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Machine learning engineer & researcher based in Nepal. Exploring computer vision and medical imaging in fundus images.

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The GAN Minimax Objective Function

May 26, 2026·1 min read
deep-learninggansgenerative-models
ml.blogDeep Learning · Generative Models
Generative Adversarial Networks

The GAN Minimax
Objective Function

An interactive visual tour of why GANs use log, what minG maxD really means, and how the two-player game reaches Nash equilibrium.

7 slidesInteractive chartsMath intuition
Slide 01 / 7

Two players, one game

A GAN is a two-player zero-sum game. The Generator G tries to produce fake data so convincing that the Discriminator D cannot tell it apart from real data.

Generator G

Takes random noise z from pz(z) and maps it to fake data G(z).

Discriminator D

Outputs D(x) in [0,1], the probability that x is real.

Architecture flow
Generator path
Discriminator path
Real data
Based on Goodfellow et al. (2014), "Generative Adversarial Nets"

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