Neural network

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(also called artificial neural network, abbr. ANN). A network where the nodes correspond to neurons and the arcs correspond to synaptic connections in the biological metaphor. The following properties are included:


neural state. Each node has a state variable, say x. In the brain, this could be the potassium level; in computing applications, it could be anything the modeler chooses.
arc weight. Each arc has a weight that affects the state of its neighboring nodes when firing. If the weight is positive, it said to be excitatory; if it is negative, it is inhibitory.
state equations. The neural states change by some differential (or difference) equation, say LaTeX: \textstyle x' = F(x,w,t). Typically (but not necessarily), LaTeX: -F is the gradient of an energy function (in keeping with the biological metaphor), say LaTeX: \textstyle F(x,w,t) = -\nabla x[E(x,w,t)], so that LaTeX: x(t) follows a path of steepest descent towards a minimum energy state.
learning mechanism. This could be equations to change the weights: LaTeX: \textstyle w' = L(x,w,t). Various learning mechanisms are represented this way, including a form of supervised learning that uses a training set to provide feedback on errors. Other elements can be learned besides the arc weights, including the topology of the network.


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