iteration
• ${\displaystyle \lambda }$ is the iteration limit
• ${\displaystyle t}$ is the index of the target input data vector in the input data set ${\displaystyle \mathbf {D} }$
• ${\displaystyle {D}(t)}$ is a target input data vector
• ${\displaystyle v}$ is the index of the node in the map
• ${\displaystyle \mathbf {W} _{v}}$ is the current weight vector of node ${\displaystyle v}$
• ${\displaystyle u}$ is the index of the best matching unit (BMU) in the map
• ${\displaystyle \theta (u,v,s)}$ is a restraint due to distance from BMU, usually called the neighborhood function, and
• ${\displaystyle \alpha (s)}$ is a learning restraint due to iteration progress.

Algorithm

1. Randomize the node weight vectors in a map
2. Randomly pick an input vector ${\displaystyle {D}(t)}$
3. Traverse each node in the map
   1. Use the Euclidean distance formula to find the similarity between the input vector and the map's node's weight vector
   2. Track the node that produces the smallest distance (this node is the best matching unit, BMU)
4. Update the weight vectors of the nodes in the neighborhood of the BMU (including the BMU itself) by pulling them closer to the input vector
   
   
   1. ${\displaystyle W_{v}(s+1)=W_{v}(s)+\theta (u,v,s)\cdot \alpha (s)\cdot (D(t)-W_{v}(s))}$
      
5. Increase ${\displaystyle s}$ and repeat from step 2 while ${\displaystyle s<\lambda }$

A variant algorithm:

1. Randomize the map's nodes' weight vectors
2. Traverse each input vector in the input data set
   1. Traverse each node in the map
      1. Use the Euclidean distance formula to find the similarity between the input vector and the map's node's weight vector
      2. Track the node that produces the smallest distance (this node is the best matching unit, BMU)
   2. Update the nodes in the neighborhood of the BMU (including the BMU itself) by pulling them closer to the input vector
      
      
      1. ${\displaystyle W_{v}(s+1)=W_{v}(s)+\theta (u,v,s)\cdot \alpha (s)\cdot (D(t)-W_{v}(s))}$
         
3. Increase ${\displaystyle s}$ and repeat from step 2 while ${\displaystyle s<\lambda }$

SOM Initialization

Selection of a good initial approximation is a well-known problem for all iterative methods of learning neural networks. Kohonen^[12] used random initiation of SOM weights. Recently, principal component initialization, in which initial map weights are chosen from the space of the first principal components, has become popular due to the exact reproducibility of the results.^[13]

Careful comparison of the random initiation approach to principal component initialization for one-dimensional SOM (models of principal curves) demonstrated that the advantages of principal component SOM initialization are not universal. The best initialization method depends on the geometry of the specific dataset. Principal component initialization is preferable (in dimension one) if the principal curve approximating the dataset can be univalently and linearly projected on the first principal component (quasilinear sets). For nonlinear datasets, however, random initiation performs better.^[14]

Examples

Fisher's Iris Flower Data

Consider an n×m array of nodes, each of which contains a weight vector and is aware of its location in the array. Each weight vector is of the same dimension as the node's input vector. The weights may initially be set to random values.

Now we need input to feed the map. Colors can be represented by their red, green, and blue components. Consequently, we will represent colors as vectors in the unit cube of the free vector space over ℝ generated by the basis:

R = <255 0="">

G = <0 0="" 255="">

B = <0 0="" 255="">

The diagram shown

Self organizing maps (SOM) of three and eight colors with U-Matrix.

compares the results of training on the data sets^{[Note 1]}

threeColors = [255, 0, 0], [0, 255, 0], [0, 0, 255]

eightColors = [0, 0, 0], [255, 0, 0], [0, 255, 0], [0, 0, 255], [255, 255, 0], [0, 255, 255], [255, 0, 255], [255, 255, 255]

and the original images. Note the striking resemblance between the two.

Similarly, after training a 40×40 grid of neurons for 250 iterations with a learning rate of 0.1 on Fisher's Iris, the map can already detect the main differences between species.

Self organizing map (SOM) of Fisher's Iris Flower Data Set with U-Matrix. Top left: a color image formed by the first three dimensions of the four-dimensional SOM weight vectors. Top Right: a pseudo-color image of the magnitude of the SOM weight vectors. Bottom Left: a U-Matrix (Euclidean distance between weight vectors of neighboring cells) of the SOM. Bottom Right: An overlay of data points (red: I. setosa, green: I. versicolor and blue: I. virginica) on the U-Matrix based on the minimum Euclidean distance between data vectors and SOM weight vectors.

Interpretation

Cartographical representation of a self-organizing map (U-Matrix) based on Wikipedia featured article data (word frequency). Distance is inversely proportional to similarity. The "mountains" are edges between clusters. The red lines are links between articles.

 

One-dimensional SOM versus principal component analysis (PCA) for data approximation. SOM is a red broken line with squares, 20 nodes. The first principal component is presented by a blue line. Data points are the small grey circles. For PCA, the fraction of variance unexplained in this example is 23.23%, for SOM it is 6.86%.^[15]

There are two ways to interpret a SOM. Because in the training phase weights of the whole neighborhood are moved in the same direction, similar items tend to excite adjacent neurons. Therefore, SOM forms a semantic map where similar samples are mapped close together and dissimilar ones apart. This may be visualized by a U-Matrix (Euclidean distance between weight vectors of neighboring cells) of the SOM.^[5][6][16]

The other way is to think of neuronal weights as pointers to the input space. They form a discrete approximation of the distribution of training samples. More neurons point to regions with high training sample concentration and fewer where the samples are scarce.

SOM may be considered a nonlinear generalization of Principal components analysis (PCA).^[17] It has been shown, using both artificial and real geophysical data, that SOM has many advantages^[18][19] over the conventional feature extraction methods such as Empirical Orthogonal Functions (EOF) or PCA.

Originally, SOM was not formulated as a solution to an optimisation problem. Nevertheless, there have been several attempts to modify the definition of SOM and to formulate an optimisation problem which gives similar results.^[20] For example, Elastic maps use the mechanical metaphor of elasticity to approximate principal manifolds:^[21] the analogy is an elastic membrane and plate.

Alternatives

• The generative topographic map (GTM) is a potential alternative to SOMs. In the sense that a GTM explicitly requires a smooth and continuous mapping from the input space to the map space, it is topology preserving. However, in a practical sense, this measure of topological preservation is lacking.^[22]
• The time adaptive self-organizing map (TASOM) network is an extension of the basic SOM. The TASOM employs adaptive learning rates and neighborhood functions. It also includes a scaling parameter to make the network invariant to scaling, translation and rotation of the input space. The TASOM and its variants have been used in several applications including adaptive clustering, multilevel thresholding, input space approximation, and active contour modeling.^[23] Moreover, a Binary Tree TASOM or BTASOM, resembling a binary natural tree having nodes composed of TASOM networks has been proposed where the number of its levels and the number of its nodes are adaptive with its environment.^[24]
• The growing self-organizing map (GSOM) is a growing variant of the self-organizing map. The GSOM was developed to address the issue of identifying a suitable map size in the SOM. It starts with a minimal number of nodes (usually four) and grows new nodes on the boundary based on a heuristic. By using a value called the spread factor, the data analyst has the ability to control the growth of the GSOM.
• The elastic maps approach^[25] borrows from the spline interpolation the idea of minimization of the elastic energy. In learning, it minimizes the sum of quadratic bending and stretching energy with the least squares approximation error.
• The conformal approach ^[26][27] that uses conformal mapping to interpolate each training sample between grid nodes in a continuous surface. A one-to-one smooth mapping is possible in this approach.

Applications

• Meteorology and oceanography^[28]
• Project prioritization and selection ^[29]
• Seismic facies analysis for oil and gas exploration ^[30]
• Failure Mode and Effect Analysis ^[31]
• Creation of artwork ^[32]

Artificial neuron

From Wikipedia, the free encyclopedia

An artificial neuron is a mathematical function conceived as a model of biological neurons, a neural network. Artificial neurons are elementary units in an artificial neural network. The artificial neuron receives one or more inputs (representing excitatory postsynaptic potentials and inhibitory postsynaptic potentials at neural dendrites) and sums them to produce an output (or activation, representing a neuron's action potential which is transmitted along its axon). Usually each input is separately weighted, and the sum is passed through a non-linear function known as an activation function or transfer function. The transfer functions usually have a sigmoid shape, but they may also take the form of other non-linear functions, piecewise linear functions, or step functions. They are also often monotonically increasing, continuous, differentiable and bounded. The thresholding function has inspired building logic gates referred to as threshold logic; applicable to building logic circuits resembling brain processing. For example, new devices such as memristors have been extensively used to develop such logic in recent times.

The artificial neuron transfer function should not be confused with a linear system's transfer function.

Basic structure

For a given artificial neuron, let there be m + 1 inputs with signals x₀ through x_m and weights w₀ through w_m. Usually, the x₀ input is assigned the value +1, which makes it a bias input with w_k0 = b_k. This leaves only m actual inputs to the neuron: from x₁ to x_m.

The output of the kth neuron is:

${\displaystyle y_{k}=\varphi \left(\sum _{j=0}^{m}w_{kj}x_{j}\right)}$

Where ${\displaystyle \varphi }$ (phi) is the transfer function.



The output is analogous to the axon of a biological neuron, and its value propagates to the input of the next layer, through a synapse. It may also exit the system, possibly as part of an output vector.

It has no learning process as such. Its transfer function weights are calculated and threshold value are predetermined.

Types

Depending on the specific model used they may be called a semi-linear unit, Nv neuron, binary neuron, linear threshold function, or McCulloch–Pitts (MCP) neuron.
Simple artificial neurons, such as the McCulloch–Pitts model, are sometimes described as "caricature models", since they are intended to reflect one or more neurophysiological observations, but without regard to realism.^[2]

Biological models

Artificial neurons are designed to mimic aspects of their biological counterparts.

• Dendrites – In a biological neuron, the dendrites act as the input vector. These dendrites allow the cell to receive signals from a large (>1000) number of neighboring neurons. As in the above mathematical treatment, each dendrite is able to perform "multiplication" by that dendrite's "weight value." The multiplication is accomplished by increasing or decreasing the ratio of synaptic neurotransmitters to signal chemicals introduced into the dendrite in response to the synaptic neurotransmitter. A negative multiplication effect can be achieved by transmitting signal inhibitors (i.e. oppositely charged ions) along the dendrite in response to the reception of synaptic neurotransmitters.
• Soma – In a biological neuron, the soma acts as the summation function, seen in the above mathematical description. As positive and negative signals (exciting and inhibiting, respectively) arrive in the soma from the dendrites, the positive and negative ions are effectively added in summation, by simple virtue of being mixed together in the solution inside the cell's body.
• Axon – The axon gets its signal from the summation behavior which occurs inside the soma. The opening to the axon essentially samples the electrical potential of the solution inside the soma. Once the soma reaches a certain potential, the axon will transmit an all-in signal pulse down its length. In this regard, the axon behaves as the ability for us to connect our artificial neuron to other artificial neurons.

Unlike most artificial neurons, however, biological neurons fire in discrete pulses. Each time the electrical potential inside the soma reaches a certain threshold, a pulse is transmitted down the axon. This pulsing can be translated into continuous values. The rate (activations per second, etc.) at which an axon fires converts directly into the rate at which neighboring cells get signal ions introduced into them. The faster a biological neuron fires, the faster nearby neurons accumulate electrical potential (or lose electrical potential, depending on the "weighting" of the dendrite that connects to the neuron that fired). It is this conversion that allows computer scientists and mathematicians to simulate biological neural networks using artificial neurons which can output distinct values (often from −1 to 1).

Encoding

Research has shown that unary coding is used in the neural circuits responsible for birdsong production.^[3][4] The use of unary in biological networks is presumably due to the inherent simplicity of the coding. Another contributing factor could be that unary coding provides a certain degree of error correction.^[5]

History

The first artificial neuron was the Threshold Logic Unit (TLU), or Linear Threshold Unit,^[6] first proposed by Warren McCulloch and Walter Pitts in 1943. The model was specifically targeted as a computational model of the "nerve net" in the brain.^[7] As a transfer function, it employed a threshold, equivalent to using the Heaviside step function. Initially, only a simple model was considered, with binary inputs and outputs, some restrictions on the possible weights, and a more flexible threshold value. Since the beginning it was already noticed that any boolean function could be implemented by networks of such devices, what is easily seen from the fact that one can implement the AND and OR functions, and use them in the disjunctive or the conjunctive normal form. Researchers also soon realized that cyclic networks, with feedbacks through neurons, could define dynamical systems with memory, but most of the research concentrated (and still does) on strictly feed-forward networks because of the smaller difficulty they present.

One important and pioneering artificial neural network that used the linear threshold function was the perceptron, developed by Frank Rosenblatt. This model already considered more flexible weight values in the neurons, and was used in machines with adaptive capabilities. The representation of the threshold values as a bias term was introduced by Bernard Widrow in 1960 – see ADALINE.

In the late 1980s, when research on neural networks regained strength, neurons with more continuous shapes started to be considered. The possibility of differentiating the activation function allows the direct use of the gradient descent and other optimization algorithms for the adjustment of the weights. Neural networks also started to be used as a general function approximation model. The best known training algorithm called backpropagation has been rediscovered several times but its first development goes back to the work of Paul Werbos.^[8][9]

Types of transfer functions

The transfer function of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron. Crucially, for instance, any multilayer perceptron using a linear transfer function has an equivalent single-layer network; a non-linear function is therefore necessary to gain the advantages of a multi-layer network.

Below, u refers in all cases to the weighted sum of all the inputs to the neuron, i.e. for n inputs,

${\displaystyle u=\sum _{i=1}^{n}w_{i}x_{i}}$

where w is a vector of synaptic weights and x is a vector of inputs.

Step function

The output y of this transfer function is binary, depending on whether the input meets a specified threshold, θ. The "signal" is sent, i.e. the output is set to one, if the activation meets the threshold.

${\displaystyle y={\begin{cases}1&{\text{if }}u\geq \theta \\0&{\text{if }}u<\theta \end{cases}}}$

This function is used in perceptrons and often shows up in many other models. It performs a division of the space of inputs by a hyperplane. It is specially useful in the last layer of a network intended to perform binary classification of the inputs. It can be approximated from other sigmoidal functions by assigning large values to the weights.

Linear combination

In this case, the output unit is simply the weighted sum of its inputs plus a bias term. A number of such linear neurons perform a linear transformation of the input vector. This is usually more useful in the first layers of a network. A number of analysis tools exist based on linear models, such as harmonic analysis, and they can all be used in neural networks with this linear neuron. The bias term allows us to make affine transformations to the data.

Sigmoid

A fairly simple non-linear function, the sigmoid function such as the logistic function also has an easily calculated derivative, which can be important when calculating the weight updates in the network. It thus makes the network more easily manipulable mathematically, and was attractive to early computer scientists who needed to minimize the computational load of their simulations. It was previously commonly seen in multilayer perceptrons. However, recent work has shown sigmoid neurons to be less effective than rectified linear neurons. The reason is that the gradients computed by the backpropagation algorithm tend to diminish towards zero as activations propagate through layers of sigmoidal neurons, making it difficult to optimize neural networks using multiple layers of sigmoidal neurons.

Pseudocode algorithm

The following is a simple pseudocode implementation of a single TLU which takes boolean inputs (true or false), and returns a single boolean output when activated. An object-oriented model is used. No method of training is defined, since several exist. If a purely functional model were used, the class TLU below would be replaced with a function TLU with input parameters threshold, weights, and inputs that returned a boolean value.

 class TLU defined as:
  data member threshold : number
  data member weights : list of numbers of size X
  function member fire( inputs : list of booleans of size X ) : boolean defined as:
   variable T : number
   T ← 0
   for each i in 1 to X :
    if inputs(i) is true :
     T ← T + weights(i)
    end if
   end for each
   if T > threshold :
    return true
   else:
    return false
   end if
  end function
 end class

Spindle neuron

From Wikipedia, the free encyclopedia

Spindle neuron
Cartoon of a spindle cell (right) compared to a normal pyramidal cell (left).
Details
Location	Anterior cingulate cortex and Fronto-insular cortex
Shape	Unique spindle-shaped projection neuron
Function	Global firing rate regulation and regulation of emotional state
Presynaptic connections	Local input to ACC and FI
Postsynaptic connections	Frontal and temporal cortex.
Identifiers
Anatomical terms of neuroanatomy

Micrograph showing a spindle neuron of the cingulate. HE-LFB stain.

Spindle neurons, also called von Economo neurons (VENs), are a specific class of neurons that are characterized by a large spindle-shaped soma (or body), gradually tapering into a single apical axon in one direction, with only a single dendrite facing opposite. Other neurons tend to have many dendrites, and the polar-shaped morphology of spindle neurons is unique. A neuron's dendrites receive signals, and its axon sends them.

Spindle neurons are found in two very restricted regions in the brains of hominids—the family of species comprising humans and other great apes—the anterior cingulate cortex (ACC) and the fronto-insular cortex (FI). Recently they have been discovered in the dorsolateral prefrontal cortex of humans.^[1] Spindle cells are also found in the brains of the humpback whales, fin whales, killer whales, sperm whales,^[2][3] bottlenose dolphin, Risso's dolphin, beluga whales,^[4] African and Asian elephants,^[5] and to a lesser extent in macaque monkeys^[6] and raccoons.^[7] The appearance of spindle neurons in distantly related clades suggests that they represent convergent evolution, specifically an adaptation to larger brains.

Austrian psychiatrist and neurologist Constantin von Economo (1876–1931) discovered spindle neurons and described them in 1929, which is why they are sometimes called von Economo neurons.^[8]

Function

Spindle neurons are relatively large cells that may allow rapid communication across the relatively large brains of great apes, elephants, and cetaceans. Although rare in comparison to other neurons, spindle neurons are abundant, and large, in humans. However, the concentration of spindle cells has been measured to be three times higher in cetaceans in comparison to humans.^[3][9] They have only been found thus far in the anterior cingulate cortex (ACC), fronto-insular cortex (FI), and the dorsolateral prefrontal cortex.

Evolutionary significance

The observation that spindle neurons only occur in a highly significant group of animals (from a human point of view) has led to speculation that they are of great importance in human evolution and/or brain function. Their restriction (among the primates) to great apes leads to the hypothesis that they developed no earlier than 15–20 million years ago, prior to the divergence of orangutans from the African great apes. The discovery of spindle neurons in diverse whale species^[3][4] has led to the suggestion that they are "a possible obligatory neuronal adaptation in very large brains, permitting fast information processing and transfer along highly specific projections and that evolved in relation to emerging social behaviors."^[4]p. 254 Their presence in the brains of these species supports this theory, pointing towards the existence of these specialized neurons only in highly intelligent mammals, and may be an example of convergent evolution.^[10] Recently, primitive forms of spindle neurons have also been discovered in macaque monkey brains^[11] and raccoons.^[7]

ACC spindle neurons

In 1999, Professor John Allman, a neuroscientist, and colleagues at the California Institute of Technology first published a report^[12] on spindle neurons found in the anterior cingulate cortex (ACC) of hominids, but not in any other species. Neuronal volumes of ACC spindle neurons were larger in humans and bonobos (Pan paniscus) than the spindle neurons of the common chimpanzee, gorilla, and orangutan.

Allman and his colleagues^[13] have delved beyond the level of brain infrastructure to investigate how spindle neurons function at the superstructural level, focusing on their role as 'air traffic controllers' for emotions. Allman's team proposes that spindle neurons help channel neural signals from deep within the cortex to relatively distant parts of the brain.

Specifically, Allman's team^[14] found signals from the ACC are received in Brodmann's area 10, in the frontal polar cortex, where regulation of cognitive dissonance (disambiguation between alternatives) is thought to occur. According to Allman, this neural relay appears to convey motivation to act, and concerns the recognition of error. Self-control – and avoidance of error – is thus facilitated by the executive gatekeeping function of the ACC, as it regulates the interference patterns of neural signals between these two brain regions.

In humans, intense emotion activates the anterior cingulate cortex, as it relays neural signals transmitted from the amygdala (a primary processing center for emotions) to the frontal cortex, perhaps by functioning as a sort of lens to focus the complex texture of neural signal interference patterns^{[citation needed]}. The ACC is also active during demanding tasks requiring judgment and discrimination, and when errors are detected by an individual. During difficult tasks, or when experiencing intense love, anger, or lust, activation of the ACC increases. In brain imaging studies, the ACC has specifically been found to be active when mothers hear infants cry, underscoring its role in affording a heightened degree of social sensitivity.

The ACC is a relatively ancient cortical region, and is involved with many autonomic functions, including motor and digestive functions, while also playing a role in the regulation of blood pressure and heart rate. Significant olfactory and gustatory capabilities of the ACC and fronto-insular cortex appear to have been usurped, during recent evolution, to serve enhanced roles related to higher cognition – ranging from planning and self-awareness to role playing and deception. The diminished olfactory function of humans, compared to other primates, may be related to the fact that spindle cells located at crucial neural network hubs have only two dendrites rather than many, resulting in reduced neurological integration.

Fronto-insular spindle neurons

At a Society for Neuroscience meeting in 2003, Allman reported on spindle cells his team found in another brain region, the fronto-insular cortex, a region which appears to have undergone significant evolutionary adaptations in mankind – perhaps as recently as 100,000 years ago.

This fronto-insular cortex is closely connected to the insula, a region that is roughly the size of a thumb in each hemisphere of the human brain. The insula and fronto-insular cortex are part of the insular cortex, wherein the elaborate circuitry associated with spatial awareness are found, and where self-awareness and the complexities of emotion are thought to be generated and experienced. Moreover, this region of the right hemisphere is crucial to navigation and perception of three-dimensional rotations.

Spindle neuron concentrations

ACC

The largest number of ACC spindle neurons are found in humans, fewer in the gracile great apes, and fewest in the robust great apes. In both humans and bonobos they are often found in clusters of 3 to 6 neurons. They are found in humans, bonobos, common chimpanzees, gorillas, orangutans, some cetaceans, and elephants.^[15]:245 While total quantities of ACC spindle neurons were not reported by Allman in his seminal research report (as they were in a later report describing their presence in the frontoinsular cortex, below), his team's initial analysis of the ACC layer V in hominids revealed an average of ~9 spindle neurons per section for orangutans (rare, 0.6% of section cells), ~22 for gorillas (frequent, 2.3%), ~37 for chimpanzees (abundant, 3.8%), ~68 for bonobos (abundant/clusters, 4.8%), ~89 for humans (abundant/clusters, 5.6%).^[16]

Fronto-insula

All of the primates examined had more spindle cells in the fronto-insula of the right hemisphere than in the left. In contrast to the higher number of spindle cells found in the ACC of the gracile bonobos and chimpanzees, the number of fronto-insular spindle cells was far higher in the cortex of robust gorillas (no data for Orangutans was given). An adult human had 82,855 such cells, a gorilla had 16,710, a bonobo had 2,159, and a chimpanzee had a mere 1,808 – despite the fact that chimpanzees and bonobos are great apes most closely related to humans.

Dorsolateral PFC

Von Economo neurons have been located in the Dorsolateral prefrontal cortex of humans^[1] and elephants.^[5] In humans they have been observed in higher concentration in Brodmann area 9 (BA9) – mostly isolated or in clusters of 2, while in Brodmann area 24 (BA24) they have been found mostly in clusters of 2-4.^[1]

Clinical significance

Abnormal spindle neuron development may be linked to several psychotic disorders, typically those characterized by distortions of reality, disturbances of thought, disturbances of language, and withdrawal from social contact. Altered spindle neuron states have been implicated in both schizophrenia and autism, but research into these correlations remains at a very early stage.  Frontotemporal dementia involves loss of mostly spindle neurons.^[17] An initial study suggested that Alzheimer's disease specifically targeted Von Economo neurons; this study was performed with end-stage Alzheimer brains in which cell destruction was widespread, but later, it was found that Alzheimer's disease doesn't affect the spindle neurons.