herethe (ij)-th element of the weight matrix wl [wl, is the weight that connects the -th node in the ( )-st layer with the -th node in the -th layer the name given to (the number of layers without the input layeris the network depth and maxl pl is called the network width while we mostly study networks that have an equal number of nodes in the hidden layers ( pl- )in general there can be different numbers of nodes in each hidden layer the output (xof multiple-layer neural network is obtained from the input via the following sequence of computationsx - ( ( |{ { { |{ |{za - - bl sl (zl (xl { |{zzl ( al denoting the function wl bl by ml the output (xcan thus be written as the function composition (xsl ( ( the algorithm for computing the output (xfor an input is summarized next note that we leave open the possibility that the activation functions {sl have different definitions for each layer in some casessl may even depend on some or all of the already computed and algorithm feed-forward propagation for neural network inputfeature vector xweights {wl, }biases {bl, for each layer outputthe value of the prediction function ( /the zero or input layer for to do compute the hidden variable zl, for each node in layer lzl wl al- bl compute the activation function al, for each node in layer lal sl (zl return (xal /the output layer network depth network width