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The perceptron algorithm is also termed the single-layer perceptron, to distinguish it from a multilayer perceptron, which is a misnomer for a more complicated neural network. As a linear classifier, the single-layer perceptron is the simplest feedforward neural network .
If a multilayer perceptron has a linear activation function in all neurons, that is, a linear function that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output model.
Each block consists of a simplified multi-layer perceptron (MLP) with a single hidden layer. The hidden layer h has logistic sigmoidal units, and the output layer has linear units. Connections between these layers are represented by weight matrix U; input-to-hidden-layer connections have weight matrix W.
The bottom layer of inputs is not always considered a real neural network layer. A multilayer perceptron (MLP) is a misnomer for a modern feedforward artificial neural network, consisting of fully connected neurons (hence the synonym sometimes used of fully connected network (FCN)), often with a nonlinear kind of activation function, organized ...
Neurons of one layer connect only to neurons of the immediately preceding and immediately following layers. The layer that receives external data is the input layer. The layer that produces the ultimate result is the output layer. In between them are zero or more hidden layers. Single layer and unlayered networks are also used.
These perceptrons were modified forms of the perceptrons introduced by Rosenblatt in 1958. They consisted of a retina, a single layer of input functions and a single output. [15] [12] Besides this, the authors restricted the "order", or maximum number of incoming connections, of their perceptrons.
In particular, this shows that a perceptron network with a single infinitely wide hidden layer can approximate arbitrary functions. Such an can also be approximated by a network of greater depth by using the same construction for the first layer and approximating the identity function with later layers.
Crucially, for instance, any multilayer perceptron using a linear activation function has an equivalent single-layer network; a non-linear function is therefore necessary to gain the advantages of a multi-layer network. [citation needed]