为什么 GAN 无法从某些分布中生成样本？

Question

我尝试在 Keras 中实现基本的 GAN，基于 this 实现。

如果我在抛物线上采样点，GAN 是收敛的，并且能够从这个分布中生成样本，但是如果我在圆上采样点，它就会失败。我想知道为什么 GAN 很难？如何解决？

抛物线的学习过程如下：

以下是圈子的学习过程：

这里是重现的代码：

from __future__ import print_function, division

import warnings
warnings.filterwarnings('ignore')

import os
import shutil
from datetime import datetime

from keras.layers import Input, Dense
from keras.layers.advanced_activations import LeakyReLU
from keras.models import Sequential, Model
from keras.optimizers import Adam

from sklearn import datasets
import numpy as np
import tensorflow as tf
from tqdm import tqdm
import matplotlib.pyplot as plt
import cv2

# Derived from original code https://github.com/eriklindernoren/Keras-GAN/blob/master/gan/gan.py

def print_env_info():
    print('-' * 60)
    import keras
    print('keras.__version__', keras.__version__)
    print('-' * 60)
    import tensorflow as tf
    print('tf.__version__', tf.__version__)
    print('-' * 60)

class GAN():
    def __init__(self):
        self.latent_dim = 128

        optimizer = Adam(0.0002, 0.5)

        # Build and compile the discriminator
        self.discriminator = self.build_discriminator()
        self.discriminator.compile(loss='binary_crossentropy',
            optimizer=optimizer,
            metrics=['accuracy'])

        # Build the generator
        self.generator = self.build_generator()

        # The generator takes noise as input and generates imgs
        z = Input(shape=(self.latent_dim,))
        img = self.generator(z)

        # For the combined model we will only train the generator
        self.discriminator.trainable = False

        # The discriminator takes generated images as input and determines validity
        validity = self.discriminator(img)

        # The combined model  (stacked generator and discriminator)
        # Trains the generator to fool the discriminator
        self.combined = Model(z, validity)
        self.combined.compile(loss='binary_crossentropy', optimizer=optimizer)

        # Tensorboard writer
        log_dir = "logs/" + datetime.now().strftime("%Y%m%d-%H%M%S")
        self.writer = tf.summary.FileWriter(log_dir)

    def build_generator(self):

        model = Sequential()

        model.add(Dense(64, input_dim=self.latent_dim))
        model.add(LeakyReLU(alpha=0.2))
        model.add(Dense(128, input_dim=2))
        model.add(LeakyReLU(alpha=0.2))
        model.add(Dense(2, activation='tanh'))

        model.summary()

        noise = Input(shape=(self.latent_dim,))
        img = model(noise)

        return Model(noise, img)

    def build_discriminator(self):

        model = Sequential()

        model.add(Dense(64, input_dim=2))
        model.add(LeakyReLU(alpha=0.2))
        model.add(Dense(128, input_dim=2))
        model.add(LeakyReLU(alpha=0.2))
        model.add(Dense(1, activation='sigmoid'))
        model.summary()

        img = Input(shape=(2, ))
        validity = model(img)

        return Model(img, validity)

    def generate_dataset(self, n_samples=10000):
        # # V1: y = x^2
        x = np.random.uniform(-1, 1, size=n_samples)
        y = x ** 2
        data = np.stack([x, y], axis=1)

        # V2: x ^ 2 + y ^ 2 = 1
        # angle = np.random.uniform(0, 1, size=n_samples) * (np.pi * 2)
        # x = np.cos(angle)
        # y = np.sin(angle)
        # data = np.stack([x, y], axis=1)

        # V3: swiss roll
        # data, _ = datasets.make_swiss_roll(n_samples=n_samples, noise=0.0, random_state=0)
        # data = np.stack([data[:, 0], data[:, 2]], axis=1)
        # data = data - np.min(data, axis=0)
        # data = data / np.max(data, axis=0)
        # data = 2 * data - 1.0

        # # V4:
        # data, _ = datasets.make_moons(n_samples=n_samples, shuffle=False, noise=None, random_state=0)
        # data = data - np.min(data, axis=0)
        # data = data / np.max(data, axis=0)
        # data = 2 * data - 1.0

        return data

    def summary_image(self, tensor):
        import io
        from PIL import Image

        tensor = tensor.astype(np.uint8)

        height, width, channel = tensor.shape
        image = Image.fromarray(tensor)
        output = io.BytesIO()
        image.save(output, format='PNG')
        image_string = output.getvalue()
        output.close()
        return tf.Summary.Image(height=height,
                                width=width,
                                colorspace=channel,
                                encoded_image_string=image_string)

    def get_visualization(self, epoch):
        def generate_fake_data(n_samples):
            noise = np.random.normal(0, 1, (n_samples, self.latent_dim))
            X_hat = self.generator.predict(noise)
            x = X_hat[:, 0]
            y = X_hat[:, 1]
            return x, y

        def save_figure():
            x_fake, y_fake = generate_fake_data(n_samples=100)
            data = self.generate_dataset(n_samples=1000)
            x_real, y_real = data[:, 0], data[:, 1]

            axes = plt.gca()
            axes.set_xlim([-1, 1])
            axes.set_ylim([-1, 1])
            axes.set_aspect('equal', 'datalim')
            plt.scatter(x_real, y_real, s=1, color='b', alpha=0.2)
            plt.scatter(x_fake, y_fake, s=1, color='r')
            plt.savefig(f'images/{epoch}.png')
            plt.close()

        save_figure()

        image = cv2.imread(f'images/{epoch}.png')
        image = self.summary_image(image)

        return image


    def train(self, epochs, batch_size, sample_interval):
        # Load the dataset
        X_train = self.generate_dataset()

        print('X_train.shape', X_train.shape)

        # Adversarial ground truths
        valid = np.ones((batch_size, 1))
        fake = np.zeros((batch_size, 1))

        for epoch in tqdm(range(epochs), total=epochs):
            # ---------------------
            #  Train Discriminator
            # ---------------------

            # Select a random batch of images
            idx = np.random.randint(0, X_train.shape[0], batch_size)
            imgs = X_train[idx]

            noise = np.random.normal(0, 1, (batch_size, self.latent_dim))

            # Generate a batch of new images
            gen_imgs = self.generator.predict(noise)

            # Train the discriminator
            d_loss_real = self.discriminator.train_on_batch(imgs, valid)
            d_loss_fake = self.discriminator.train_on_batch(gen_imgs, fake)
            d_loss = 0.5 * np.add(d_loss_real, d_loss_fake)

            # ---------------------
            #  Train Generator
            # ---------------------

            noise = np.random.normal(0, 1, (batch_size, self.latent_dim))

            # Train the generator (to have the discriminator label samples as valid)
            g_loss = self.combined.train_on_batch(noise, valid)

            # Print the progress
            # print ("%d [D loss: %f, acc.: %.2f%%] [G loss: %f]" % (epoch, d_loss[0], 100*d_loss[1], g_loss))

            if epoch % sample_interval == 0:
                image_summary = tf.Summary(value=[tf.Summary.Value(tag='fake', image=self.get_visualization(epoch))])
                self.writer.add_summary(image_summary, epoch)

            if epoch % sample_interval == 0:
                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="loss/D_loss", simple_value=d_loss[0]),
                ])
                self.writer.add_summary(summary, epoch)

                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="D_loss/D_loss_real", simple_value=d_loss_real[0]),
                ])
                self.writer.add_summary(summary, epoch)

                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="D_loss/D_loss_fake", simple_value=d_loss_fake[0]),
                ])
                self.writer.add_summary(summary, epoch)

                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="loss/Acc", simple_value=100*d_loss[1]),
                ])
                self.writer.add_summary(summary, epoch)

                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="D_loss/Acc_real", simple_value=100*d_loss_real[1]),
                ])
                self.writer.add_summary(summary, epoch)

                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="D_loss/Acc_fake", simple_value=100*d_loss_fake[1]),
                ])
                self.writer.add_summary(summary, epoch)

                summary = tf.Summary(value=[
                    tf.Summary.Value(tag="loss/G_loss", simple_value=g_loss),
                ])
                self.writer.add_summary(summary, epoch)


if __name__ == '__main__':
    print_env_info()

    if os.path.exists('logs'):
        shutil.rmtree('logs')

    if os.path.exists('images'):
        shutil.rmtree('images')
    os.makedirs('images')

    gan = GAN()
    gan.train(epochs=10000, batch_size=32, sample_interval=200)

Answer 1

从 Tensorboard 中的准确度图中可以看出，这里的主要问题在于判别器。因为它的准确度在 50-60% 左右波动并且没有提高。这是非常糟糕的，因为生成器在下游并且在鉴别器达到不错的准确性之前无法训练。那么判别器有什么问题呢？

首先，这是你训练它的方式。你分两批给它正样本和负样本。这会产生梯度，将模型系数随机推向相反的方向，收敛性很差。如果您将两种类型的样本组合在一个批次中，收敛性会显着提高。

第二，批量大小。围绕一个圆圈的 32 个随机点太少，模型无法感受到与 32 个随机点的差异。您需要有至少 256 个批量大小。

第三，隐藏层的神经元数量。实际上，对于生成器和判别器中的这种简单数据，您的神经元太多了。判别器中有太多的神经元似乎并没有太大的危害，但是生成器中有太多的神经元会使它变得太不稳定，判别器每次都会收到不同的训练数据，这也是它无法正确训练的另一个原因.如果在生成器中放入 16 和 32 个隐藏神经元，而不是 64 和 128 个，效果会好很多。

最后一点：不仅圆形让你的圆圈难以学习，而且它的大小也很重要。它的半径为 1，而 1 是生成器的饱和值，因此它很容易生成 1 左右的值。这给生成器带来了额外的麻烦：它开始接收与真实数据太接近的假数据在它达到不错的准确性之前。

总结一下：

1. 将真假数据合并到一个批次中。
2. 使用更大的批量大小（至少 256 个）。
3. 至少减少生成器中的神经元数量（例如减少到 16 个和 32 个）。

享受结果：

还有一件事：最好在这个社区https://stats.stackexchange.com/问这样的问题。