Multilayer Perceptron
A multilayer perceptron, or MLP, is a feedforward neural network made of an input layer, one or more hidden layers and an output layer, in which every unit in a layer is connected to every unit in the next and each unit applies a nonlinear activation function to a weighted sum of its inputs. It is the canonical "plain" neural network: information flows in one direction, there is no memory, convolution or attention, and the weights are learned by gradient descent using backpropagation.
The hidden layers are what overcame the perceptron's famous limit. A single-layer perceptron (Frank Rosenblatt, 1958) can only separate classes with a straight line, and Minsky and Papert's 1969 book pointed out that it cannot represent the exclusive-or (XOR) function. Adding a hidden layer solves this: two hidden units can each carve out one half-plane, and the output unit combines them so that XOR is true exactly when one input is on and the other off. The difficulty was training such networks, and the answer was backpropagation, the application of the chain rule to compute how the loss changes with every weight, popularized by David Rumelhart, Geoffrey Hinton and Ronald Williams in their 1986 Nature paper "Learning representations by back-propagating errors."
Nonlinearity is not optional, and the arithmetic of an MLP is simple. Each layer computes h = f(Wx + b), where W is a weight matrix, b a bias vector and f an activation such as ReLU, tanh or the sigmoid. If f were linear, stacked layers would collapse into one linear map, no more powerful than a single layer. Parameter counts follow directly: a layer with n inputs and m outputs has n × m weights plus m biases. For a classic digit classifier reading 28 × 28 = 784 pixels, with one hidden layer of 128 units and 10 outputs, the count is 784 × 128 + 128 = 100,480 for the first layer plus 128 × 10 + 10 = 1,290 for the second, totaling 101,770 trainable parameters.
An MLP treats its input as an unstructured vector, which defines both its generality and its weakness. Because every input connects to every unit, it has no built-in assumption that neighboring pixels are related or that a pattern is the same wherever it appears; convolutional networks add locality and weight sharing, and transformers add attention over tokens. For images, text and sequences, those structured architectures need far fewer parameters and generalize better. For tabular data, MLPs are competitive but often not dominant: studies such as Grinsztajn and colleagues (2022) found that tree-based models like gradient-boosted trees still tended to outperform standard deep networks on typical medium-sized tabular datasets. Depth also introduces training difficulties such as vanishing gradients, mitigated by ReLU, careful initialization, normalization layers and residual connections.
Far from being obsolete, MLPs are embedded inside nearly every modern model. In each transformer layer, a position-wise feed-forward network is an MLP with two linear layers and a nonlinearity applied to every token independently; in the original 2017 transformer the model width of 512 expanded to a hidden width of 2048, a factor of four that many successors keep. Much of a large language model's parameter count sits in these blocks, and interpretability researchers study them as stores of learned associations. MLPs also serve as classifier heads on top of pretrained encoders, as value and policy networks in reinforcement learning, and as the coordinate networks in neural radiance fields. The 2021 MLP-Mixer even built an image model almost entirely from them.
A common misconception is that "perceptron" and "multilayer perceptron" are interchangeable, or that more layers always mean a better model. The original perceptron used a hard threshold and a simple update rule, while an MLP uses differentiable activations and backpropagation, and added depth without data, regularization and good optimization simply overfits or fails to train.
Read the multilayer perceptron as the basic unit of deep learning: a stack of linear maps separated by nonlinearities that can bend a decision boundary into any needed shape, rarely the final architecture on its own, but the component that nearly every larger architecture still contains.