A feedforward neural network (aka multilayer perceptron or deep feedforward network) is a supervised learning network in which information only flows forward. Unlike recurrent neural networks, which have feedback connections, nodes in a feedforward neural network can only pass input in the direction of the output layer.

The goal of a feedforward network is to approximate some function $f^{\ast }\left(x\right)$ that will map input $x$ to a category $y$, $f^{\ast }\left(x\right)=y$. The network defines the mapping $f(x;\theta )=y$ and learns the parameters of $\theta$ to develop the best function approximation. The network does this by means of a composed set of functions, each of which describes a different layer in the network:

The depth of the network is the number of layers, the interior of which are “hidden” because they do not show the desired output. The goal of the interior functions is to help $f\left(x\right)$ approximate $f^{\ast }\left(x\right)$.

As the input moves through the network, some activation function calculates the layer values, based on the sum of the product of the weights and input, and determines whether the node (neuron) should fire. The function can compute continuous and differentiable output (unlike a step function). This enables a back-propagation algorithm to compute gradients, which will in turn be used to improve the performance of each layer.