In deep learning, a multilayer perceptron (MLP) is a kind of modern feedforward neural network consisting of fully connected neurons with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is not linearly separable.

Modern neural networks are trained using backpropagation and are colloquially referred to as "vanilla" networks. MLPs grew out of an effort to improve on single-layer perceptrons, which could only be applied to linearly separable data. A perceptron traditionally used a Heaviside step function as its nonlinear activation function. However, the backpropagation algorithm requires that modern MLPs use continuous activation functions such as sigmoid or ReLU.

Multilayer perceptrons form the basis of deep learning, and are applicable across a vast set of diverse domains.

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. In MLPs some neurons use a nonlinear activation function that was developed to model the frequency of action potentials, or firing, of biological neurons.

The two historically common activation functions are both sigmoids, and are described by

The first is a hyperbolic tangent that ranges from −1 to 1, while the other is the logistic function, which is similar in shape but ranges from 0 to 1. Here ${\displaystyle y_{i}}$ is the output of the ${\displaystyle i}$th node (neuron) and ${\displaystyle v_{i}}$ is the weighted sum of the input connections. Alternative activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial basis functions (used in radial basis networks, another class of supervised neural network models).

In recent developments of deep learning the rectified linear unit (ReLU) is more frequently used as one of the possible ways to overcome the numerical problems related to the sigmoids.

The MLP consists of three or more layers (an input and an output layer with one or more hidden layers) of nonlinearly-activating nodes. Since MLPs are fully connected, each node in one layer connects with a certain weight ${\displaystyle w_{ij}}$ to every node in the following layer.