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In computer science and related fields, artificial neural networks are computational models inspired by animal central nervous systems (in particular the brain) that are capable of machine learning and pattern recognition. They are usually presented as systems of interconnected "neurons" that can compute values from inputs by feeding information through the network.
For example, in a neural network for handwriting recognition, a set of input neurons may be activated by the pixels of an input image representing a letter or digit. The activations of these neurons are then passed on, weighted and transformed by some function determined by the network's designer, to other neurons, etc., until finally an output neuron is activated that determines which character was read.
Like other machine learning methods, neural networks have been used to solve a wide variety of tasks that are hard to solve using ordinary rulebased programming, including computer vision and speech recognition.
Background
The inspiration for neural networks came from examination of central nervous systems. In an artificial neural network, simple artificial nodes, called "neurons", "neurodes", "processing elements" or "units", are connected together to form a network which mimics a biological neural network.
There is no single formal definition of what an artificial neural network is. Commonly, though, a class of statistical models will be called "neural" if they
 consist of sets of adaptive weights, i.e. numerical parameters that are tuned by a learning algorithm, and
 are capable of approximating nonlinear functions of their inputs.
The adaptive weights are conceptually connection strengths between neurons, which are activated during training and prediction.
Neural networks are also similar to biological neural networks in performing functions collectively and in parallel by the units, rather than there being a clear delineation of subtasks to which various units are assigned. The term "neural network" usually refers to models employed in statistics, cognitive psychology and artificial intelligence. Neural network models which emulate the central nervous system are part of theoretical neuroscience and computational neuroscience.
In modern software implementations of artificial neural networks, the approach inspired by biology has been largely abandoned for a more practical approach based on statistics and signal processing. In some of these systems, neural networks or parts of neural networks (like artificial neurons) form components in larger systems that combine both adaptive and nonadaptive elements. While the more general approach of such systems is more suitable for realworld problem solving, it has far less to do with the traditional artificial intelligence connectionist models. What they do have in common, however, is the principle of nonlinear, distributed, parallel and local processing and adaptation. Historically, the use of neural networks models marked a paradigm shift in the late eighties from highlevel (symbolic) artificial intelligence, characterized by expert systems with knowledge embodied in ifthen rules, to lowlevel (subsymbolic) machine learning, characterized by knowledge embodied in the parameters of a dynamical system.
History
Warren McCulloch and Walter Pitts^{[1]} (1943) created a computational model for neural networks based on mathematics and algorithms. They called this model threshold logic. The model paved the way for neural network research to split into two distinct approaches. One approach focused on biological processes in the brain and the other focused on the application of neural networks to artificial intelligence.
In the late 1940s psychologist Donald Hebb^{[2]} created a hypothesis of learning based on the mechanism of neural plasticity that is now known as Hebbian learning. Hebbian learning is considered to be a 'typical' unsupervised learning rule and its later variants were early models for long term potentiation. These ideas started being applied to computational models in 1948 with Turing's Btype machines.
Farley and Clark^{[3]} (1954) first used computational machines, then called calculators, to simulate a Hebbian network at MIT. Other neural network computational machines were created by Rochester, Holland, Habit, and Duda^{[4]} (1956).
Frank Rosenblatt^{[5]} (1958) created the perceptron, an algorithm for pattern recognition based on a twolayer learning computer network using simple addition and subtraction. With mathematical notation, Rosenblatt also described circuitry not in the basic perceptron, such as the exclusiveor circuit, a circuit whose mathematical computation could not be processed until after the backpropagation algorithm was created by Paul Werbos^{[6]} (1975).
Neural network research stagnated after the publication of machine learning research by Marvin Minsky and Seymour Papert^{[7]} (1969). They discovered two key issues with the computational machines that processed neural networks. The first issue was that singlelayer neural networks were incapable of processing the exclusiveor circuit. The second significant issue was that computers were not sophisticated enough to effectively handle the long run time required by large neural networks. Neural network research slowed until computers achieved greater processing power. Also key in later advances was the backpropagation algorithm which effectively solved the exclusiveor problem (Werbos 1975).^{[6]}
The parallel distributed processing of the mid1980s became popular under the name connectionism. The text by David E. Rumelhart and James McClelland^{[8]} (1986) provided a full exposition on the use of connectionism in computers to simulate neural processes.
Neural networks, as used in artificial intelligence, have traditionally been viewed as simplified models of neural processing in the brain, even though the relation between this model and brain biological architecture is debated, as it is not clear to what degree artificial neural networks mirror brain function.^{[9]}
In the 1990s, neural networks were overtaken in popularity in machine learning by support vector machines and other, much simpler methods such as linear classifiers. Renewed interest in neural nets was sparked in the 2000s by the advent of deep learning.
Recent improvements
While initially research had been concerned mostly with the electrical characteristics of neurons, a particularly important part of the investigation in recent years has been the exploration of the role of neuromodulators such as dopamine, acetylcholine, and serotonin on behaviour and learning.
Biophysical models, such as BCM theory, have been important in understanding mechanisms for synaptic plasticity, and have had applications in both computer science and neuroscience. Research is ongoing in understanding the computational algorithms used in the brain, with some recent biological evidence for radial basis networks and neural backpropagation as mechanisms for processing data.
Computational devices have been created in CMOS for both biophysical simulation and neuromorphic computing. More recent efforts show promise for creating nanodevices^{[10]} for very large scale principal components analyses and convolution. If successful, these efforts could usher in a new era of neural computing^{[11]} that is a step beyond digital computing, because it depends on learning rather than programming and because it is fundamentally analog rather than digital even though the first instantiations may in fact be with CMOS digital devices.
Between 2009 and 2012, the recurrent neural networks and deep feedforward neural networks developed in the research group of Jürgen Schmidhuber at the Swiss AI Lab IDSIA have won eight international competitions in pattern recognition and machine learning.^{[12]} For example, multidimensional long short term memory (LSTM)^{[13]}^{[14]} won three competitions in connected handwriting recognition at the 2009 International Conference on Document Analysis and Recognition (ICDAR), without any prior knowledge about the three different languages to be learned.
Variants of the backpropagation algorithm as well as unsupervised methods by Geoff Hinton and colleagues at the University of Toronto^{[15]}^{[16]} can be used to train deep, highly nonlinear neural architectures similar to the 1980 Neocognitron by Kunihiko Fukushima,^{[17]} and the "standard architecture of vision",^{[18]} inspired by the simple and complex cells identified by David H. Hubel and Torsten Wiesel in the primary visual cortex.
Deep learning feedforward networks alternate convolutional layers and maxpooling layers, topped by several pure classification layers. Fast GPUbased implementations of this approach have won several pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition^{[19]} and the ISBI 2012 Segmentation of Neuronal Structures in Electron Microscopy Stacks challenge.^{[20]} Such neural networks also were the first artificial pattern recognizers to achieve humancompetitive or even superhuman performance^{[21]} on benchmarks such as traffic sign recognition (IJCNN 2012), or the MNIST handwritten digits problem of Yann LeCun and colleagues at NYU.
Models
Neural network models in artificial intelligence are usually referred to as artificial neural networks (ANNs); these are essentially simple mathematical models defining a function $\backslash scriptstyle\; f:\; X\; \backslash rightarrow\; Y$ or a distribution over $\backslash scriptstyle\; X$ or both $\backslash scriptstyle\; X$ and $\backslash scriptstyle\; Y$, but sometimes models are also intimately associated with a particular learning algorithm or learning rule. A common use of the phrase ANN model really means the definition of a class of such functions (where members of the class are obtained by varying parameters, connection weights, or specifics of the architecture such as the number of neurons or their connectivity).
Network function
The word network in the term 'artificial neural network' refers to the inter–connections between the neurons in the different layers of each system. An example system has three layers. The first layer has input neurons, which send data via synapses to the second layer of neurons, and then via more synapses to the third layer of output neurons. More complex systems will have more layers of neurons with some having increased layers of input neurons and output neurons. The synapses store parameters called "weights" that manipulate the data in the calculations.
An ANN is typically defined by three types of parameters:
 The interconnection pattern between different layers of neurons
 The learning process for updating the weights of the interconnections
 The activation function that converts a neuron's weighted input to its output activation.
Mathematically, a neuron's network function $\backslash scriptstyle\; f(x)$ is defined as a composition of other functions $\backslash scriptstyle\; g\_i(x)$, which can further be defined as a composition of other functions. This can be conveniently represented as a network structure, with arrows depicting the dependencies between variables. A widely used type of composition is the nonlinear weighted sum, where $\backslash scriptstyle\; f\; (x)\; =\; K\; \backslash left(\backslash sum\_i\; w\_i\; g\_i(x)\backslash right)$, where $\backslash scriptstyle\; K$ (commonly referred to as the activation function^{[22]}) is some predefined function, such as the hyperbolic tangent. It will be convenient for the following to refer to a collection of functions $\backslash scriptstyle\; g\_i$ as simply a vector $\backslash scriptstyle\; g\; =\; (g\_1,\; g\_2,\; \backslash ldots,\; g\_n)$.
This figure depicts such a decomposition of $\backslash scriptstyle\; f$, with dependencies between variables indicated by arrows. These can be interpreted in two ways.
The first view is the functional view: the input $\backslash scriptstyle\; x$ is transformed into a 3dimensional vector $\backslash scriptstyle\; h$, which is then transformed into a 2dimensional vector $\backslash scriptstyle\; g$, which is finally transformed into $\backslash scriptstyle\; f$. This view is most commonly encountered in the context of optimization.
The second view is the probabilistic view: the random variable $\backslash scriptstyle\; F\; =\; f(G)$ depends upon the random variable $\backslash scriptstyle\; G\; =\; g(H)$, which depends upon $\backslash scriptstyle\; H=h(X)$, which depends upon the random variable $\backslash scriptstyle\; X$. This view is most commonly encountered in the context of graphical models.
The two views are largely equivalent. In either case, for this particular network architecture, the components of individual layers are independent of each other (e.g., the components of $\backslash scriptstyle\; g$ are independent of each other given their input $\backslash scriptstyle\; h$). This naturally enables a degree of parallelism in the implementation.
Networks such as the previous one are commonly called feedforward, because their graph is a directed acyclic graph. Networks with cycles are commonly called recurrent. Such networks are commonly depicted in the manner shown at the top of the figure, where $\backslash scriptstyle\; f$ is shown as being dependent upon itself. However, an implied temporal dependence is not shown.
Learning
What has attracted the most interest in neural networks is the possibility of learning. Given a specific task to solve, and a class of functions $\backslash scriptstyle\; F$, learning means using a set of observations to find $\backslash scriptstyle\; f^\{*\}\; \backslash in\; F$ which solves the task in some optimal sense.
This entails defining a cost function $\backslash scriptstyle\; C:\; F\; \backslash rightarrow\; \backslash mathbb\{R\}$ such that, for the optimal solution $\backslash scriptstyle\; f^*$, $\backslash scriptstyle\; C(f^*)\; \backslash leq\; C(f)$ $\backslash scriptstyle\; \backslash forall\; f\; \backslash in\; F$ – i.e., no solution has a cost less than the cost of the optimal solution (see Mathematical optimization).
The cost function $\backslash scriptstyle\; C$ is an important concept in learning, as it is a measure of how far away a particular solution is from an optimal solution to the problem to be solved. Learning algorithms search through the solution space to find a function that has the smallest possible cost.
For applications where the solution is dependent on some data, the cost must necessarily be a function of the observations, otherwise we would not be modelling anything related to the data. It is frequently defined as a statistic to which only approximations can be made. As a simple example, consider the problem of finding the model $\backslash scriptstyle\; f$, which minimizes $\backslash scriptstyle\; C=E\backslash left[(f(x)\; \; y)^2\backslash right]$, for data pairs $\backslash scriptstyle\; (x,y)$ drawn from some distribution $\backslash scriptstyle\; \backslash mathcal\{D\}$. In practical situations we would only have $\backslash scriptstyle\; N$ samples from $\backslash scriptstyle\; \backslash mathcal\{D\}$ and thus, for the above example, we would only minimize $\backslash scriptstyle\; \backslash hat\{C\}=\backslash frac\{1\}\{N\}\backslash sum\_\{i=1\}^N\; (f(x\_i)y\_i)^2$. Thus, the cost is minimized over a sample of the data rather than the entire data set.
When $\backslash scriptstyle\; N\; \backslash rightarrow\; \backslash infty$ some form of online machine learning must be used, where the cost is partially minimized as each new example is seen. While online machine learning is often used when $\backslash scriptstyle\; \backslash mathcal\{D\}$ is fixed, it is most useful in the case where the distribution changes slowly over time. In neural network methods, some form of online machine learning is frequently used for finite datasets.
Choosing a cost function
While it is possible to define some arbitrary, ad hoc cost function, frequently a particular cost will be used, either because it has desirable properties (such as convexity) or because it arises naturally from a particular formulation of the problem (e.g., in a probabilistic formulation the posterior probability of the model can be used as an inverse cost). Ultimately, the cost function will depend on the desired task. An overview of the three (3) main categories of learning tasks is provided below.
Learning paradigms
There are three major learning paradigm, each corresponding to a particular abstract learning task. These are supervised learning, unsupervised learning and reinforcement learning.
Supervised learning
In supervised learning, we are given a set of example pairs $\backslash scriptstyle\; (x,\; y),\; x\; \backslash in\; X,\; y\; \backslash in\; Y$ and the aim is to find a function $\backslash scriptstyle\; f:\; X\; \backslash rightarrow\; Y$ in the allowed class of functions that matches the examples. In other words, we wish to infer the mapping implied by the data; the cost function is related to the mismatch between our mapping and the data and it implicitly contains prior knowledge about the problem domain.
A commonly used cost is the meansquared error, which tries to minimize the average squared error between the network's output, f(x), and the target value y over all the example pairs. When one tries to minimize this cost using gradient descent for the class of neural networks called multilayer perceptrons, one obtains the common and wellknown backpropagation algorithm for training neural networks.
Tasks that fall within the paradigm of supervised learning are pattern recognition (also known as classification) and regression (also known as function approximation). The supervised learning paradigm is also applicable to sequential data (e.g., for speech and gesture recognition). This can be thought of as learning with a "teacher," in the form of a function that provides continuous feedback on the quality of solutions obtained thus far.
Unsupervised learning
In unsupervised learning, some data $\backslash scriptstyle\; x$ is given and the cost function to be minimized, that can be any function of the data $\backslash scriptstyle\; x$ and the network's output, $\backslash scriptstyle\; f$.
The cost function is dependent on the task (what we are trying to model) and our a priori assumptions (the implicit properties of our model, its parameters and the observed variables).
As a trivial example, consider the model $\backslash scriptstyle\; f(x)\; =\; a$, where $\backslash scriptstyle\; a$ is a constant and the cost $\backslash scriptstyle\; C=E[(x\; \; f(x))^2]$. Minimizing this cost will give us a value of $\backslash scriptstyle\; a$ that is equal to the mean of the data. The cost function can be much more complicated. Its form depends on the application: for example, in compression it could be related to the mutual information between $\backslash scriptstyle\; x$ and $\backslash scriptstyle\; f(x)$, whereas in statistical modeling, it could be related to the posterior probability of the model given the data. (Note that in both of those examples those quantities would be maximized rather than minimized).
Tasks that fall within the paradigm of unsupervised learning are in general estimation problems; the applications include clustering, the estimation of statistical distributions, compression and filtering.
Reinforcement learning
In reinforcement learning, data $\backslash scriptstyle\; x$ are usually not given, but generated by an agent's interactions with the environment. At each point in time $\backslash scriptstyle\; t$, the agent performs an action $\backslash scriptstyle\; y\_t$ and the environment generates an observation $\backslash scriptstyle\; x\_t$ and an instantaneous cost $\backslash scriptstyle\; c\_t$, according to some (usually unknown) dynamics. The aim is to discover a policy for selecting actions that minimizes some measure of a longterm cost; i.e., the expected cumulative cost. The environment's dynamics and the longterm cost for each policy are usually unknown, but can be estimated.
More formally, the environment is modeled as a Markov decision process (MDP) with states $\backslash scriptstyle\; \{s\_1,...,s\_n\}\backslash in\; S$ and actions $\backslash scriptstyle\; \{a\_1,...,a\_m\}\; \backslash in\; A$ with the following probability distributions: the instantaneous cost distribution $\backslash scriptstyle\; P(c\_ts\_t)$, the observation distribution $\backslash scriptstyle\; P(x\_ts\_t)$ and the transition $\backslash scriptstyle\; P(s\_\{t+1\}s\_t,\; a\_t)$, while a policy is defined as conditional distribution over actions given the observations. Taken together, the two define a Markov chain (MC). The aim is to discover the policy that minimizes the cost; i.e., the MC for which the cost is minimal.
ANNs are frequently used in reinforcement learning as part of the overall algorithm.^{[23]}^{[24]} Dynamic programming has been coupled with ANNs (Neuro dynamic programming) by Bertsekas and Tsitsiklis^{[25]} and applied to multidimensional nonlinear problems such as those involved in vehicle routing,^{[26]} natural resources management^{[27]}^{[28]} or medicine^{[29]} because of the ability of ANNs to mitigate losses of accuracy even when reducing the discretization grid density for numerically approximating the solution of the original control problems.
Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.
Learning algorithms
Training a neural network model essentially means selecting one model from the set of allowed models (or, in a Bayesian framework, determining a distribution over the set of allowed models) that minimizes the cost criterion. There are numerous algorithms available for training neural network models; most of them can be viewed as a straightforward application of optimization theory and statistical estimation.
Most of the algorithms used in training artificial neural networks employ some form of gradient descent. This is done by simply taking the derivative of the cost function with respect to the network parameters and then changing those parameters in a gradientrelated direction.
Evolutionary methods,^{[30]} gene expression programming,^{[31]} simulated annealing,^{[32]} expectationmaximization, nonparametric methods and particle swarm optimization^{[33]} are some commonly used methods for training neural networks.
Employing artificial neural networks
Perhaps the greatest advantage of ANNs is their ability to be used as an arbitrary function approximation mechanism that 'learns' from observed data. However, using them is not so straightforward, and a relatively good understanding of the underlying theory is essential.
 Choice of model: This will depend on the data representation and the application. Overly complex models tend to lead to problems with learning.
 Learning algorithm: There are numerous tradeoffs between learning algorithms. Almost any algorithm will work well with the correct hyperparameters for training on a particular fixed data set. However selecting and tuning an algorithm for training on unseen data requires a significant amount of experimentation.
 Robustness: If the model, cost function and learning algorithm are selected appropriately the resulting ANN can be extremely robust.
With the correct implementation, ANNs can be used naturally in online learning and large data set applications. Their simple implementation and the existence of mostly local dependencies exhibited in the structure allows for fast, parallel implementations in hardware.
Applications
The utility of artificial neural network models lies in the fact that they can be used to infer a function from observations. This is particularly useful in applications where the complexity of the data or task makes the design of such a function by hand impractical.
Reallife applications
The tasks artificial neural networks are applied to tend to fall within the following broad categories:
 Function approximation, or regression analysis, including time series prediction, fitness approximation and modeling.
 Classification, including pattern and sequence recognition, novelty detection and sequential decision making.
 Data processing, including filtering, clustering, blind source separation and compression.
 Robotics, including directing manipulators, prosthesis.
 Control, including Computer numerical control
Application areas include system identification and control (vehicle control, process control, natural resources management), quantum chemistry,^{[34]} gameplaying and decision making (backgammon, chess, poker), pattern recognition (radar systems, face identification, object recognition and more), sequence recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial applications (automated trading systems), data mining (or knowledge discovery in databases, "KDD"), visualization and email spam filtering.
Artificial neural networks have also been used to diagnose several cancers. An ANN based hybrid lung cancer detection system named HLND improves the accuracy of diagnosis and the speed of lung cancer radiology.^{[35]} These networks have also been used to diagnose prostate cancer. The diagnoses can be used to make specific models taken from a large group of patients compared to information of one given patient. The models do not depend on assumptions about correlations of different variables. Colorectal cancer has also been predicted using the neural networks. Neural networks could predict the outcome for a patient with colorectal cancer with a lot more accuracy than the current clinical methods. After training, the networks could predict multiple patient outcomes from unrelated institutions.^{[36]}
Neural networks and neuroscience
Theoretical and computational neuroscience is the field concerned with the theoretical analysis and computational modeling of biological neural systems. Since neural systems are intimately related to cognitive processes and behavior, the field is closely related to cognitive and behavioral modeling.
The aim of the field is to create models of biological neural systems in order to understand how biological systems work. To gain this understanding, neuroscientists strive to make a link between observed biological processes (data), biologically plausible mechanisms for neural processing and learning (biological neural network models) and theory (statistical learning theory and information theory).
Types of models
Many models are used in the field defined at different levels of abstraction and modeling different aspects of neural systems. They range from models of the shortterm behavior of individual neurons, models of how the dynamics of neural circuitry arise from interactions between individual neurons and finally to models of how behavior can arise from abstract neural modules that represent complete subsystems. These include models of the longterm, and shortterm plasticity, of neural systems and their relations to learning and memory from the individual neuron to the system level.
Neural network software
Neural network software is used to simulate, research, develop and apply artificial neural networks, biological neural networks and, in some cases, a wider array of adaptive systems.
Types of artificial neural networks
Artificial neural network types vary from those with only one or two layers of single direction logic, to complicated multi–input many directional feedback loops and layers. On the whole, these systems use algorithms in their programming to determine control and organization of their functions. Some may be as simple as a oneneuron layer with an input and an output, and others can mimic complex systems such as dANN, which can mimic chromosomal DNA through sizes at the cellular level, into artificial organisms and simulate reproduction, mutation and population sizes.^{[37]}
Most systems use "weights" to change the parameters of the throughput and the varying connections to the neurons. Artificial neural networks can be autonomous and learn by input from outside "teachers" or even selfteaching from writtenin rules.
Theoretical properties
Computational power
The multilayer perceptron (MLP) is a universal function approximator, as proven by the Cybenko theorem. However, the proof is not constructive regarding the number of neurons required or the settings of the weights.
Work by Hava Siegelmann and Eduardo D. Sontag has provided a proof that a specific recurrent architecture with rational valued weights (as opposed to full precision real numbervalued weights) has the full power of a Universal Turing Machine^{[38]} using a finite number of neurons and standard linear connections. They have further shown that the use of irrational values for weights results in a machine with superTuring power.
Capacity
Artificial neural network models have a property called 'capacity', which roughly corresponds to their ability to model any given function. It is related to the amount of information that can be stored in the network and to the notion of complexity.
Convergence
Nothing can be said in general about convergence since it depends on a number of factors. Firstly, there may exist many local minima. This depends on the cost function and the model. Secondly, the optimization method used might not be guaranteed to converge when far away from a local minimum. Thirdly, for a very large amount of data or parameters, some methods become impractical. In general, it has been found that theoretical guarantees regarding convergence are an unreliable guide to practical application.
Generalization and statistics
In applications where the goal is to create a system that generalizes well in unseen examples, the problem of overtraining has emerged. This arises in convoluted or overspecified systems when the capacity of the network significantly exceeds the needed free parameters. There are two schools of thought for avoiding this problem: The first is to use crossvalidation and similar techniques to check for the presence of overtraining and optimally select hyperparameters such as to minimize the generalization error. The second is to use some form of regularization. This is a concept that emerges naturally in a probabilistic (Bayesian) framework, where the regularization can be performed by selecting a larger prior probability over simpler models; but also in statistical learning theory, where the goal is to minimize over two quantities: the 'empirical risk' and the 'structural risk', which roughly corresponds to the error over the training set and the predicted error in unseen data due to overfitting.
Supervised neural networks that use an MSE cost function can use formal statistical methods to determine the confidence of the trained model. The MSE on a validation set can be used as an estimate for variance. This value can then be used to calculate the confidence interval of the output of the network, assuming a normal distribution. A confidence analysis made this way is statistically valid as long as the output probability distribution stays the same and the network is not modified.
By assigning a softmax activation function, a generalization of the logistic function, on the output layer of the neural network (or a softmax component in a componentbased neural network) for categorical target variables, the outputs can be interpreted as posterior probabilities. This is very useful in classification as it gives a certainty measure on classifications.
The softmax activation function is:
 $y\_i=\backslash frac\{e^\{x\_i\}\}\{\backslash sum\_\{j=1\}^c\; e^\{x\_j\}\}$
Dynamic properties
 This article needs attention from an expert in Technology. Please add a reason or a talk parameter to this template to explain the issue with the article. WikiProject Technology (or its Portal) may be able to help recruit an expert. (November 2008) 
Various techniques originally developed for studying disordered magnetic systems (i.e., the spin glass) have been successfully applied to simple neural network architectures, such as the Hopfield network. Influential work by E. Gardner and B. Derrida has revealed many interesting properties about perceptrons with realvalued synaptic weights, while later work by W. Krauth and M. Mezard has extended these principles to binaryvalued synapses.
Criticism
A common criticism of neural networks, particularly in robotics, is that they require a large diversity of training for realworld operation. This is not surprising, since any learning machine needs sufficient representative examples in order to capture the underlying structure that allows it to generalize to new cases. Dean Pomerleau, in his research presented in the paper "Knowledgebased Training of Artificial Neural Networks for Autonomous Robot Driving," uses a neural network to train a robotic vehicle to drive on multiple types of roads (single lane, multilane, dirt, etc.). A large amount of his research is devoted to (1) extrapolating multiple training scenarios from a single training experience, and (2) preserving past training diversity so that the system does not become overtrained (if, for example, it is presented with a series of right turns – it should not learn to always turn right). These issues are common in neural networks that must decide from amongst a wide variety of responses, but can be dealt with in several ways, for example by randomly shuffling the training examples, by using a numerical optimization algorithm that does not take too large steps when changing the network connections following an example, or by grouping examples in socalled minibatches.
A. K. Dewdney, a former Scientific American columnist, wrote in 1997, "Although neural nets do solve a few toy problems, their powers of computation are so limited that I am surprised anyone takes them seriously as a general problemsolving tool." (Dewdney, p. 82)
Arguments for Dewdney's position are that to implement large and effective software neural networks, much processing and storage resources need to be committed. While the brain has hardware tailored to the task of processing signals through a graph of neurons, simulating even a most simplified form on Von Neumann technology may compel a neural network designer to fill many millions of database rows for its connections – which can consume vast amounts of computer memory and hard disk space. Furthermore, the designer of neural network systems will often need to simulate the transmission of signals through many of these connections and their associated neurons – which must often be matched with incredible amounts of CPU processing power and time. While neural networks often yield effective programs, they too often do so at the cost of efficiency (they tend to consume considerable amounts of time and money).
Arguments against Dewdney's position are that neural nets have been successfully used to solve many complex and diverse tasks, ranging from autonomously flying aircraft [1] to detecting credit card fraud .
Technology writer Roger Bridgman commented on Dewdney's statements about neural nets:
Neural networks, for instance, are in the dock not only because they have been hyped to high heaven, (what hasn't?) but also because you could create a successful net without understanding how it worked: the bunch of numbers that captures its behaviour would in all probability be "an opaque, unreadable table...valueless as a scientific resource".
In spite of his emphatic declaration that science is not technology, Dewdney seems here to pillory neural nets as bad science when most of those devising them are just trying to be good engineers. An unreadable table that a useful machine could read would still be well worth having.^{[39]}
In response to this kind of criticism, one should note that although it is true that analyzing what has been learned by an artificial neural network is difficult, it is much easier to do so than to analyze what has been learned by a biological neural network. Furthermore, researchers involved in exploring learning algorithms for neural networks are gradually uncovering generic principles which allow a learning machine to be successful. For example, Bengio and LeCun (2007) wrote an article regarding local vs nonlocal learning, as well as shallow vs deep architecture [2].
Some other criticisms came from believers of hybrid models (combining neural networks and symbolic approaches). They advocate the intermix of these two approaches and believe that hybrid models can better capture the mechanisms of the human mind (Sun and Bookman, 1990).
Successes in pattern recognition contests since 2009
Between 2009 and 2012, the recurrent neural networks and deep feedforward neural networks developed in the research group of Jürgen Schmidhuber at the Swiss AI Lab IDSIA have won eight international competitions in pattern recognition and machine learning.^{[40]} For example, the bidirectional and multidimensional long short term memory (LSTM)^{[41]}^{[42]}
of Alex Graves et al. won three competitions in connected handwriting recognition at the 2009 International Conference on Document Analysis and Recognition (ICDAR), without any prior knowledge about the three different languages to be learned. Fast GPUbased implementations of this approach by Dan Ciresan and colleagues at IDSIA have won several pattern recognition contests, including the IJCNN 2011 Traffic Sign Recognition Competition,^{[43]}
the ISBI 2012 Segmentation of Neuronal Structures in Electron Microscopy Stacks challenge,^{[20]}
and others. Their neural networks also were the first artificial pattern recognizers to achieve humancompetitive or even superhuman performance^{[21]}
on important benchmarks such as traffic sign recognition (IJCNN 2012), or the famous MNIST handwritten digits problem of Yann LeCun at NYU. Deep, highly nonlinear neural architectures similar to the 1980 Neocognitron by Kunihiko Fukushima^{[17]}
and the "standard architecture of vision"^{[18]}
can also be pretrained by unsupervised methods^{[44]}^{[45]}
of Geoff Hinton's lab at University of Toronto. A team from this lab won a 2012 contest sponsored by Merck to design software to help find molecules that might lead to new drugs.^{[46]}
Gallery
A singlelayer feedforward artificial neural network. Arrows originating from $\backslash scriptstyle\; x\_2$ are omitted for clarity. There are p inputs to this network and q outputs. In this system, the value of the qth output, $\backslash scriptstyle\; y\_q$ would be calculated as $\backslash scriptstyle\; y\_q\; =\; \backslash sum(x\_i*w\_\{iq\})$
A twolayer feedforward artificial neural network.
See also
References
Bibliography

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 Cybenko, G.V. (1989). Approximation by Superpositions of a Sigmoidal function, electronic version
 Duda, R.O., Hart, P.E., Stork, D.G. (2001) Pattern classification (2nd edition), Wiley, ISBN 0471056693

 Gurney, K. (1997) An Introduction to Neural Networks London: Routledge. ISBN 1857286731 (hardback) or ISBN 1857285034 (paperback)
 Haykin, S. (1999) Neural Networks: A Comprehensive Foundation, Prentice Hall, ISBN 0132733501
 Fahlman, S, Lebiere, C (1991). The CascadeCorrelation Learning Architecture, created for electronic version
 Hertz, J., Palmer, R.G., Krogh. A.S. (1990) Introduction to the theory of neural computation, Perseus Books. ISBN 0201515601
 Lawrence, Jeanette (1994) Introduction to Neural Networks, California Scientific Software Press. ISBN 1883157005
 Masters, Timothy (1994) Signal and Image Processing with Neural Networks, John Wiley & Sons, Inc. ISBN 0471049638
 Ripley, Brian D. (1996) Pattern Recognition and Neural Networks, Cambridge
 Siegelmann, H.T. and electronic version
 Sergios Theodoridis, Konstantinos Koutroumbas (2009) "Pattern Recognition", 4th Edition, Academic Press, ISBN 9781597492720.
 Smith, Murray (1993) Neural Networks for Statistical Modeling, Van Nostrand Reinhold, ISBN 0442013108
 Wasserman, Philip (1993) Advanced Methods in Neural Computing, Van Nostrand Reinhold, ISBN 0442004613
 Computational Intelligence: A Methodological Introduction by Kruse, Borgelt, Klawonn, Moewes, Steinbrecher, Held, 2013, Springer, ISBN 9781447150121
 NeuroFuzzySysteme (3rd edition) by Borgelt, Klawonn, Kruse, Nauck, 2003, Vieweg, ISBN 9783528252656
External links
 DMOZro:Rețea neurală artificială
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