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Encyclopedia > Artificial neuron

An artificial neuron (also called a "node" or "Nv neuron" or "Binary neuron" or "McCulloch-Pitts neuron") is an abstraction of biological neurons and the basic unit in an artificial neural network. The Artificial Neuron receives one or more inputs (representing the one or more dendrites) and sum them to produce an output (synapse). Usually the sums of each node are weighted, and the sum is passed through a non-linear function known as an activation or transfer function. The canonical form of transfer functions is the sigmoid, but they may also take the form of other non-linear functions, piecewise linear functions, or step functions. Generally, transfer functions are monotonically increasing. Drawing by Santiago RamÃ³n y Cajal of neurons in the pigeon cerebellum. ... An artificial neural network (ANN) or commonly just neural network (NN) is an interconnected group of artificial neurons that uses a mathematical model or computational model for information processing based on a connectionist approach to computation. ... The term Dendrite stems from the Greek word dendron (literally â€œtreeâ€), and typically refers to the branched projections of a neuron that act to conduct the electrical stimulation received from other cells to and from the cell body, or soma of the neuron from which the dendrites project. ... Illustration of the major elements in a prototypical synapse. ... To do: 20th century mathematics chaos theory, fractals Lyapunov stability and non-linear control systems non-linear video editing See also: Aleksandr Mikhailovich Lyapunov Dynamical system External links http://www. ... The logistic curve A sigmoid function is a mathematical function that produces a sigmoid curve â€” a curve having an S shape. ... In mathematics, a function f(x) of a real number variable x is defined piecewise, if f(x) is given by different expressions on various intervals. ... In mathematics, functions between ordered sets are monotonic (or monotone, or even isotone) if they preserve the given order. ...

## Contents

For a given artificial neuron, let there be m inputs with signals x1 through xm and weights w1 through wm.

The output of neuron k is:

$y_k = varphi left( sum_{j=0}^m w_{kj} x_j right)$

Where $varphi$ (Phi) is the transfer function.

Wikipedia does not have an article with this exact name. ...

The output propagates to the next layer (through a weighted synapse) or finally exits the system as part or all of the output.

## History

The original artificial neuron is the Threshold Logic Unit first proposed by Warren McCulloch and Walter Pitts in 1943. As a transfer function, it employs a threshold or step function taking on the values 1 or 0 only. Warren McCulloch (November 16, 1899 - September 24, 1969) was an American neurophysiologist and cybernetician. ... Walter Pitts (1923? - 1969) was a logician who worked in the field of cognitive psychology. ... Year 1943 (MCMXLIII) was a common year starting on Friday (the link is to a full 1943 calendar). ...

## 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 multi-layer 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. An artificial neural network (ANN) or commonly just neural network (NN) is an interconnected group of artificial neurons that uses a mathematical model or computational model for information processing based on a connectionist approach to computation. ...

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

$u = sum_{i = 1}^n w_{i} x_{i}$

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.

$y = left{ begin{matrix} 1 & mbox{if }u ge theta 0 & mbox{if }u < theta end{matrix} right.$

See: Step function A function on the reals is a step function if it can be written as a finite linear combination of semi-open intervals. ...

### Linear combination

The output unit y is a linearly weighted sum of its outputs plus a bias term, similar to θ above, which is independent of the inputs. In mathematics, linear combinations are a concept central to linear algebra and related fields of mathematics. ...

$y = left(u + bright)$

Networks based on this formulation are known as perceptrons. Typically the above transfer function in its pure form would only be useful in a regression setting. For a binary classification setting, the sign of the output denotes the class predicted; in this case it is more sensible (and more convenient in the context of the learning algorithm) to consider positive outputs to be 1 and negative outputs to be 0, thus reducing the transfer function to that of the step function above, where θ = − b. Generally, regression is a move backwards; It is the opposite of progression. ...

See: Perceptron The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt. ...

### Sigmoid

A fairly simple non-linear function, the sigmoid also has an easily calculated derivative, which is used 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 minimise the computational load of their simulations. Sigmoid generally means resembling the letter S or the lower-case Greek letter sigma (&#962;). Specific uses include: In mathematics, either a specific function &#8212; the logistic curve &#8212; or any real function whose graph has a sigmoid shape: see sigmoid function. ... Sigmoid generally means resembling the letter S or the lower-case Greek letter sigma (&#962;). Specific uses include: In mathematics, either a specific function &#8212; the logistic curve &#8212; or any real function whose graph has a sigmoid shape: see sigmoid function. ...

See: Sigmoid function The logistic curve A sigmoid function is a mathematical function that produces a sigmoid curve â€” a curve having an S shape. ...

### Criticism

The Artificial neuron is generally criticized for not having a correct biophysical mapping. Although it does capture the numerous incoming dendrites, it fails to provide multiple output synapses. This helps speed up computation, but at the loss of biophysical accuracy.

The perceptron is a type of artificial neural network invented in 1957 at the Cornell Aeronautical Laboratory by Frank Rosenblatt. ... ADALINE (Adaptive Linear Neuron or later Adaptive Linear Element) is a single layer neural network. ... Connectionism is an approach in the fields of artificial intelligence, cognitive science, neuroscience, psychology and philosophy of mind. ...

## Bibliography

• McCulloch, W. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 7:115 - 133.

Results from FactBites:

 Artificial neuron - Wikipedia, the free encyclopedia (329 words) The artificial neuron (also called "node") is the basic unit of an artificial neural network, simulating a biological neuron. The original artificial neuron is the Threshold Logic Unit first proposed by Warren McCulloch and Walter Pitts in 1943. The transfer function of a neuron is chosen to have a number of properties which either enhance or simplify the network containing the neuron.
 Artificial neuron - definition of Artificial neuron in Encyclopedia (262 words) The artificial neuron is another name for the Threshold Logic Unit originally proposed by Warren McCulloch and Walter Pitts in 1940. It receives one or more inputs and produces an output based on the calculation of the sum of the inputs using a simple non-linear function as a threshold or step function which is usually a sigmoid. The artificial neurons are highly interconnected in a large single-layer or multi-layer neural network, the information processing performed in this way may be crudely summarised as follows: signals (action-potentials) appear at the unit's inputs (synapses).
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