README.md

metadata

title: Gendigit
emoji: 🚀
colorFrom: yellow
colorTo: green
sdk: gradio
sdk_version: 5.17.1
app_file: app.py
pinned: false
license: mit
short_description: 'This project implements a Generative Adversarial Network '

GenDigit

This project implements a Generative Adversarial Network (GAN) that generates images of handwritten digits using the MNIST dataset. The network consists of two primary components:

• Generator (G): A neural network that generates fake images based on random noise and the desired label (digit).
• Discriminator (D): A neural network that evaluates whether an image is real (from the dataset) or fake (generated by the generator).

Generator (G) Loss Function:

The Generator tries to minimize the binary cross-entropy loss by generating images that fool the Discriminator. The loss for the Generator is:

$$L_G=-{\mathbb{E}}_z[\log D(G(z))]L\_G\; =\; -\backslash mathbb\{E\}\_\{z\}[\; \backslash log\; D(G(z))\; ]$$

Where:

• $$ z $$ is the random noise input to the Generator.
• $$ G(z) $$ is the generated image.
• $$ D(G(z)) $$ is the Discriminator's probability that the generated image is real.

The Generator is trained to minimize this loss by improving its ability to generate realistic images.

Discriminator (D) Loss Function:

The Discriminator tries to distinguish between real and fake images. Its loss consists of two parts:

1. Loss for real images: $$ L_{D_{\text{real}}} = -\mathbb{E}{x{\text{real}}}[ \log D(x_{\text{real}}) ] $$
2. Loss for fake images: $$ L_{D_{\text{fake}}} = -\mathbb{E}_{z}[ \log (1 - D(G(z))) ] $$

Where:

• $$ x_{\text{real}} $$ is a real image from the dataset.
• $$ D(x_{\text{real}}) $$ is the Discriminator's prediction for a real image.
• $$ G(z) $$ is the fake image generated by the Generator.

The total loss for the Discriminator is:

$$L_D=L_{D_{\text{real}}}+L_{D_{\text{fake}}}L\_D\; =\; L\_\{D\_\{\backslash text\{real\}\}\}\; +\; L\_\{D\_\{\backslash text\{fake\}\}\}$$

The Discriminator is trained to minimize this loss by improving its ability to classify real and fake images correctly.