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Generative Deep Learning /
Variational AutoEncoder
Variational AutoEncoder
Author: fchollet
Date created: 2020/05/03
Last modified: 2020/05/03
Description: Convolutional Variational AutoEncoder (VAE) trained on MNIST digits.
Setup
import numpy as np
import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers
Create a sampling layer
class Sampling(layers.Layer):
"""Uses (z_mean, z_log_var) to sample z, the vector encoding a digit."""
def call(self, inputs):
z_mean, z_log_var = inputs
batch = tf.shape(z_mean)[0]
dim = tf.shape(z_mean)[1]
epsilon = tf.random.normal(shape=(batch, dim))
return z_mean + tf.exp(0.5 * z_log_var) * epsilon
Build the encoder
latent_dim = 2
encoder_inputs = keras.Input(shape=(28, 28, 1))
x = layers.Conv2D(32, 3, activation="relu", strides=2, padding="same")(encoder_inputs)
x = layers.Conv2D(64, 3, activation="relu", strides=2, padding="same")(x)
x = layers.Flatten()(x)
x = layers.Dense(16, activation="relu")(x)
z_mean = layers.Dense(latent_dim, name="z_mean")(x)
z_log_var = layers.Dense(latent_dim, name="z_log_var")(x)
z = Sampling()([z_mean, z_log_var])
encoder = keras.Model(encoder_inputs, [z_mean, z_log_var, z], name="encoder")
encoder.summary()
Model: "encoder"
__________________________________________________________________________________________________
Layer (type) Output Shape Param # Connected to
==================================================================================================
input_1 (InputLayer) [(None, 28, 28, 1)] 0 []
conv2d (Conv2D) (None, 14, 14, 32) 320 ['input_1[0][0]']
conv2d_1 (Conv2D) (None, 7, 7, 64) 18496 ['conv2d[0][0]']
flatten (Flatten) (None, 3136) 0 ['conv2d_1[0][0]']
dense (Dense) (None, 16) 50192 ['flatten[0][0]']
z_mean (Dense) (None, 2) 34 ['dense[0][0]']
z_log_var (Dense) (None, 2) 34 ['dense[0][0]']
sampling (Sampling) (None, 2) 0 ['z_mean[0][0]',
'z_log_var[0][0]']
==================================================================================================
Total params: 69,076
Trainable params: 69,076
Non-trainable params: 0
__________________________________________________________________________________________________
Build the decoder
latent_inputs = keras.Input(shape=(latent_dim,))
x = layers.Dense(7 * 7 * 64, activation="relu")(latent_inputs)
x = layers.Reshape((7, 7, 64))(x)
x = layers.Conv2DTranspose(64, 3, activation="relu", strides=2, padding="same")(x)
x = layers.Conv2DTranspose(32, 3, activation="relu", strides=2, padding="same")(x)
decoder_outputs = layers.Conv2DTranspose(1, 3, activation="sigmoid", padding="same")(x)
decoder = keras.Model(latent_inputs, decoder_outputs, name="decoder")
decoder.summary()
Model: "decoder"
_________________________________________________________________
Layer (type) Output Shape Param #
=================================================================
input_2 (InputLayer) [(None, 2)] 0
dense_1 (Dense) (None, 3136) 9408
reshape (Reshape) (None, 7, 7, 64) 0
conv2d_transpose (Conv2DTra (None, 14, 14, 64) 36928
nspose)
conv2d_transpose_1 (Conv2DT (None, 28, 28, 32) 18464
ranspose)
conv2d_transpose_2 (Conv2DT (None, 28, 28, 1) 289
ranspose)
=================================================================
Total params: 65,089
Trainable params: 65,089
Non-trainable params: 0
_________________________________________________________________
Define the VAE as a Model with a custom train_step
class VAE(keras.Model):
def __init__(self, encoder, decoder, **kwargs):
super().__init__(**kwargs)
self.encoder = encoder
self.decoder = decoder
self.total_loss_tracker = keras.metrics.Mean(name="total_loss")
self.reconstruction_loss_tracker = keras.metrics.Mean(
name="reconstruction_loss"
)
self.kl_loss_tracker = keras.metrics.Mean(name="kl_loss")
@property
def metrics(self):
return [
self.total_loss_tracker,
self.reconstruction_loss_tracker,
self.kl_loss_tracker,
]
def train_step(self, data):
with tf.GradientTape() as tape:
z_mean, z_log_var, z = self.encoder(data)
reconstruction = self.decoder(z)
reconstruction_loss = tf.reduce_mean(
tf.reduce_sum(
keras.losses.binary_crossentropy(data, reconstruction), axis=(1, 2)
)
)
kl_loss = -0.5 * (1 + z_log_var - tf.square(z_mean) - tf.exp(z_log_var))
kl_loss = tf.reduce_mean(tf.reduce_sum(kl_loss, axis=1))
total_loss = reconstruction_loss + kl_loss
grads = tape.gradient(total_loss, self.trainable_weights)
self.optimizer.apply_gradients(zip(grads, self.trainable_weights))
self.total_loss_tracker.update_state(total_loss)
self.reconstruction_loss_tracker.update_state(reconstruction_loss)
self.kl_loss_tracker.update_state(kl_loss)
return {
"loss": self.total_loss_tracker.result(),
"reconstruction_loss": self.reconstruction_loss_tracker.result(),
"kl_loss": self.kl_loss_tracker.result(),
}
Train the VAE
(x_train, _), (x_test, _) = keras.datasets.mnist.load_data()
mnist_digits = np.concatenate([x_train, x_test], axis=0)
mnist_digits = np.expand_dims(mnist_digits, -1).astype("float32") / 255
vae = VAE(encoder, decoder)
vae.compile(optimizer=keras.optimizers.Adam())
vae.fit(mnist_digits, epochs=30, batch_size=128)
WARNING:absl:At this time, the v2.11+ optimizer [`tf.keras.optimizers.Adam`](/api/optimizers/adam#adam-class) runs slowly on M1/M2 Macs, please use the legacy Keras optimizer instead, located at [`tf.keras.optimizers.legacy.Adam`](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/legacy/Adam).
WARNING:absl:There is a known slowdown when using v2.11+ Keras optimizers on M1/M2 Macs. Falling back to the legacy Keras optimizer, i.e., [`tf.keras.optimizers.legacy.Adam`](https://www.tensorflow.org/api_docs/python/tf/keras/optimizers/legacy/Adam).
Epoch 1/30
547/547 [==============================] - 13s 24ms/step - loss: 253.6647 - reconstruction_loss: 205.1592 - kl_loss: 3.9604
Epoch 2/30
547/547 [==============================] - 13s 24ms/step - loss: 175.3276 - reconstruction_loss: 166.0741 - kl_loss: 5.6646
Epoch 3/30
547/547 [==============================] - 13s 25ms/step - loss: 164.6180 - reconstruction_loss: 157.1289 - kl_loss: 5.9575
Epoch 4/30
547/547 [==============================] - 14s 25ms/step - loss: 159.9903 - reconstruction_loss: 153.2397 - kl_loss: 6.1860
Epoch 5/30
547/547 [==============================] - 13s 24ms/step - loss: 157.7517 - reconstruction_loss: 150.9847 - kl_loss: 6.2957
Epoch 6/30
547/547 [==============================] - 13s 24ms/step - loss: 156.3130 - reconstruction_loss: 149.4794 - kl_loss: 6.3866
Epoch 7/30
547/547 [==============================] - 13s 24ms/step - loss: 154.8179 - reconstruction_loss: 148.2143 - kl_loss: 6.4271
Epoch 8/30
547/547 [==============================] - 13s 24ms/step - loss: 154.1232 - reconstruction_loss: 147.2314 - kl_loss: 6.4529
Epoch 9/30
547/547 [==============================] - 13s 24ms/step - loss: 153.2196 - reconstruction_loss: 146.4478 - kl_loss: 6.4943
Epoch 10/30
547/547 [==============================] - 13s 24ms/step - loss: 152.1982 - reconstruction_loss: 145.7807 - kl_loss: 6.5371
Epoch 11/30
547/547 [==============================] - 13s 24ms/step - loss: 151.8797 - reconstruction_loss: 145.1918 - kl_loss: 6.5670
Epoch 12/30
547/547 [==============================] - 13s 24ms/step - loss: 151.3647 - reconstruction_loss: 144.6646 - kl_loss: 6.5975
Epoch 13/30
547/547 [==============================] - 13s 24ms/step - loss: 151.0302 - reconstruction_loss: 144.2068 - kl_loss: 6.6063
Epoch 14/30
547/547 [==============================] - 13s 24ms/step - loss: 150.4563 - reconstruction_loss: 143.8471 - kl_loss: 6.6398
Epoch 15/30
547/547 [==============================] - 13s 24ms/step - loss: 150.0985 - reconstruction_loss: 143.4100 - kl_loss: 6.6441
Epoch 16/30
547/547 [==============================] - 13s 24ms/step - loss: 149.6108 - reconstruction_loss: 143.0211 - kl_loss: 6.6628
Epoch 17/30
547/547 [==============================] - 13s 24ms/step - loss: 149.2437 - reconstruction_loss: 142.7990 - kl_loss: 6.6927
Epoch 18/30
547/547 [==============================] - 13s 24ms/step - loss: 149.2876 - reconstruction_loss: 142.5346 - kl_loss: 6.7011
Epoch 19/30
547/547 [==============================] - 13s 24ms/step - loss: 149.0014 - reconstruction_loss: 142.2537 - kl_loss: 6.7251
Epoch 20/30
547/547 [==============================] - 13s 24ms/step - loss: 148.2962 - reconstruction_loss: 142.0005 - kl_loss: 6.7257
Epoch 21/30
547/547 [==============================] - 13s 24ms/step - loss: 148.6063 - reconstruction_loss: 141.8341 - kl_loss: 6.7373
Epoch 22/30
547/547 [==============================] - 13s 24ms/step - loss: 148.4330 - reconstruction_loss: 141.5164 - kl_loss: 6.7565
Epoch 23/30
547/547 [==============================] - 13s 24ms/step - loss: 148.2596 - reconstruction_loss: 141.3924 - kl_loss: 6.7423
Epoch 24/30
547/547 [==============================] - 13s 24ms/step - loss: 147.8061 - reconstruction_loss: 141.1230 - kl_loss: 6.7710
Epoch 25/30
547/547 [==============================] - 13s 24ms/step - loss: 147.8897 - reconstruction_loss: 141.0627 - kl_loss: 6.7728
Epoch 26/30
547/547 [==============================] - 13s 24ms/step - loss: 147.5552 - reconstruction_loss: 140.7714 - kl_loss: 6.7679
Epoch 27/30
547/547 [==============================] - 13s 24ms/step - loss: 147.3100 - reconstruction_loss: 140.6762 - kl_loss: 6.7815
Epoch 28/30
547/547 [==============================] - 13s 24ms/step - loss: 147.2303 - reconstruction_loss: 140.4241 - kl_loss: 6.7965
Epoch 29/30
547/547 [==============================] - 13s 24ms/step - loss: 147.1390 - reconstruction_loss: 140.3612 - kl_loss: 6.7862
Epoch 30/30
547/547 [==============================] - 13s 24ms/step - loss: 146.9508 - reconstruction_loss: 140.1473 - kl_loss: 6.7960
<keras.callbacks.History at 0x17cdeb850>
Display a grid of sampled digits
import matplotlib.pyplot as plt
def plot_latent_space(vae, n=30, figsize=15):
# display an n*n 2D manifold of digits
digit_size = 28
scale = 1.0
figure = np.zeros((digit_size * n, digit_size * n))
# linearly spaced coordinates corresponding to the 2D plot
# of digit classes in the latent space
grid_x = np.linspace(-scale, scale, n)
grid_y = np.linspace(-scale, scale, n)[::-1]
for i, yi in enumerate(grid_y):
for j, xi in enumerate(grid_x):
z_sample = np.array([[xi, yi]])
x_decoded = vae.decoder.predict(z_sample)
digit = x_decoded[0].reshape(digit_size, digit_size)
figure[
i * digit_size : (i + 1) * digit_size,
j * digit_size : (j + 1) * digit_size,
] = digit
plt.figure(figsize=(figsize, figsize))
start_range = digit_size // 2
end_range = n * digit_size + start_range
pixel_range = np.arange(start_range, end_range, digit_size)
sample_range_x = np.round(grid_x, 1)
sample_range_y = np.round(grid_y, 1)
plt.xticks(pixel_range, sample_range_x)
plt.yticks(pixel_range, sample_range_y)
plt.xlabel("z[0]")
plt.ylabel("z[1]")
plt.imshow(figure, cmap="Greys_r")
plt.show()
plot_latent_space(vae)
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Display how the latent space clusters different digit classes
def plot_label_clusters(vae, data, labels):
# display a 2D plot of the digit classes in the latent space
z_mean, _, _ = vae.encoder.predict(data)
plt.figure(figsize=(12, 10))
plt.scatter(z_mean[:, 0], z_mean[:, 1], c=labels)
plt.colorbar()
plt.xlabel("z[0]")
plt.ylabel("z[1]")
plt.show()
(x_train, y_train), _ = keras.datasets.mnist.load_data()
x_train = np.expand_dims(x_train, -1).astype("float32") / 255
plot_label_clusters(vae, x_train, y_train)
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