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Making new Layers and Models via subclassing

コレクションでコンテンツを整理 必要に応じて、コンテンツの保存と分類を行います。

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Setup

import tensorflow as tf
from tensorflow import keras
2022-08-09 05:26:01.542776: E tensorflow/stream_executor/cuda/cuda_blas.cc:2981] Unable to register cuBLAS factory: Attempting to register factory for plugin cuBLAS when one has already been registered
2022-08-09 05:26:02.226786: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer.so.7'; dlerror: libnvrtc.so.11.1: cannot open shared object file: No such file or directory
2022-08-09 05:26:02.227020: W tensorflow/stream_executor/platform/default/dso_loader.cc:64] Could not load dynamic library 'libnvinfer_plugin.so.7'; dlerror: libnvrtc.so.11.1: cannot open shared object file: No such file or directory
2022-08-09 05:26:02.227032: W tensorflow/compiler/tf2tensorrt/utils/py_utils.cc:38] TF-TRT Warning: Cannot dlopen some TensorRT libraries. If you would like to use Nvidia GPU with TensorRT, please make sure the missing libraries mentioned above are installed properly.

The Layer class: the combination of state (weights) and some computation

Keras の中心的な抽象概念の 1 つは、Layer クラスです。 レイヤーは、状態(レイヤーの「重み」) と入力から出力への変換 (「呼び出し」、レイヤーのフォワードパス) をカプセル化します。

以下の密に接続されたレイヤーでは、状態は次のとおりです: 変数 wb

class Linear(keras.layers.Layer):
    def __init__(self, units=32, input_dim=32):
        super(Linear, self).__init__()
        w_init = tf.random_normal_initializer()
        self.w = tf.Variable(
            initial_value=w_init(shape=(input_dim, units), dtype="float32"),
            trainable=True,
        )
        b_init = tf.zeros_initializer()
        self.b = tf.Variable(
            initial_value=b_init(shape=(units,), dtype="float32"), trainable=True
        )

    def call(self, inputs):
        return tf.matmul(inputs, self.w) + self.b

You would use a layer by calling it on some tensor input(s), much like a Python function.

x = tf.ones((2, 2))
linear_layer = Linear(4, 2)
y = linear_layer(x)
print(y)
tf.Tensor(
[[ 0.14135079 -0.03866047 -0.03704323  0.0229008 ]
 [ 0.14135079 -0.03866047 -0.03704323  0.0229008 ]], shape=(2, 4), dtype=float32)

Note that the weights w and b are automatically tracked by the layer upon being set as layer attributes:

assert linear_layer.weights == [linear_layer.w, linear_layer.b]

Note you also have access to a quicker shortcut for adding weight to a layer: the add_weight() method:

class Linear(keras.layers.Layer):
    def __init__(self, units=32, input_dim=32):
        super(Linear, self).__init__()
        self.w = self.add_weight(
            shape=(input_dim, units), initializer="random_normal", trainable=True
        )
        self.b = self.add_weight(shape=(units,), initializer="zeros", trainable=True)

    def call(self, inputs):
        return tf.matmul(inputs, self.w) + self.b


x = tf.ones((2, 2))
linear_layer = Linear(4, 2)
y = linear_layer(x)
print(y)
tf.Tensor(
[[ 0.07598154 -0.10093731 -0.06651957 -0.19503188]
 [ 0.07598154 -0.10093731 -0.06651957 -0.19503188]], shape=(2, 4), dtype=float32)

Layers can have non-trainable weights

Besides trainable weights, you can add non-trainable weights to a layer as well. Such weights are meant not to be taken into account during backpropagation, when you are training the layer.

Here's how to add and use a non-trainable weight:

class ComputeSum(keras.layers.Layer):
    def __init__(self, input_dim):
        super(ComputeSum, self).__init__()
        self.total = tf.Variable(initial_value=tf.zeros((input_dim,)), trainable=False)

    def call(self, inputs):
        self.total.assign_add(tf.reduce_sum(inputs, axis=0))
        return self.total


x = tf.ones((2, 2))
my_sum = ComputeSum(2)
y = my_sum(x)
print(y.numpy())
y = my_sum(x)
print(y.numpy())
[2. 2.]
[4. 4.]

It's part of layer.weights, but it gets categorized as a non-trainable weight:

print("weights:", len(my_sum.weights))
print("non-trainable weights:", len(my_sum.non_trainable_weights))

# It's not included in the trainable weights:
print("trainable_weights:", my_sum.trainable_weights)
weights: 1
non-trainable weights: 1
trainable_weights: []

Best practice: deferring weight creation until the shape of the inputs is known

Our Linear layer above took an input_dimargument that was used to compute the shape of the weights w and b in __init__():

class Linear(keras.layers.Layer):
    def __init__(self, units=32, input_dim=32):
        super(Linear, self).__init__()
        self.w = self.add_weight(
            shape=(input_dim, units), initializer="random_normal", trainable=True
        )
        self.b = self.add_weight(shape=(units,), initializer="zeros", trainable=True)

    def call(self, inputs):
        return tf.matmul(inputs, self.w) + self.b

In many cases, you may not know in advance the size of your inputs, and you would like to lazily create weights when that value becomes known, some time after instantiating the layer.

In the Keras API, we recommend creating layer weights in the build(self, inputs_shape) method of your layer. Like this:

class Linear(keras.layers.Layer):
    def __init__(self, units=32):
        super(Linear, self).__init__()
        self.units = units

    def build(self, input_shape):
        self.w = self.add_weight(
            shape=(input_shape[-1], self.units),
            initializer="random_normal",
            trainable=True,
        )
        self.b = self.add_weight(
            shape=(self.units,), initializer="random_normal", trainable=True
        )

    def call(self, inputs):
        return tf.matmul(inputs, self.w) + self.b

The __call__() method of your layer will automatically run build the first time it is called. You now have a layer that's lazy and thus easier to use:

# At instantiation, we don't know on what inputs this is going to get called
linear_layer = Linear(32)

# The layer's weights are created dynamically the first time the layer is called
y = linear_layer(x)

上記のように build() を個別に実装すると、重みの一回の作成とすべての呼び出しでの重みの使用が分離されます。ただし、一部の高度なカスタムレイヤーでは、状態の作成と計算を分離することが非現実的になる可能性があります。レイヤーを実装する際に、重みの作成を最初の __call__() に延期することができますが、後の呼び出しで同じ重みが使用されるように注意する必要があります。さらに、__call__()tf.function 内で初めに実行される可能性が高いため、 __call__() で作成される変数は tf.init_scope でラップする必要があります。

Layers are recursively composable

レイヤーインスタンスを別のレイヤーの属性として割り当てると、外部レイヤーは内部レイヤーの重みを追跡し始めます。

__init__() メソッドでこのようなサブレイヤーを作成し、それを最初の __call__() で、重みの作成をトリガーすることをお勧めします。

class MLPBlock(keras.layers.Layer):
    def __init__(self):
        super(MLPBlock, self).__init__()
        self.linear_1 = Linear(32)
        self.linear_2 = Linear(32)
        self.linear_3 = Linear(1)

    def call(self, inputs):
        x = self.linear_1(inputs)
        x = tf.nn.relu(x)
        x = self.linear_2(x)
        x = tf.nn.relu(x)
        return self.linear_3(x)


mlp = MLPBlock()
y = mlp(tf.ones(shape=(3, 64)))  # The first call to the `mlp` will create the weights
print("weights:", len(mlp.weights))
print("trainable weights:", len(mlp.trainable_weights))
weights: 6
trainable weights: 6

The add_loss() method

When writing the call() method of a layer, you can create loss tensors that you will want to use later, when writing your training loop. This is doable by calling self.add_loss(value):

# A layer that creates an activity regularization loss
class ActivityRegularizationLayer(keras.layers.Layer):
    def __init__(self, rate=1e-2):
        super(ActivityRegularizationLayer, self).__init__()
        self.rate = rate

    def call(self, inputs):
        self.add_loss(self.rate * tf.reduce_sum(inputs))
        return inputs

These losses (including those created by any inner layer) can be retrieved via layer.losses. This property is reset at the start of every __call__() to the top-level layer, so that layer.losses always contains the loss values created during the last forward pass.

class OuterLayer(keras.layers.Layer):
    def __init__(self):
        super(OuterLayer, self).__init__()
        self.activity_reg = ActivityRegularizationLayer(1e-2)

    def call(self, inputs):
        return self.activity_reg(inputs)


layer = OuterLayer()
assert len(layer.losses) == 0  # No losses yet since the layer has never been called

_ = layer(tf.zeros(1, 1))
assert len(layer.losses) == 1  # We created one loss value

# `layer.losses` gets reset at the start of each __call__
_ = layer(tf.zeros(1, 1))
assert len(layer.losses) == 1  # This is the loss created during the call above

In addition, the loss property also contains regularization losses created for the weights of any inner layer:

class OuterLayerWithKernelRegularizer(keras.layers.Layer):
    def __init__(self):
        super(OuterLayerWithKernelRegularizer, self).__init__()
        self.dense = keras.layers.Dense(
            32, kernel_regularizer=tf.keras.regularizers.l2(1e-3)
        )

    def call(self, inputs):
        return self.dense(inputs)


layer = OuterLayerWithKernelRegularizer()
_ = layer(tf.zeros((1, 1)))

# This is `1e-3 * sum(layer.dense.kernel ** 2)`,
# created by the `kernel_regularizer` above.
print(layer.losses)
[<tf.Tensor: shape=(), dtype=float32, numpy=0.0022129943>]

これらの損失は、以下のようにトレーニングループを記述するときに考慮されることを意図しています。

# Instantiate an optimizer.
optimizer = tf.keras.optimizers.SGD(learning_rate=1e-3)
loss_fn = keras.losses.SparseCategoricalCrossentropy(from_logits=True)

# Iterate over the batches of a dataset.
for x_batch_train, y_batch_train in train_dataset:
  with tf.GradientTape() as tape:
    logits = layer(x_batch_train)  # Logits for this minibatch
    # Loss value for this minibatch
    loss_value = loss_fn(y_batch_train, logits)
    # Add extra losses created during this forward pass:
    loss_value += sum(model.losses)

  grads = tape.gradient(loss_value, model.trainable_weights)
  optimizer.apply_gradients(zip(grads, model.trainable_weights))

For a detailed guide about writing training loops, see the guide to writing a training loop from scratch.

These losses also work seamlessly with fit() (they get automatically summed and added to the main loss, if any):

import numpy as np

inputs = keras.Input(shape=(3,))
outputs = ActivityRegularizationLayer()(inputs)
model = keras.Model(inputs, outputs)

# If there is a loss passed in `compile`, the regularization
# losses get added to it
model.compile(optimizer="adam", loss="mse")
model.fit(np.random.random((2, 3)), np.random.random((2, 3)))

# It's also possible not to pass any loss in `compile`,
# since the model already has a loss to minimize, via the `add_loss`
# call during the forward pass!
model.compile(optimizer="adam")
model.fit(np.random.random((2, 3)), np.random.random((2, 3)))
1/1 [==============================] - 0s 113ms/step - loss: 0.1907
1/1 [==============================] - 0s 49ms/step - loss: 0.0195
<keras.callbacks.History at 0x7f78e8285c10>

add_metric()メソッド

add_loss()と同様に、レイヤーではadd_metric()メソッドでトレーニング中の数量の移動平均を追跡できます。

「ロジスティックエンドポイント」レイヤーでは、入力として予測とターゲットを受け取り、 add_loss()を介して追跡する損失を計算し、add_metric()を介して追跡する精度スカラーを計算します。

class LogisticEndpoint(keras.layers.Layer):
    def __init__(self, name=None):
        super(LogisticEndpoint, self).__init__(name=name)
        self.loss_fn = keras.losses.BinaryCrossentropy(from_logits=True)
        self.accuracy_fn = keras.metrics.BinaryAccuracy()

    def call(self, targets, logits, sample_weights=None):
        # Compute the training-time loss value and add it
        # to the layer using `self.add_loss()`.
        loss = self.loss_fn(targets, logits, sample_weights)
        self.add_loss(loss)

        # Log accuracy as a metric and add it
        # to the layer using `self.add_metric()`.
        acc = self.accuracy_fn(targets, logits, sample_weights)
        self.add_metric(acc, name="accuracy")

        # Return the inference-time prediction tensor (for `.predict()`).
        return tf.nn.softmax(logits)

Metrics tracked in this way are accessible via layer.metrics:

layer = LogisticEndpoint()

targets = tf.ones((2, 2))
logits = tf.ones((2, 2))
y = layer(targets, logits)

print("layer.metrics:", layer.metrics)
print("current accuracy value:", float(layer.metrics[0].result()))
layer.metrics: [<keras.metrics.metrics.BinaryAccuracy object at 0x7f78e822dc10>]
current accuracy value: 1.0

Just like for add_loss(), these metrics are tracked by fit():

inputs = keras.Input(shape=(3,), name="inputs")
targets = keras.Input(shape=(10,), name="targets")
logits = keras.layers.Dense(10)(inputs)
predictions = LogisticEndpoint(name="predictions")(logits, targets)

model = keras.Model(inputs=[inputs, targets], outputs=predictions)
model.compile(optimizer="adam")

data = {
    "inputs": np.random.random((3, 3)),
    "targets": np.random.random((3, 10)),
}
model.fit(data)
1/1 [==============================] - 0s 275ms/step - loss: 0.9023 - binary_accuracy: 0.0000e+00
<keras.callbacks.History at 0x7f7954183c10>

You can optionally enable serialization on your layers

If you need your custom layers to be serializable as part of a Functional model, you can optionally implement a get_config() method:

class Linear(keras.layers.Layer):
    def __init__(self, units=32):
        super(Linear, self).__init__()
        self.units = units

    def build(self, input_shape):
        self.w = self.add_weight(
            shape=(input_shape[-1], self.units),
            initializer="random_normal",
            trainable=True,
        )
        self.b = self.add_weight(
            shape=(self.units,), initializer="random_normal", trainable=True
        )

    def call(self, inputs):
        return tf.matmul(inputs, self.w) + self.b

    def get_config(self):
        return {"units": self.units}


# Now you can recreate the layer from its config:
layer = Linear(64)
config = layer.get_config()
print(config)
new_layer = Linear.from_config(config)
{'units': 64}

Note that the __init__() method of the base Layer class takes some keyword arguments, in particular a name and a dtype. It's good practice to pass these arguments to the parent class in __init__() and to include them in the layer config:

class Linear(keras.layers.Layer):
    def __init__(self, units=32, **kwargs):
        super(Linear, self).__init__(**kwargs)
        self.units = units

    def build(self, input_shape):
        self.w = self.add_weight(
            shape=(input_shape[-1], self.units),
            initializer="random_normal",
            trainable=True,
        )
        self.b = self.add_weight(
            shape=(self.units,), initializer="random_normal", trainable=True
        )

    def call(self, inputs):
        return tf.matmul(inputs, self.w) + self.b

    def get_config(self):
        config = super(Linear, self).get_config()
        config.update({"units": self.units})
        return config


layer = Linear(64)
config = layer.get_config()
print(config)
new_layer = Linear.from_config(config)
{'name': 'linear_8', 'trainable': True, 'dtype': 'float32', 'units': 64}

If you need more flexibility when deserializing the layer from its config, you can also override the from_config() class method. This is the base implementation of from_config():

def from_config(cls, config):
  return cls(**config)

To learn more about serialization and saving, see the complete guide to saving and serializing models.

Privileged training argument in the call() method

Some layers, in particular the BatchNormalization layer and the Dropout layer, have different behaviors during training and inference. For such layers, it is standard practice to expose a training (boolean) argument in the call() method.

By exposing this argument in call(), you enable the built-in training and evaluation loops (e.g. fit()) to correctly use the layer in training and inference.

class CustomDropout(keras.layers.Layer):
    def __init__(self, rate, **kwargs):
        super(CustomDropout, self).__init__(**kwargs)
        self.rate = rate

    def call(self, inputs, training=None):
        if training:
            return tf.nn.dropout(inputs, rate=self.rate)
        return inputs

Privileged mask argument in the call() method

The other privileged argument supported by call() is the mask argument.

You will find it in all Keras RNN layers. A mask is a boolean tensor (one boolean value per timestep in the input) used to skip certain input timesteps when processing timeseries data.

Keras will automatically pass the correct mask argument to __call__() for layers that support it, when a mask is generated by a prior layer. Mask-generating layers are the Embedding layer configured with mask_zero=True, and the Masking layer.

To learn more about masking and how to write masking-enabled layers, please check out the guide "understanding padding and masking".

モデルクラス

一般的に、レイヤークラスを使用して内部計算ブロックを定義し、モデルクラスを使用して外部モデル(トレーニングするオブジェクト)を定義します。

たとえば、ResNet50モデルでは、レイヤーをサブクラス化する複数のResNetブロックと、ResNet50ネットワーク全体を包含する1つの モデルがあります。

モデルクラスはレイヤークラスと同じAPIをもちますが、以下の点で異なります。

  • 組み込みのトレーニング、評価、予測ループを公開します(model.fit()model.evaluate(),、model.predict())。
  • model.layersプロパティを介して、その内部レイヤーのリストを公開します。
  • 保存およびシリアル化APIを公開します(save()save_weights()...)

実質的にレイヤークラスは、文献で「レイヤー」(「畳み込みレイヤー」または「リカレントレイヤー」など)または「ブロック」(「ResNetブロック」または「Inceptionブロック」など)と呼ばれているものに対応します。

一方、モデルクラスは、文献で「モデル」(「ディープラーニングモデル」など)または「ネットワーク」(「ディープニューラルネットワーク」など)と呼ばれているものに対応します 。

LayerクラスまたはModelクラスのどちらを使用すべきか迷っている場合は、次の点を確認してください。 fit()save()を呼び出す必要がある場合は、Modelを使用してください。 そうでない場合(クラスがより大きなシステムの単なるブロックである場合や自分でトレーニングを記述してコードを保存する場合)Layerを使用します。

たとえば、上のmini-resnetの例を使用してModel を構築し、fit()でトレーニングし、save_weights()で保存できます。

class ResNet(tf.keras.Model):

    def __init__(self, num_classes=1000):
        super(ResNet, self).__init__()
        self.block_1 = ResNetBlock()
        self.block_2 = ResNetBlock()
        self.global_pool = layers.GlobalAveragePooling2D()
        self.classifier = Dense(num_classes)

    def call(self, inputs):
        x = self.block_1(inputs)
        x = self.block_2(x)
        x = self.global_pool(x)
        return self.classifier(x)


resnet = ResNet()
dataset = ...
resnet.fit(dataset, epochs=10)
resnet.save(filepath)

Putting it all together: an end-to-end example

Here's what you've learned so far:

  • A Layer encapsulate a state (created in __init__() or build()) and some computation (defined in call()).
  • Layers can be recursively nested to create new, bigger computation blocks.
  • Layers can create and track losses (typically regularization losses) as well as metrics, via add_loss() and add_metric()
  • The outer container, the thing you want to train, is a Model. A Model is just like a Layer, but with added training and serialization utilities.

Let's put all of these things together into an end-to-end example: we're going to implement a Variational AutoEncoder (VAE). We'll train it on MNIST digits.

Our VAE will be a subclass of Model, built as a nested composition of layers that subclass Layer. It will feature a regularization loss (KL divergence).

from tensorflow.keras import layers


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.keras.backend.random_normal(shape=(batch, dim))
        return z_mean + tf.exp(0.5 * z_log_var) * epsilon


class Encoder(layers.Layer):
    """Maps MNIST digits to a triplet (z_mean, z_log_var, z)."""

    def __init__(self, latent_dim=32, intermediate_dim=64, name="encoder", **kwargs):
        super(Encoder, self).__init__(name=name, **kwargs)
        self.dense_proj = layers.Dense(intermediate_dim, activation="relu")
        self.dense_mean = layers.Dense(latent_dim)
        self.dense_log_var = layers.Dense(latent_dim)
        self.sampling = Sampling()

    def call(self, inputs):
        x = self.dense_proj(inputs)
        z_mean = self.dense_mean(x)
        z_log_var = self.dense_log_var(x)
        z = self.sampling((z_mean, z_log_var))
        return z_mean, z_log_var, z


class Decoder(layers.Layer):
    """Converts z, the encoded digit vector, back into a readable digit."""

    def __init__(self, original_dim, intermediate_dim=64, name="decoder", **kwargs):
        super(Decoder, self).__init__(name=name, **kwargs)
        self.dense_proj = layers.Dense(intermediate_dim, activation="relu")
        self.dense_output = layers.Dense(original_dim, activation="sigmoid")

    def call(self, inputs):
        x = self.dense_proj(inputs)
        return self.dense_output(x)


class VariationalAutoEncoder(keras.Model):
    """Combines the encoder and decoder into an end-to-end model for training."""

    def __init__(
        self,
        original_dim,
        intermediate_dim=64,
        latent_dim=32,
        name="autoencoder",
        **kwargs
    ):
        super(VariationalAutoEncoder, self).__init__(name=name, **kwargs)
        self.original_dim = original_dim
        self.encoder = Encoder(latent_dim=latent_dim, intermediate_dim=intermediate_dim)
        self.decoder = Decoder(original_dim, intermediate_dim=intermediate_dim)

    def call(self, inputs):
        z_mean, z_log_var, z = self.encoder(inputs)
        reconstructed = self.decoder(z)
        # Add KL divergence regularization loss.
        kl_loss = -0.5 * tf.reduce_mean(
            z_log_var - tf.square(z_mean) - tf.exp(z_log_var) + 1
        )
        self.add_loss(kl_loss)
        return reconstructed

Let's write a simple training loop on MNIST:

original_dim = 784
vae = VariationalAutoEncoder(original_dim, 64, 32)

optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)
mse_loss_fn = tf.keras.losses.MeanSquaredError()

loss_metric = tf.keras.metrics.Mean()

(x_train, _), _ = tf.keras.datasets.mnist.load_data()
x_train = x_train.reshape(60000, 784).astype("float32") / 255

train_dataset = tf.data.Dataset.from_tensor_slices(x_train)
train_dataset = train_dataset.shuffle(buffer_size=1024).batch(64)

epochs = 2

# Iterate over epochs.
for epoch in range(epochs):
    print("Start of epoch %d" % (epoch,))

    # Iterate over the batches of the dataset.
    for step, x_batch_train in enumerate(train_dataset):
        with tf.GradientTape() as tape:
            reconstructed = vae(x_batch_train)
            # Compute reconstruction loss
            loss = mse_loss_fn(x_batch_train, reconstructed)
            loss += sum(vae.losses)  # Add KLD regularization loss

        grads = tape.gradient(loss, vae.trainable_weights)
        optimizer.apply_gradients(zip(grads, vae.trainable_weights))

        loss_metric(loss)

        if step % 100 == 0:
            print("step %d: mean loss = %.4f" % (step, loss_metric.result()))
Start of epoch 0
step 0: mean loss = 0.3527
step 100: mean loss = 0.1248
step 200: mean loss = 0.0988
step 300: mean loss = 0.0889
step 400: mean loss = 0.0841
step 500: mean loss = 0.0807
step 600: mean loss = 0.0786
step 700: mean loss = 0.0770
step 800: mean loss = 0.0759
step 900: mean loss = 0.0749
Start of epoch 1
step 0: mean loss = 0.0746
step 100: mean loss = 0.0740
step 200: mean loss = 0.0734
step 300: mean loss = 0.0730
step 400: mean loss = 0.0727
step 500: mean loss = 0.0723
step 600: mean loss = 0.0720
step 700: mean loss = 0.0717
step 800: mean loss = 0.0714
step 900: mean loss = 0.0712

Note that since the VAE is subclassing Model, it features built-in training loops. So you could also have trained it like this:

vae = VariationalAutoEncoder(784, 64, 32)

optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)

vae.compile(optimizer, loss=tf.keras.losses.MeanSquaredError())
vae.fit(x_train, x_train, epochs=2, batch_size=64)
Epoch 1/2
938/938 [==============================] - 3s 2ms/step - loss: 0.0747
Epoch 2/2
938/938 [==============================] - 2s 2ms/step - loss: 0.0676
<keras.callbacks.History at 0x7f78e8148a90>

Beyond object-oriented development: the Functional API

Was this example too much object-oriented development for you? You can also build models using the Functional API. Importantly, choosing one style or another does not prevent you from leveraging components written in the other style: you can always mix-and-match.

For instance, the Functional API example below reuses the same Sampling layer we defined in the example above:

original_dim = 784
intermediate_dim = 64
latent_dim = 32

# Define encoder model.
original_inputs = tf.keras.Input(shape=(original_dim,), name="encoder_input")
x = layers.Dense(intermediate_dim, activation="relu")(original_inputs)
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 = tf.keras.Model(inputs=original_inputs, outputs=z, name="encoder")

# Define decoder model.
latent_inputs = tf.keras.Input(shape=(latent_dim,), name="z_sampling")
x = layers.Dense(intermediate_dim, activation="relu")(latent_inputs)
outputs = layers.Dense(original_dim, activation="sigmoid")(x)
decoder = tf.keras.Model(inputs=latent_inputs, outputs=outputs, name="decoder")

# Define VAE model.
outputs = decoder(z)
vae = tf.keras.Model(inputs=original_inputs, outputs=outputs, name="vae")

# Add KL divergence regularization loss.
kl_loss = -0.5 * tf.reduce_mean(z_log_var - tf.square(z_mean) - tf.exp(z_log_var) + 1)
vae.add_loss(kl_loss)

# Train.
optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)
vae.compile(optimizer, loss=tf.keras.losses.MeanSquaredError())
vae.fit(x_train, x_train, epochs=3, batch_size=64)
Epoch 1/3
938/938 [==============================] - 3s 2ms/step - loss: 0.0746
Epoch 2/3
938/938 [==============================] - 2s 2ms/step - loss: 0.0676
Epoch 3/3
938/938 [==============================] - 2s 2ms/step - loss: 0.0676
<keras.callbacks.History at 0x7f78e0671940>

For more information, make sure to read the Functional API guide.