GAN

A generative adversarial network (GAN) is a class of generative models that consists of two neural networks, a generator and a discriminator, which are trained simultaneously through adversarial training. The generator aims to produce realistic data samples from random noise, while the discriminator's objective is to distinguish between real data samples and those generated by the generator. The training process involves a minimax game, where the generator tries to maximize the probability of the discriminator making a mistake, and the discriminator tries to minimize its classification error. Mathematically, this can be expressed as a two-player game where the generator's loss function is defined as the negative log probability of the discriminator's output for generated samples, and the discriminator's loss is the sum of the log probabilities for real and generated samples. GANs have become a foundational framework in generative modeling, with numerous variants and applications in image synthesis, video generation, and data augmentation.