Case Introduction
Generative Adversarial Networks (GANs) are a type of deep learning model consisting of a generator network and a discriminator network. They improve their capabilities through adversarial training, competing against each other. The generator network attempts to produce samples that resemble real data, while the discriminator network tries to distinguish between samples generated by the generator and real samples. Through this process, the generator network gradually learns to create more realistic samples.
In this case, we will use GANs to generate handwritten digit images. We will utilize the MNIST dataset, which contains a large number of handwritten digit images along with their corresponding labels. By training the GAN model, we can generate new handwritten digit images that are similar to those in the MNIST dataset.
Algorithm Principle
GANs consist of a generator and a discriminator. The generator attempts to produce realistic samples, while the discriminator tries to distinguish between samples generated by the generator and real samples. These two networks learn and improve through adversarial training.
Both the generator and the discriminator are deep neural networks, typically constructed using Convolutional Neural Networks (CNN). The generator network takes a noise vector as input and gradually generates samples that resemble real data. The discriminator network receives both the samples generated by the generator and the real samples, attempting to differentiate between them.
The training process of GANs can be divided into the following steps:
1. Initialize the parameters of the generator and discriminator networks.
2. Sample a batch of noise vectors from a noise distribution.
3. Use the generator network to create a batch of samples.
4. Mix the generated samples with real samples and assign labels to each sample, for example, 1 for real samples and 0 for generated samples.
5. Train the discriminator network using the mixed samples so that it can distinguish between real samples and generated samples.
6. Sample another batch of noise vectors from the noise distribution.
7. Use the generator network to create a batch of samples and assign a label of 1 to each sample.
8. Train the discriminator network using the generated samples so that it classifies them as real samples as accurately as possible.
9. Repeat steps 2 to 8 until the predetermined number of training iterations is reached or convergence is achieved.
During the training of GANs, the generator and discriminator networks compete against each other. The generator continuously adjusts its parameters to produce more realistic samples, while the discriminator adjusts its parameters to more accurately differentiate between real samples and generated samples. This competitive and adversarial process ultimately leads to the generator network producing high-quality samples.
Formula Derivation
The goal of GANs is to minimize the loss functions of both the generator and the discriminator. During training, we iteratively update the parameters of the generator and discriminator to maximize the following loss function:
Through an iterative optimization process, the generator and discriminator will gradually learn and improve their capabilities, generating realistic samples.
Dataset
We will use the MNIST dataset to train the GANs model. The MNIST dataset contains handwritten digit images and their corresponding labels. It includes 60,000 training samples and 10,000 test samples. Each sample is a 28×28 pixel grayscale image, with the label representing the digit on the image.
Computational Steps
Prepare the dataset: Load handwritten digit image samples from the MNIST dataset.
Build the generator network: The generator network typically consists of convolutional layers, deconvolutional layers, and activation functions. The input is a noise vector, and the output is a handwritten digit image similar to those in the MNIST dataset.
Build the discriminator network: The discriminator network also typically consists of convolutional layers and activation functions. The input is a handwritten digit image, and the output is a real number representing the probability that the image is a real sample.
Define the loss function and optimizer: Use cross-entropy as the loss function for both the discriminator and the generator, and use different optimizers to update the network parameters.
Train the GANs model: Train the GANs model using the training dataset and noise vectors. In each training batch, the parameters of the discriminator and generator are updated sequentially.
Generate new handwritten digit images: Use the trained generator network to generate new handwritten digit images.
CodeExplanation
We define the Generator and Discriminator classes to construct the structures of the generator and discriminator networks. When building the networks, we use fully connected layers, LeakyReLU activation functions, and Tanh activation functions.
In the train_gan function, we define the training process of the GAN model. In each training batch, we first train the discriminator network and then the generator network. The discriminator’s loss includes the loss for real samples and the loss for fake samples, while the generator’s loss is the loss for the generated samples being classified as real samples.
In the generate_images function, we use the trained generator network to generate new handwritten digit images. We input the noise vector into the generator network and visualize the generated images.
In the main program, we load the MNIST dataset, initialize the generator and discriminator networks, define the training parameters, and then call the train_gan function to train the GAN model. Finally, we use the generate_images function to generate new handwritten digit images.
Python Code (available for paid reading if needed; otherwise, you can practice with the content above!)
Below is an example code based on PyTorch for training and generating handwritten digit images using the GANs model.