» Code examples / 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.

View in Colab GitHub source


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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png


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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png