# Chapter 6: Project: Handwritten Digit Generation with VAEs

## 6.3 Training the VAE

After we have assembled our Variational Autoencoder (VAE), the next step is to compile and train the model on our data.

**6.3.1 Compiling the VAE**

Before we can train our VAE, we need to compile it. As part of the compilation process, we need to specify a loss function and an optimizer.

The loss function for VAEs is a bit different from the loss functions we've seen so far. It consists of two parts:

- A reconstruction loss that encourages the decoder to recreate the input data as accurately as possible, and
- A KL divergence loss that pushes the distribution of the latent space to approximate a standard normal distribution.

Let's define this loss function:

`from tensorflow.keras import backend as K`

def vae_loss(x, x_decoded_mean):

xent_loss = original_dim * tf.keras.losses.binary_crossentropy(x, x_decoded_mean)

kl_loss = - 0.5 * K.sum(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma), axis=-1)

return K.mean(xent_loss + kl_loss)

In this code,

is the reconstruction loss and **xent_loss**

is the KL divergence loss. We calculate the mean of these losses across the batch to get the final loss value.**kl_loss**

Next, we compile the model:

`# Compile VAE model`

vae.compile(optimizer='rmsprop', loss=vae_loss)

**6.3.2 Training the VAE**

Once our model is compiled, we can train it on our data. Here's how we might do this:

`# Train the VAE`

vae.fit(x_train, x_train,

shuffle=True,

epochs=50,

batch_size=batch_size,

validation_data=(x_test, x_test))

In this code, we're calling the

method of our VAE model and passing in our training data **fit**

as both the input and the target data. This is because we want our VAE to learn to recreate its input data.**x_train**

We're also passing a few additional arguments:

: This shuffles our data before each epoch, which can help to avoid patterns and dependencies that might arise from the order of the data points.**shuffle=True**

: This tells Keras to run the training process for 50 epochs.**epochs=50**

: This specifies the number of samples per gradient update.**batch_size=batch_size**

: This is our validation data, which Keras will use to evaluate the loss and any model metrics at the end of each epoch. This allows us to see how well our model is doing without touching the test data.**validation_data=(x_test, x_test)**

After running this code, our VAE should be trained and ready to generate new handwritten digits!

Remember that this is just a simple example. In practice, we might want to use more sophisticated techniques such as early stopping, learning rate decay, or other forms of regularization to improve the training process and the final model.

## 6.3 Training the VAE

After we have assembled our Variational Autoencoder (VAE), the next step is to compile and train the model on our data.

**6.3.1 Compiling the VAE**

Before we can train our VAE, we need to compile it. As part of the compilation process, we need to specify a loss function and an optimizer.

The loss function for VAEs is a bit different from the loss functions we've seen so far. It consists of two parts:

- A reconstruction loss that encourages the decoder to recreate the input data as accurately as possible, and
- A KL divergence loss that pushes the distribution of the latent space to approximate a standard normal distribution.

Let's define this loss function:

`from tensorflow.keras import backend as K`

def vae_loss(x, x_decoded_mean):

xent_loss = original_dim * tf.keras.losses.binary_crossentropy(x, x_decoded_mean)

kl_loss = - 0.5 * K.sum(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma), axis=-1)

return K.mean(xent_loss + kl_loss)

In this code,

is the reconstruction loss and **xent_loss**

is the KL divergence loss. We calculate the mean of these losses across the batch to get the final loss value.**kl_loss**

Next, we compile the model:

`# Compile VAE model`

vae.compile(optimizer='rmsprop', loss=vae_loss)

**6.3.2 Training the VAE**

Once our model is compiled, we can train it on our data. Here's how we might do this:

`# Train the VAE`

vae.fit(x_train, x_train,

shuffle=True,

epochs=50,

batch_size=batch_size,

validation_data=(x_test, x_test))

In this code, we're calling the

method of our VAE model and passing in our training data **fit**

as both the input and the target data. This is because we want our VAE to learn to recreate its input data.**x_train**

We're also passing a few additional arguments:

: This shuffles our data before each epoch, which can help to avoid patterns and dependencies that might arise from the order of the data points.**shuffle=True**

: This tells Keras to run the training process for 50 epochs.**epochs=50**

: This specifies the number of samples per gradient update.**batch_size=batch_size**

: This is our validation data, which Keras will use to evaluate the loss and any model metrics at the end of each epoch. This allows us to see how well our model is doing without touching the test data.**validation_data=(x_test, x_test)**

After running this code, our VAE should be trained and ready to generate new handwritten digits!

Remember that this is just a simple example. In practice, we might want to use more sophisticated techniques such as early stopping, learning rate decay, or other forms of regularization to improve the training process and the final model.

## 6.3 Training the VAE

After we have assembled our Variational Autoencoder (VAE), the next step is to compile and train the model on our data.

**6.3.1 Compiling the VAE**

Before we can train our VAE, we need to compile it. As part of the compilation process, we need to specify a loss function and an optimizer.

The loss function for VAEs is a bit different from the loss functions we've seen so far. It consists of two parts:

- A reconstruction loss that encourages the decoder to recreate the input data as accurately as possible, and
- A KL divergence loss that pushes the distribution of the latent space to approximate a standard normal distribution.

Let's define this loss function:

`from tensorflow.keras import backend as K`

def vae_loss(x, x_decoded_mean):

xent_loss = original_dim * tf.keras.losses.binary_crossentropy(x, x_decoded_mean)

kl_loss = - 0.5 * K.sum(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma), axis=-1)

return K.mean(xent_loss + kl_loss)

In this code,

is the reconstruction loss and **xent_loss**

is the KL divergence loss. We calculate the mean of these losses across the batch to get the final loss value.**kl_loss**

Next, we compile the model:

`# Compile VAE model`

vae.compile(optimizer='rmsprop', loss=vae_loss)

**6.3.2 Training the VAE**

Once our model is compiled, we can train it on our data. Here's how we might do this:

`# Train the VAE`

vae.fit(x_train, x_train,

shuffle=True,

epochs=50,

batch_size=batch_size,

validation_data=(x_test, x_test))

In this code, we're calling the

method of our VAE model and passing in our training data **fit**

as both the input and the target data. This is because we want our VAE to learn to recreate its input data.**x_train**

We're also passing a few additional arguments:

: This shuffles our data before each epoch, which can help to avoid patterns and dependencies that might arise from the order of the data points.**shuffle=True**

: This tells Keras to run the training process for 50 epochs.**epochs=50**

: This specifies the number of samples per gradient update.**batch_size=batch_size**

: This is our validation data, which Keras will use to evaluate the loss and any model metrics at the end of each epoch. This allows us to see how well our model is doing without touching the test data.**validation_data=(x_test, x_test)**

After running this code, our VAE should be trained and ready to generate new handwritten digits!

Remember that this is just a simple example. In practice, we might want to use more sophisticated techniques such as early stopping, learning rate decay, or other forms of regularization to improve the training process and the final model.

## 6.3 Training the VAE

**6.3.1 Compiling the VAE**

Let's define this loss function:

`from tensorflow.keras import backend as K`

def vae_loss(x, x_decoded_mean):

xent_loss = original_dim * tf.keras.losses.binary_crossentropy(x, x_decoded_mean)

kl_loss = - 0.5 * K.sum(1 + z_log_sigma - K.square(z_mean) - K.exp(z_log_sigma), axis=-1)

return K.mean(xent_loss + kl_loss)

is the reconstruction loss and **xent_loss**

is the KL divergence loss. We calculate the mean of these losses across the batch to get the final loss value.**kl_loss**

Next, we compile the model:

`# Compile VAE model`

vae.compile(optimizer='rmsprop', loss=vae_loss)

**6.3.2 Training the VAE**

Once our model is compiled, we can train it on our data. Here's how we might do this:

`# Train the VAE`

vae.fit(x_train, x_train,

shuffle=True,

epochs=50,

batch_size=batch_size,

validation_data=(x_test, x_test))

method of our VAE model and passing in our training data **fit**

as both the input and the target data. This is because we want our VAE to learn to recreate its input data.**x_train**

We're also passing a few additional arguments:

: This shuffles our data before each epoch, which can help to avoid patterns and dependencies that might arise from the order of the data points.**shuffle=True**

: This tells Keras to run the training process for 50 epochs.**epochs=50**

: This specifies the number of samples per gradient update.**batch_size=batch_size**

: This is our validation data, which Keras will use to evaluate the loss and any model metrics at the end of each epoch. This allows us to see how well our model is doing without touching the test data.**validation_data=(x_test, x_test)**

After running this code, our VAE should be trained and ready to generate new handwritten digits!