Artificial neuron
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The artificial neuron (also called "node") is the basic unit of an artificial neural network, simulating a biological neuron. It receives one or more inputs, sums these, and produces an output after passing the sum through a (usually) non-linear function known as an activation or transfer function. The canonical form of this function is a sigmoid, but may also be another non-linear function, a piecewise linear function, or a step function. Generally, transfer functions are monotonically increasing.
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Basic structure
For a given artificial neuron, let there be m inputs with signals 1,x1 through xm and weights bk,w1 through wm.
The output of the neuron k is y:
- <math>y_k = \varphi( \sum_{j=0}^m w_{kj} x_j)<math>
Where <math>\varphi<math> (Phi) is the activation (or transfer) function.
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Artificial_neuron.png
Image:artificial_neuron.png
The output propogates 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.
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.
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.
- <math>y = \left\{ \begin{matrix} 1 & \mbox{if }u \ge \theta \\ 0 & \mbox{if }u < \theta \end{matrix} \right.<math>
See: Step function
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.
See: Sigmoid function
Bibliography
- McCulloch, W. and Pitts, W. (1943). A logical calculus of the ideas immanent in nervous activity. Bulletin of Mathematical Biophysics, 7:115 - 133.fr:Neurone formel