A generative adversarial network (GAN) is a class of machine learning frameworks and a prominent framework for approaching generative AI. The concept was initially developed by Ian Goodfellow and his colleagues in June 2014. In a GAN, two neural networks compete with each other in the form of a zero-sum game, where one agent's gain is another agent's loss.
Given a training set, this technique learns to generate new data with the same statistics as the training set. For example, a GAN trained on photographs can generate new photographs that look at least superficially authentic to human observers, having many realistic characteristics. Though originally proposed as a form of generative model for unsupervised learning, GANs have also proved useful for semi-supervised learning, fully supervised learning, and reinforcement learning.
The core idea of a GAN is based on the "indirect" training through the discriminator, another neural network that can tell how "realistic" the input seems, which itself is also being updated dynamically. This means that the generator is not trained to minimize the distance to a specific image, but rather to fool the discriminator. This enables the model to learn in an unsupervised manner.
GANs are similar to mimicry in evolutionary biology, with an evolutionary arms race between both networks.
Mathematical Definition
The original GAN is defined as a game. Each probability space \((\Omega, \mu_{\text{ref}})\) defines a GAN game. There are two players: generator and discriminator. The generator's strategy set is \(\mathcal{P}(\Omega)\), the set of all probability measures \(\mu_G\) on \(\Omega\). The discriminator's strategy set is the set of Markov kernels \(\mu_D: \Omega \to \mathcal{P}[0,1]\), where \(\mathcal{P}[0,1]\) is the set of probability measures on \([0,1]\).
The GAN game is a zero-sum game, with objective function:
\[ L(\mu_G, \mu_D) := \mathbb{E}_{x \sim \mu_{\text{ref}}, y \sim \mu_D(x)}[\ln y] + \mathbb{E}_{x \sim \mu_G, y \sim \mu_D(x)}[\ln(1-y)]. \]
The generator aims to minimize the objective, and the discriminator aims to maximize the objective. The generator's task is to approach \(\mu_G \approx \mu_{\text{ref}}\), matching its output distribution as closely as possible to the reference distribution. The discriminator's task is to output a value close to 1 when the input appears to be from the reference distribution, and close to 0 when the input looks like it came from the generator distribution.
In Practice
The generative network generates candidates while the discriminative network evaluates them. This creates a contest based on data distributions, where the generator learns to map from a latent space to the true data distribution, aiming to produce candidates that the discriminator cannot distinguish from real data. The discriminator's goal is to correctly identify these candidates, but as the generator improves, its task becomes more challenging, increasing the discriminator's error rate.
A known dataset serves as the initial training data for the discriminator. Training involves presenting it with samples from the training dataset until it achieves acceptable accuracy. The generator is trained based on whether it succeeds in fooling the discriminator. Typically, the generator is seeded with randomized input sampled from a predefined latent space (e.g., a multivariate normal distribution). Thereafter, candidates synthesized by the generator are evaluated by the discriminator. Independent backpropagation procedures are applied to both networks so that the generator produces better samples, while the discriminator becomes more skilled at flagging synthetic samples. When used for image generation, the generator is typically a deconvolutional neural network, and the discriminator is a convolutional neural network.
Relation to Other Statistical Machine Learning Methods
GANs are implicit generative models, meaning they do not explicitly model the likelihood function nor provide a means for finding the latent variable corresponding to a given sample, unlike alternatives such as flow-based generative models.
Compared to fully visible belief networks such as WaveNet and PixelRNN and autoregressive models in general, GANs can generate one complete sample in one pass, rather than multiple passes through the network. Compared to Boltzmann machines and linear ICA, there is no restriction on the type of function used by the network.
Since neural networks are universal approximators, GANs are asymptotically consistent. As of 2026, variational autoencoders have been proven to be universal approximators, but GANs remain a distinct and influential approach in the field of machine learning and deep learning. The framework has inspired numerous variants and applications, contributing to the broader development of artificial intelligence and neural network research.