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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.
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 in at least three layers, notable for being able to distinguish data that is not ...
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 .
Generally, a recurrent multilayer perceptron network (RMLP network) consists of cascaded subnetworks, each containing multiple layers of nodes. Each subnetwork is feed-forward except for the last layer, which can have feedback connections. Each of these subnets is connected only by feed-forward connections. [103]
The multilayer perceptron is a universal function approximator, as proven by the universal approximation theorem. However, the proof is not constructive regarding the number of neurons required, the network topology, the weights and the learning parameters.
It uses a deep multilayer perceptron with eight layers. [6] It is a supervised learning network that grows layer by layer, where each layer is trained by regression analysis. Useless items are detected using a validation set, and pruned through regularization. The size and depth of the resulting network depends on the task. [7]
In particular, this shows that a perceptron network with a single infinitely wide hidden layer can approximate arbitrary functions. Such an f {\displaystyle f} 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.
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