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Deep Dive into GANs: The Math Behind Generative Adversarial Networks

2025-08-28

This post delves into the mathematical foundations of Generative Adversarial Networks (GANs). Starting with the basic concepts, the author meticulously explains the loss functions of the generator and discriminator, deriving conditions for optimal discriminator and generator. Using mathematical tools like binary cross-entropy and JS divergence, the adversarial process between generator and discriminator during GAN training is clearly illustrated. The ultimate goal is to make the distribution of generated data as close as possible to that of real data. The post also briefly introduces GAN training methods and highlights subtle differences in formulas compared to Goodfellow's original paper.

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(jaketae.github.io)
AI Generative Adversarial Networks

Astonishing Patterns of Prime Numbers in Polar Coordinates

2024-12-16

This article explores the phenomenon of prime numbers plotted on polar coordinates exhibiting spiral or linear patterns. The author uses Python code, employing SymPy to generate prime numbers and Matplotlib for visualization. Results show that as the number of primes increases, the pattern transitions from spirals to straight lines. This isn't unique to primes; it's related to rational approximations of $2pi$. The article explains the underlying mathematics and explores the connection between prime distribution and pattern sparsity.

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(jaketae.github.io)
Misc polar coordinates