What is a multi-layer perceptron (MLP)?

A multi-layer perceptron (MLP) is a type of artificial neural network consisting of at least three layers of nodes: an input layer, one or more hidden layers, and an output layer. Each layer is fully connected to the next, meaning every node in a layer has a weighted connection to every node in the following layer. Unlike simpler models like single-layer perceptrons, MLPs use non-linear activation functions (e.g., ReLU, sigmoid) in the hidden layers, enabling them to learn complex patterns in data. For example, an MLP might take pixel values from an image as input, process them through hidden layers to detect edges or shapes, and output probabilities for different object classes. This architecture makes MLPs capable of approximating virtually any continuous function, given sufficient data and computational resources.

Training an MLP involves two key phases: forward propagation and backpropagation. During forward propagation, input data passes through the network, and each layer applies weights, sums the inputs, and applies an activation function to produce outputs. The final output is compared to the target using a loss function (e.g., mean squared error for regression, cross-entropy for classification). Backpropagation then calculates gradients of the loss with respect to each weight using the chain rule, starting from the output layer and moving backward. Optimizers like stochastic gradient descent adjust the weights to minimize the loss. For instance, in a handwritten digit recognition task (like MNIST), the MLP might start with random weights, misclassify most digits initially, and iteratively refine its parameters to reduce classification errors. The inclusion of hidden layers allows the network to model interactions between input features that simpler linear models cannot capture.

MLPs are widely used in tasks like regression, classification, and even reinforcement learning. However, they have limitations. For high-dimensional data like images or sequences, fully connected layers become computationally expensive due to the sheer number of parameters. This led to the development of specialized architectures like convolutional neural networks (CNNs) for images or recurrent neural networks (RNNs) for sequences. MLPs also require careful tuning of hyperparameters, such as the number of hidden layers, neurons per layer, and learning rates. Despite these limitations, MLPs remain foundational in deep learning. Developers might use them for tabular data tasks or as components in larger systems, like the final classification layer in a CNN. Understanding MLPs provides a basis for grasping more advanced architectures and their trade-offs.