はじめに
Coulomb GANでMNISTの手書き数字を生成してみます。生成した画像の良さはFréchet Inception Distance (FID)を使ってとりあえずは測定できるので、普通のGANと比較してみます。
生成器と識別器
生成器と識別器は、以前の利用したものとほぼ同じものを利用します。 Kerasのコードで、生成器は、
g = Sequential()
g.add(Dense(1024, input_dim=100))
g.add(BatchNormalization())
g.add(Activation('relu'))
g.add(Dense(128*7*7))
g.add(BatchNormalization())
g.add(Activation('relu'))
g.add(Reshape((128, 7, 7), input_shape=(128*7*7,)))
g.add(UpSampling2D((2, 2), data_format='channels_first'))
g.add(Conv2D(64, (5, 5), padding='same', data_format='channels_first'))
g.add(BatchNormalization())
g.add(Activation('relu'))
g.add(UpSampling2D((2, 2), data_format='channels_first'))
g.add(Conv2D(1, (5, 5), padding='same', data_format='channels_first'))
g.add(Activation('tanh'))
識別器は、
d = Sequential()
d.add(Conv2D(64, (5, 5), strides=(2, 2), padding='same', input_shape=(1, 28, 28),
data_format='channels_first'))
d.add(LeakyReLU(0.2))
d.add(Conv2D(128, (5, 5), strides=(2, 2), data_format='channels_first'))
d.add(LeakyReLU(0.2))
d.add(Flatten())
d.add(Dense(256))
d.add(LeakyReLU(0.2))
d.add(Dropout(0.5))
d.add(Dense(1))
を使います。最後のsigmoidは省略しています。Coulomb GANはポテンシャルを模擬するので、sigmoidがあると模擬ができません。一方、普通のGANでは真偽を1と0で表すのでsigmoidがあったほうが良さそうですが、試してみたところ問題なく学習できました。
実験結果
さっそく、Coulomb GANと普通のGANを比較してみます。結果は下表の通りです。 FIDの比較対象は全てMNISTの訓練用のデータです。Coulomb GANは自身のポテンシャルを無視する設定で動作させました。また、Plummer kernelの\(\varepsilon\)の半減期は5000、次元は3に固定しました。FIDは3000サンプルで計算しました。
| Type | Parameters | FID | Generated images |
|---|---|---|---|
| Standard GAN |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-4 \(D\), Adam lr =1e-5 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-4 \(G\), Adam lr =1e-4 | 14.66 |
Epoch=99, Batch=400 |
| Coulomb GAN No. 1 |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-3 \(D\), Adam lr =1e-3 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-3 \(G\), Adam lr =1e-3 Plummer kernel \(\varepsilon\)=1.0 | 52.32 |
Epoch=99, Batch=400
|
| Coulomb GAN No. 2 |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-3 \(D\), Adam lr =1e-4 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-3 \(G\), Adam lr =1e-3 Plummer kernel \(\varepsilon\)=1.0 | 90.82 |
Epoch=99, Batch=400
|
| Coulomb GAN No. 3 |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-4 \(D\), Adam lr =1e-3 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-3 \(G\), Adam lr =1e-4 Plummer kernel \(\varepsilon\)=1.0 | 106.5 |
Epoch=99, Batch=400
|
| Coulomb GAN No. 4 |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-3 \(D\), Adam lr =1e-3 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-3 \(G\), Adam lr =1e-3 Plummer kernel \(\varepsilon\)=0.1 | 108.0 |
Epoch=99, Batch=400
|
| Coulomb GAN No. 5 |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-2 \(D\), Adam lr =1e-3 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-2 \(G\), Adam lr =1e-3 Plummer kernel \(\varepsilon\)=10.0 | 118.4 |
Epoch=70, Batch=0 |
| Coulomb GAN No. 6 |
Batch size=128 \(D\), Adam \(\beta_1\) =0.5 \(D\), Adam decay =1e-4 \(D\), Adam lr =1e-3 \(G\), Adam \(\beta_1\) =0.5 \(G\), Adam decay =1e-4 \(G\), Adam lr =1e-3 Plummer kernel \(\varepsilon\)=1.0 | 149.9 |
Epoch=99, Batch=400
|
まとめ
点の分布の学習では安定して良さげな結果を出していたCoulomb GANでしたが、今回のMNISTの画像生成ではいまいちな結果となりました。真の画像よりバリエーションが豊富な画像を生成したいときはFIDは適度に大きくなる必要がありますが、どのくらいのFIDになると良いのかは今回の実験では分かりませんでした。
コード
今回の実験で使ったコードです。最後のパラメータ部分は実験ごとに書き換えています。
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 | # -*- coding: utf-8 -*-
# Coulomb GAN
import sys, os, math
sys.path.append(os.path.dirname(os.path.abspath(__file__)) + '/../keras-examples/src')
import numpy as np
from util.history import ExperimentHistory
from gan.coulomb import CoulombPotentials
from gan.gaussian_mixture.datagen import RandomSampler
from keras.models import Sequential
from keras.optimizers import Adam
import keras.backend as K
from keras.models import Sequential
from keras.layers import Dense, Activation, Reshape
from keras.layers.normalization import BatchNormalization
from keras.layers.convolutional import UpSampling2D, Conv2D
from keras.layers.advanced_activations import LeakyReLU
from keras.layers import Flatten, Dropout
from keras.datasets import mnist
from PIL import Image
GENERATED_IMAGE_PATH = 'coulomb_images/'
BATCH_SIZE = 32*4
NUM_EPOCH = 100
def raw_loss(y_true, y_pred):
return K.mean(y_pred, axis=-1)
def combine_images(generated_images):
total = generated_images.shape[0]
cols = int(math.sqrt(total))
rows = math.ceil(float(total)/cols)
width, height = generated_images.shape[2:]
combined_image = np.zeros((height*rows, width*cols), dtype=generated_images.dtype)
for index, image in enumerate(generated_images):
i = int(index/cols)
j = index % cols
combined_image[width*i:width*(i+1), height*j:height*(j+1)] = image[0, :, :]
return combined_image
def gan_model_mnist(initializer='glorot_uniform'):
"""
return: (generator, discriminator)
"""
g = Sequential()
g.add(Dense(1024, input_dim=100))
g.add(BatchNormalization())
g.add(Activation('relu'))
g.add(Dense(128*7*7))
g.add(BatchNormalization())
g.add(Activation('relu'))
g.add(Reshape((128, 7, 7), input_shape=(128*7*7,)))
g.add(UpSampling2D((2, 2), data_format='channels_first'))
g.add(Conv2D(64, (5, 5), padding='same', data_format='channels_first'))
g.add(BatchNormalization())
g.add(Activation('relu'))
g.add(UpSampling2D((2, 2), data_format='channels_first'))
g.add(Conv2D(1, (5, 5), padding='same', data_format='channels_first'))
g.add(Activation('tanh'))
print(g.summary())
d = Sequential()
d.add(Conv2D(64, (5, 5), strides=(2, 2), padding='same', input_shape=(1, 28, 28),
data_format='channels_first'))
d.add(LeakyReLU(0.2))
d.add(Conv2D(128, (5, 5), strides=(2, 2), data_format='channels_first'))
d.add(LeakyReLU(0.2))
d.add(Flatten())
d.add(Dense(256))
d.add(LeakyReLU(0.2))
d.add(Dropout(0.5))
d.add(Dense(1))
#d.add(Activation('sigmoid'))
print(d.summary())
return g, d
class DiscriminatorLabelNormal:
def __call__(self, points_real, points_fake):
assert len(points_real) == BATCH_SIZE
assert len(points_fake) == BATCH_SIZE
return [1]*len(points_real) + [0]*len(points_fake)
def get_eps(self):
return 0
class DiscriminatorLabelCoulomb:
def __init__(self, eh):
self.total_num_batches = 0
self.cp = CoulombPotentials(eh.plummer_kernel_dim, eh.plummer_kernel_eps,
eh.plummer_kernel_ignore_self_potential)
self.eps_half_life = eh.plummer_kernel_eps_half_life
def __call__(self, points_real, points_fake):
self.cp.eps = eh.plummer_kernel_eps * math.pow(2, -self.total_num_batches/self.eps_half_life)
self.total_num_batches += 1
potential_real, potential_fake = self.cp(points_real, points_fake)
return np.concatenate((potential_real, potential_fake))
def get_eps(self):
return self.cp.eps
def train(eh):
(X_train, y_train), (_, _) = mnist.load_data()
X_train = (X_train.astype(np.float32) - 127.5)/127.5
X_train = X_train.reshape(X_train.shape[0], 1, X_train.shape[1], X_train.shape[2])
# Random sampler for each batch
rs = RandomSampler(100, "normal" if eh.random_with_normal_dist else "uniform")
# Make an object for making correct labels of D
dl = DiscriminatorLabelCoulomb(eh) if eh.coulomb_gan else DiscriminatorLabelNormal()
# Make a generator G and a discriminator D
generator, discriminator = gan_model_mnist()
d_opt = Adam(lr=eh.disc_Adam_lr, beta_1=eh.disc_Adam_beta_1, decay=eh.disc_Adam_decay)
g_opt = Adam(lr=eh.gen_Adam_lr, beta_1=eh.gen_Adam_beta_1, decay=eh.gen_Adam_decay)
discriminator.compile(loss='mse' if eh.coulomb_gan else 'binary_crossentropy', optimizer=d_opt)
discriminator.trainable = False
cgan = Sequential([generator, discriminator]) # G+D with fixed weights of D
cgan.compile(loss=raw_loss if eh.coulomb_gan else 'binary_crossentropy', optimizer=g_opt)
num_batches = int(X_train.shape[0] / BATCH_SIZE)
print('Number of batches:', num_batches)
eh.write(GENERATED_IMAGE_PATH+"history.log", {"Generator":generator, "Discriminator":discriminator},
{"Generator opt":g_opt, "Discriminator opt":d_opt}, None)
for epoch in range(NUM_EPOCH):
if eh.X_train_is_shuffled:
np.random.shuffle(X_train)
for index in range(num_batches):
noise = np.array(rs(BATCH_SIZE))
points_real = X_train[index*BATCH_SIZE:(index+1)*BATCH_SIZE]
points_fake = generator.predict(noise, verbose=0)
# Output generated images
if index % 200 == 0:
image = combine_images(points_fake)
image = image*127.5 + 127.5
if not os.path.exists(GENERATED_IMAGE_PATH):
os.mkdir(GENERATED_IMAGE_PATH)
Image.fromarray(image.astype(np.uint8))\
.save(GENERATED_IMAGE_PATH+"%04d_%04d.png" % (epoch, index))
generator.save(GENERATED_IMAGE_PATH+"generator.model")
discriminator.save(GENERATED_IMAGE_PATH+"discriminator.model")
# Update a discriminator
X = np.concatenate((points_real, points_fake))
Y = dl(points_real, points_fake)
d_loss = discriminator.train_on_batch(X, Y)
# Update a generator
noise = np.array(rs(BATCH_SIZE))
g_loss = cgan.train_on_batch(noise, [1]*BATCH_SIZE) # labels are ignored if Coulomb GAN
print("epoch: %d, batch: %d, g_loss: %e, d_loss: %e, eps: %e" %
(epoch, index, g_loss, d_loss, dl.get_eps()))
if __name__ == '__main__':
GENERATED_IMAGE_PATH = 'coulomb_images/'
eh = ExperimentHistory()
eh.batch_size = BATCH_SIZE
eh.random_with_normal_dist = False
eh.X_train_is_shuffled = True
eh.plummer_kernel_dim = 3.0
eh.plummer_kernel_eps = 0.1
eh.plummer_kernel_eps_half_life = 5000.0
eh.plummer_kernel_ignore_self_potential = True
eh.disc_Adam_decay = 1e-3
eh.disc_Adam_lr = 1e-3
eh.disc_Adam_beta_1 = 0.5
eh.gen_Adam_decay = 1e-3
eh.gen_Adam_lr = 1e-3
eh.gen_Adam_beta_1 = 0.5
eh.coulomb_gan = True
if not eh.coulomb_gan:
GENERATED_IMAGE_PATH = 'generated_images/'
if not os.path.exists(GENERATED_IMAGE_PATH):
os.mkdir(GENERATED_IMAGE_PATH)
train(eh)
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