feed-forward neural networks rn weights associated with it that isthe weights associated with the first layer are matrix of the form while this is not shown in the figure - each unit also has bias term associated with it the first layer produces an output where oi xk *wk bi note that the index corresponds to each of the inputs/weights (going from )and the index corresponds to the units in the first layer (going from let' now look at the output of first layer in vectorized notation by vectorized notationwe simply mean linear algebraic operationssuch as vector matrix multiplications and computation of the activation function on vector producing vector (rather than scalar to scalarthe output of the first layer can be represented as ( herewe are treating the input rn to be of dimensionality nthe weight matrix to be of dimensionality and the bias term to be vector of dimensionality noticethenthat produces vector of dimensionality and the function simply transforms each element of the vector to produce similar process follows for the second layer that goes from to this can be written in vectorized form as ( we can also write the entire computation up to layer in vectorized form as ( figure - illustrates neural network in vector form