[R1 Regular Item] Detailed Explanation of R1 Regular Item in GAN

The R1 regularization term is a commonly used generative adversarial network (GAN) training technique to stabilize the GAN training process and improve the quality of generated images.

During training, we need to supervise the output of the generator to ensure that the images generated by the generator are as similar as possible to real images. Among them, the R1 regularization term is a method of penalizing the gradient of the discriminator to encourage the discriminator to distinguish the image generated by the generator from the real image.

Specifically, in the R1 regularization term, we first compute the discriminator's prediction for the real image and find its gradient for the input image. We then square these gradients, sum them, and finally take the average. This average is the R1 regularization term, which is used to penalize the prediction results of the discriminator. For the output of the generator, we can also perform similar processing on it to obtain the corresponding R1 regular term.

In the PaddlePaddle framework, we can use the paddle.grad() function to calculate the gradient, and use tensor operations to calculate the sum and average of the squared gradients. Here is a simple example showing how to compute the R1 regularizer:

import paddle

# 定义一个函数计算 R1 正则项
def r1_penalty(real_pred, real_img):
    grad_real = paddle.grad(outputs=real_pred.sum(), inputs=real_img, create_graph=True)[0]
    grad_penalty = (grad_real * grad_real).reshape([grad_real.shape[0], -1]).sum(1).mean()
    return grad_penalty

In this example, we first define a function named r1_penalty to calculate the R1 regularization term. The input of the function includes the discriminator's prediction result of the real image real_pred and the real image itself real_img. Next, we calculate the gradient of real_pred with respect to real_img using the paddle.grad() function and save it in the grad_real variable. We then square each element in grad_real and sum and average them to get the final R1 regularized term grad_penalty.

It should be noted that in actual GAN ​​training, we usually calculate the R1 regularization term for the output of the generator and the real image separately, and add them to the loss function of the discriminator. This can effectively improve the quality of generated images and stabilize the GAN training process.