Neural network

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Simplified view of a feedforward artificial neural network

Traditionally, the term neural network had been used to refer to a network or circuit of biological neurons[citation needed]. The modern usage of the term often refers to artificial neural networks, which are composed of artificial neurons or nodes. Thus the term has two distinct usages:

  1. Biological neural networks are made up of real biological neurons that are connected or functionally related in the peripheral nervous system or the central nervous system. In the field of neuroscience, they are often identified as groups of neurons that perform a specific physiological function in laboratory analysis.
  2. Artificial neural networks are made up of interconnecting artificial neurons (programming constructs that mimic the properties of biological neurons). Artificial neural networks may either be used to gain an understanding of biological neural networks, or for solving artificial intelligence problems without necessarily creating a model of a real biological system. The real, biological nervous system is highly complex and includes some features that may seem superfluous based on an understanding of artificial networks.

This article focuses on the relationship between the two concepts; for detailed coverage of the two different concepts refer to the separate articles: Biological neural network and Artificial neural network.


In general a biological neural network is composed of a group or groups of chemically connected or functionally associated neurons. A single neuron may be connected to many other neurons and the total number of neurons and connections in a network may be extensive. Connections, called synapses, are usually formed from axons to dendrites, though dendrodendritic microcircuits[1] and other connections are possible. Apart from the electrical signaling, there are other forms of signaling that arise from neurotransmitter diffusion, which have an effect on electrical signaling. As such, neural networks are extremely complex.

Artificial intelligence and cognitive modeling try to simulate some properties of neural networks. While similar in their techniques, the former has the aim of solving particular tasks, while the latter aims to build mathematical models of biological neural systems.

In the artificial intelligence field, artificial neural networks have been applied successfully to speech recognition, image analysis and adaptive control, in order to construct software agents (in computer and video games) or autonomous robots. Most of the currently employed artificial neural networks for artificial intelligence are based on statistical estimation, optimization and control theory.

The cognitive modelling field involves the physical or mathematical modeling of the behaviour of neural systems; ranging from the individual neural level (e.g. modelling the spike response curves of neurons to a stimulus), through the neural cluster level (e.g. modelling the release and effects of dopamine in the basal ganglia) to the complete organism (e.g. behavioural modelling of the organism's response to stimuli).

History of the neural network analogy

The concept neural networks started in the late-1800s as an effort to describe how the human mind performed. These ideas started being applied to computational models with Turing's B-type machines and the perceptron.

In early 1950s Friedrich Hayek was one of the first to posit the idea of spontaneous order[citation needed] in the brain arising out of decentralized networks of simple units (neurons). In the late 1940s, Donald Hebb made one of the first hypotheses for a mechanism of neural plasticity (i.e. learning), Hebbian learning. Hebbian learning is considered to be a 'typical' unsupervised learning rule and it (and variants of it) was an early model for long term potentiation.

The Perceptron is essentially a linear classifier for classifying data  x \in R^n specified by parameters w \in R^n, b \in R and an output function f = w'x + b. Its parameters are adapted with an ad-hoc rule similar to stochastic steepest gradient descent. Because the inner product is a linear operator in the input space, the Perceptron can only perfectly classify a set of data for which different classes are linearly separable in the input space, while it often fails completely for non-separable data. While the development of the algorithm initially generated some enthusiasm, partly because of its apparent relation to biological mechanisms, the later discovery of this inadequacy caused such models to be abandoned until the introduction of non-linear models into the field.

The Cognitron (1975) was an early multilayered neural network with a training algorithm. The actual structure of the network and the methods used to set the interconnection weights change from one neural strategy to another, each with its advantages and disadvantages. Networks can propagate information in one direction only, or they can bounce back and forth until self-activation at a node occurs and the network settles on a final state. The ability for bi-directional flow of inputs between neurons/nodes was produced with the Hopfield's network (1982), and specialization of these node layers for specific purposes was introduced through the first hybrid network.

The parallel distributed processing of the mid-1980s became popular under the name connectionism.

The rediscovery of the backpropagation algorithm was probably the main reason behind the repopularisation of neural networks after the publication of "Learning Internal Representations by Error Propagation" in 1986 (Though backpropagation itself dates from 1974). The original network utilised multiple layers of weight-sum units of the type f = g(w'x + b), where g was a sigmoid function or logistic function such as used in logistic regression. Training was done by a form of stochastic steepest gradient descent. The employment of the chain rule of differentiation in deriving the appropriate parameter updates results in an algorithm that seems to 'backpropagate errors', hence the nomenclature. However it is essentially a form of gradient descent. Determining the optimal parameters in a model of this type is not trivial, and steepest gradient descent methods cannot be relied upon to give the solution without a good starting point. In recent times, networks with the same architecture as the backpropagation network are referred to as Multi-Layer Perceptrons. This name does not impose any limitations on the type of algorithm used for learning.

The backpropagation network generated much enthusiasm at the time and there was much controversy about whether such learning could be implemented in the brain or not, partly because a mechanism for reverse signalling was not obvious at the time, but most importantly because there was no plausible source for the 'teaching' or 'target' signal.

The brain, neural networks and computers

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[citation needed].

A subject of current research in theoretical neuroscience is the question surrounding the degree of complexity and the properties that individual neural elements should have to reproduce something resembling animal intelligence.

Historically, computers evolved from the von Neumann architecture, which is based on sequential processing and execution of explicit instructions. On the other hand, the origins of neural networks are based on efforts to model information processing in biological systems, which may rely largely on parallel processing as well as implicit instructions based on recognition of patterns of 'sensory' input from external sources. In other words, at its very heart a neural network is a complex statistical processor (as opposed to being tasked to sequentially process and execute).

Neural networks and artificial intelligence

An artificial neural network (ANN), also called a simulated neural network (SNN) or commonly just neural network (NN) is an interconnected group of artificial neurons that uses a mathematical or computational model for information processing based on a connectionistic approach to computation. In most cases an ANN is an adaptive system that changes its structure based on external or internal information that flows through the network.

In more practical terms neural networks are non-linear statistical data modeling or decision making tools. They can be used to model complex relationships between inputs and outputs or to find patterns in data.


An artificial neural network involves a network of simple processing elements (artificial neurons) which can exhibit complex global behavior, determined by the connections between the processing elements and element parameters. Artificial neurons were first proposed in 1943 by Warren McCulloch, a neurophysiologist, and Walter Pitts, an MIT logician.[1] One classical type of artificial neural network is the Hopfield net.

In a neural network model simple nodes, which can be called variously "neurons", "neurodes", "Processing Elements" (PE) or "units", are connected together to form a network of nodes — hence the term "neural network". While a neural network does not have to be adaptive per se, its practical use comes with algorithms designed to alter the strength (weights) of the connections in the network to produce a desired signal flow.

In modern software implementations of artificial neural networks the approach inspired by biology has more or less been abandoned for a more practical approach based on statistics and signal processing. In some of these systems, neural networks, or parts of neural networks (such as artificial neurons), are used as components in larger systems that combine both adaptive and non-adaptive elements.

The concept of a neural network appears to have first been proposed by Alan Turing in his 1948 paper "Intelligent Machinery".


The utility of artificial neural network models lies in the fact that they can be used to infer a function from observations and also to use it. This is particularly useful in applications where the complexity of the data or task makes the design of such a function by hand impractical.

Real life applications

The tasks to which artificial neural networks are applied tend to fall within the following broad categories:

  • Function approximation, or regression analysis, including time series prediction and modelling.
  • Classification, including pattern and sequence recognition, novelty detection and sequential decision making.
  • Data processing, including filtering, clustering, blind signal separation and compression.

Application areas include system identification and control (vehicle control, process control), game-playing and decision making (backgammon, chess, racing), pattern recognition (radar systems, face identification, object recognition, etc.), sequence recognition (gesture, speech, handwritten text recognition), medical diagnosis, financial applications, data mining (or knowledge discovery in databases, "KDD"), visualization and e-mail spam filtering.

Use in Teaching Strategy

Neural Networks are being used to determine the significance of a seating arrangement in a classroom learning environment. In this application, neural networks have proven that there is a correlation between the location of high and low-performing students in the room and how well they do in the class. An article in Complexity explains that when low-performing students are seated in the front, their chance to do better increases. The results of high-performing students who are seated in the back are not affected. In addition, when high-performing students are seated in the outer four corners, the performance of the class as a whole increases. [2][2]

Neural network software

Main article: 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.

Learning paradigms

There are three major learning paradigms, each corresponding to a particular abstract learning task. These are supervised learning, unsupervised learning and reinforcement learning. Usually any given type of network architecture can be employed in any of those tasks.

Supervised learning

In supervised learning, we are given a set of example pairs  (x, y), x \in X, y \in Y and the aim is to find a function f in the allowed class of functions that matches the examples. In other words, we wish to infer how the mapping implied by the data and the cost function is related to the mismatch between our mapping and the data.

Unsupervised learning

In unsupervised learning we are given some data x, and a cost function which is to be minimized which can be any function of x and the network's output, f. The cost function is determined by the task formulation. Most applications fall within the domain of estimation problems such as statistical modeling, compression, filtering, blind source separation and clustering.

Reinforcement learning

In reinforcement learning, data x is usually not given, but generated by an agent's interactions with the environment. At each point in time t, the agent performs an action y_t and the environment generates an observation x_t and an instantaneous cost c_t, according to some (usually unknown) dynamics. The aim is to discover a policy for selecting actions that minimizes some measure of a long-term cost, i.e. the expected cumulative cost. The environment's dynamics and the long-term cost for each policy are usually unknown, but can be estimated. ANNs are frequently used in reinforcement learning as part of the overall algorithm. Tasks that fall within the paradigm of reinforcement learning are control problems, games and other sequential decision making tasks.

Learning algorithms

There are many algorithms for training neural networks; most of them can be viewed as a straightforward application of optimization theory and statistical estimation. They include: Back propagation by gradient descent, Rprop, BFGS, CG etc.

Evolutionary computation methods, simulated annealing, expectation maximization and non-parametric methods are among other commonly used methods for training neural networks. See also machine learning.

Recent developments in this field also saw the use of optimization and other swarm intelligence techniques used in the training of neural networks.

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 behaviour, the field is closely related to cognitive and behavioural 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, each defined at a different level of abstraction and trying to model different aspects of neural systems. They range from models of the short-term behaviour of individual neurons, through models of how the dynamics of neural circuitry arise from interactions between individual neurons, to models of how behaviour can arise from abstract neural modules that represent complete subsystems. These include models of the long-term and short-term plasticity of neural systems and its relation to learning and memory, from the individual neuron to the system level.

Current research

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.


A common criticism of neural networks, particularly in robotics, is that they require a large diversity of training for real-world operation. Dean Pomerleau, in his research presented in the paper "Knowledge-based 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, multi-lane, 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.

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 problem-solving 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 NN designer to fill many millions of database rows for its connections - which can lead to abusive RAM and HD necessities. Furthermore, the designer of NN 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 time and money efficiency.

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[3] to detecting credit card fraud[4].

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.[3]

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 1994).

See also

  • Artificial neural network
  • Biological cybernetics
  • Biologically inspired computing
  • Cerebellar Model Articulation Controller
  • Cognitive architecture
  • Cognitive science
  • Cultured neuronal networks
  • Memristor
  • Neural network software


  1. Arbib, p.666
  2. Monterola, C., Roxas, R.M., and Carreon-Monterola, S. (2008). Characterizing the Effect of Seating Arrangement on Classroom Learning Using Neural Networks. Complexity, 14(4), 26-33. ISSN 1076-2782.
  3. Roger Bridgman's defence of neural networks

Further reading

  • Arbib, Michael A. (Ed.) (1995). The Handbook of Brain Theory and Neural Networks. 
  • Alspector, U.S. Patent 4,874,963 "Neuromorphic learning networks". October 17, 1989.
  • Agre, Philip E. (1997). Computation and Human Experience. Cambridge University Press. ISBN 0-521-38603-9. , p. 80
  • Yaneer Bar-Yam (2003). Dynamics of Complex Systems, Chapter 2. 
  • Yaneer Bar-Yam (2003). Dynamics of Complex Systems, Chapter 3. 
  • Yaneer Bar-Yam (2005). Making Things Work.  See chapter 3.
  • Bertsekas, Dimitri P. (1999). Nonlinear Programming. 
  • Bertsekas, Dimitri P. & Tsitsiklis, John N. (1996). Neuro-dynamic Programming. 
  • Bhadeshia H. K. D. H. (1992). "Neural Networks in Materials Science". ISIJ International 39: 966–979. doi:10.2355/isijinternational.39.966. 
  • Boyd, Stephen & Vandenberghe, Lieven (2004). Convex Optimization. 
  • Dewdney, A. K. (1997). Yes, We Have No Neutrons: An Eye-Opening Tour through the Twists and Turns of Bad Science. Wiley, 192 pp.  See chapter 5.
  • Egmont-Petersen, M., de Ridder, D., Handels, H. (2002). "Image processing with neural networks - a review". Pattern Recognition 35 (10): 2279–2301. doi:10.1016/S0031-3203(01)00178-9. 
  • Fukushima, K. (1975). "Cognitron: A Self-Organizing Multilayered Neural Network". Biological Cybernetics 20: 121–136. doi:10.1007/BF00342633. 
  • Frank, Michael J. (2005). "Dynamic Dopamine Modulation in the Basal Ganglia: A Neurocomputational Account of Cognitive Deficits in Medicated and Non-medicated Parkinsonism". Journal of Cognitive Neuroscience 17: 51–72. doi:10.1162/0898929052880093. 
  • Gardner, E.J., & Derrida, B. (1988). "Optimal storage properties of neural network models". Journal of Physics a 21: 271–284. doi:10.1088/0305-4470/21/1/031. 
  • Krauth, W., & Mezard, M. (1989). "Storage capacity of memory with binary couplings". Journal de Physique 50: 3057–3066. doi:10.1051/jphys:0198900500200305700. 
  • Maass, W., & Markram, H. (2002). "On the computational power of recurrent circuits of spiking neurons". Journal of Computer and System Sciences 69(4): 593–616. 
  • MacKay, David (2003). Information Theory, Inference, and Learning Algorithms. 
  • Mandic, D. & Chambers, J. (2001). Recurrent Neural Networks for Prediction: Architectures, Learning algorithms and Stability. Wiley. 
  • Minsky, M. & Papert, S. (1969). An Introduction to Computational Geometry. MIT Press. 
  • Muller, P. & Insua, D.R. (1995). "Issues in Bayesian Analysis of Neural Network Models". Neural Computation 10: 571–592. 
  • Reilly, D.L., Cooper, L.N. & Elbaum, C. (1982). "A Neural Model for Category Learning". Biological Cybernetics 45: 35–41. doi:10.1007/BF00387211. 
  • Rosenblatt, F. (1962). Principles of Neurodynamics. Spartan Books. 
  • Sun, R. & Bookman,L. (eds.) (1994.). Computational Architectures Integrating Neural and Symbolic Processes.. Kluwer Academic Publishers, Needham, MA.. 
  • Sutton, Richard S. & Barto, Andrew G. (1998). Reinforcement Learning : An introduction. 
  • Van den Bergh, F. Engelbrecht, AP. Cooperative Learning in Neural Networks using Particle Swarm Optimizers. CIRG 2000. 
  • Wilkes, A.L. & Wade, N.J. (1997). "Bain on Neural Networks". Brain and Cognition 33: 295–305. doi:10.1006/brcg.1997.0869. 
  • Wasserman, P.D. (1989). Neural computing theory and practice. Van Nostrand Reinhold. 
  • Jeffrey T. Spooner, Manfredi Maggiore, Raul Ord onez, and Kevin M. Passino, Stable Adaptive Control and Estimation for Nonlinear Systems: Neural and Fuzzy Approximator Techniques, John Wiley and Sons, NY, 2002.
  • Peter Dayan, L.F. Abbott. Theoretical Neuroscience. MIT Press. 
  • Wulfram Gerstner, Werner Kistler. Spiking Neuron Models:Single Neurons, Populations, Plasticity. Cambridge University Press. 
  • Steeb, W-H (2008). The Nonlinear Workbook: Chaos, Fractals, Neural Networks, Genetic Algorithms, Gene Expression Programming, Support Vector Machine, Wavelets, Hidden Markov Models, Fuzzy Logic with C++, Java and SymbolicC++ Programs: 4th edition. World Scientific Publishing. ISBN 981-281-852-9. 

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