Generative Adversarial Networks (d2l.ai)

generative-modelsgansdeep-learningminimax

Abstraction: GAN architecture as minimax game between generator and discriminator networks

Key points:

Introduced by Goodfellow et al. (2014); GANs use a discriminative model as a signal to train a generative model — data generator is good when fake data cannot be distinguished from real data (two-sample test framing)
Generator G maps latent noise z ~ N(0,1) to synthetic data x' = G(z); discriminator D outputs probability that input is real; trained with cross-entropy loss
Minimax objective: min_D max_G { -E[log D(x)] - E[log(1 - D(G(z)))] }; in practice generator maximizes log D(G(z)) to avoid vanishing gradients when D is confident
Both networks trained with Adam; discriminator updated first each iteration, then generator; batch size 8 for toy Gaussian example
Training is unstable when generator improves to near-perfect — gradients become too small for the discriminator to make progress
d2l.ai implements GAN on a 2D Gaussian dataset as a minimal pedagogical example, with separate update_D and update_G functions

Connections: Ian Goodfellow · D2l AI · Generative Adversarial Networks · Generative Models · Deep Learning