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Introduction to Keras for Researchers

Author: fchollet
Date created: 2020/04/01
Last modified: 2020/10/02
Description: Everything you need to know to use Keras & TensorFlow for deep learning research.

View in Colab • GitHub source

Setup

import tensorflow as tf
from tensorflow import keras

Introduction

Are you a machine learning researcher? Do you publish at NeurIPS and push the state-of-the-art in CV and NLP? This guide will serve as your first introduction to core Keras & TensorFlow API concepts.

In this guide, you will learn about:

  • Tensors, variables, and gradients in TensorFlow
  • Creating layers by subclassing the Layer class
  • Writing low-level training loops
  • Tracking losses created by layers via the add_loss() method
  • Tracking metrics in a low-level training loop
  • Speeding up execution with a compiled tf.function
  • Executing layers in training or inference mode
  • The Keras Functional API

You will also see the Keras API in action in two end-to-end research examples: a Variational Autoencoder, and a Hypernetwork.

Tensors

TensorFlow is an infrastructure layer for differentiable programming. At its heart, it's a framework for manipulating N-dimensional arrays (tensors), much like NumPy.

However, there are three key differences between NumPy and TensorFlow:

  • TensorFlow can leverage hardware accelerators such as GPUs and TPUs.
  • TensorFlow can automatically compute the gradient of arbitrary differentiable tensor expressions.
  • TensorFlow computation can be distributed to large numbers of devices on a single machine, and large number of machines (potentially with multiple devices each).

Let's take a look at the object that is at the core of TensorFlow: the Tensor.

Here's a constant tensor:

x = tf.constant([[5, 2], [1, 3]])
print(x)
``` tf.Tensor( [[5 2] [1 3]], shape=(2, 2), dtype=int32) 
</div>
You can get its value as a NumPy array by calling `.numpy()`:


```python
x.numpy()
``` array([[5, 2], [1, 3]], dtype=int32) 
</div>
Much like a NumPy array, it features the attributes `dtype` and `shape`:


```python
print("dtype:", x.dtype)
print("shape:", x.shape)
``` dtype: shape: (2, 2) 
</div>
A common way to create constant tensors is via `tf.ones` and `tf.zeros` (just like `np.ones` and `np.zeros`):


```python
print(tf.ones(shape=(2, 1)))
print(tf.zeros(shape=(2, 1)))
``` tf.Tensor( [[1.] [1.]], shape=(2, 1), dtype=float32) tf.Tensor( [[0.] [0.]], shape=(2, 1), dtype=float32) 
</div>
You can also create random constant tensors:


```python
x = tf.random.normal(shape=(2, 2), mean=0.0, stddev=1.0)

x = tf.random.uniform(shape=(2, 2), minval=0, maxval=10, dtype="int32")

Variables

Variables are special tensors used to store mutable state (such as the weights of a neural network). You create a Variable using some initial value:

initial_value = tf.random.normal(shape=(2, 2))
a = tf.Variable(initial_value)
print(a)
``` 
</div>
You update the value of a `Variable` by using the methods `.assign(value)`, `.assign_add(increment)`, or `.assign_sub(decrement)`:


```python
new_value = tf.random.normal(shape=(2, 2))
a.assign(new_value)
for i in range(2):
    for j in range(2):
        assert a[i, j] == new_value[i, j]

added_value = tf.random.normal(shape=(2, 2))
a.assign_add(added_value)
for i in range(2):
    for j in range(2):
        assert a[i, j] == new_value[i, j] + added_value[i, j]

Doing math in TensorFlow

If you've used NumPy, doing math in TensorFlow will look very familiar. The main difference is that your TensorFlow code can run on GPU and TPU.

a = tf.random.normal(shape=(2, 2))
b = tf.random.normal(shape=(2, 2))

c = a + b
d = tf.square(c)
e = tf.exp(d)

Gradients

Here's another big difference with NumPy: you can automatically retrieve the gradient of any differentiable expression.

Just open a GradientTape, start "watching" a tensor via tape.watch(), and compose a differentiable expression using this tensor as input:

a = tf.random.normal(shape=(2, 2))
b = tf.random.normal(shape=(2, 2))

with tf.GradientTape() as tape:
    tape.watch(a)  # Start recording the history of operations applied to `a`
    c = tf.sqrt(tf.square(a) + tf.square(b))  # Do some math using `a`
    # What's the gradient of `c` with respect to `a`?
    dc_da = tape.gradient(c, a)
    print(dc_da)
``` tf.Tensor( [[-0.3224076 0.69120544] [-0.7068095 -0.53885883]], shape=(2, 2), dtype=float32) 
</div>
By default, variables are watched automatically, so you don't need to manually `watch` them:


```python
a = tf.Variable(a)

with tf.GradientTape() as tape:
    c = tf.sqrt(tf.square(a) + tf.square(b))
    dc_da = tape.gradient(c, a)
    print(dc_da)
``` tf.Tensor( [[-0.3224076 0.69120544] [-0.7068095 -0.53885883]], shape=(2, 2), dtype=float32) 
</div>
Note that you can compute higher-order derivatives by nesting tapes:


```python
with tf.GradientTape() as outer_tape:
    with tf.GradientTape() as tape:
        c = tf.sqrt(tf.square(a) + tf.square(b))
        dc_da = tape.gradient(c, a)
    d2c_da2 = outer_tape.gradient(dc_da, a)
    print(d2c_da2)
``` tf.Tensor( [[1.6652625 0.6523223 ] [0.20117798 0.41852283]], shape=(2, 2), dtype=float32) 
</div>
---
## Keras layers

While TensorFlow is an **infrastructure layer for differentiable programming**,
dealing with tensors, variables, and gradients,
Keras is a **user interface for deep learning**, dealing with
layers, models, optimizers, loss functions, metrics, and more.

Keras serves as the high-level API for TensorFlow:
Keras is what makes TensorFlow simple and productive.

The `Layer` class is the fundamental abstraction in Keras.
A `Layer` encapsulates a state (weights) and some computation
(defined in the call method).

A simple layer looks like this:


```python

class Linear(keras.layers.Layer):
    """y = w.x + b"""

    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 instance much like a Python function:

# Instantiate our layer.
linear_layer = Linear(units=4, input_dim=2)

# The layer can be treated as a function.
# Here we call it on some data.
y = linear_layer(tf.ones((2, 2)))
assert y.shape == (2, 4)

The weight variables (created in __init__) are automatically tracked under the weights property:

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

You have many built-in layers available, from Dense to Conv2D to LSTM to fancier ones like Conv3DTranspose or ConvLSTM2D. Be smart about reusing built-in functionality.

Layer weight creation

The self.add_weight() method gives you a shortcut for creating weights:

class Linear(keras.layers.Layer):
    """y = w.x + b"""

    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


# Instantiate our lazy layer.
linear_layer = Linear(4)

# This will also call `build(input_shape)` and create the weights.
y = linear_layer(tf.ones((2, 2)))

Layer gradients

You can automatically retrieve the gradients of the weights of a layer by calling it inside a GradientTape. Using these gradients, you can update the weights of the layer, either manually, or using an optimizer object. Of course, you can modify the gradients before using them, if you need to.

# Prepare a dataset.
(x_train, y_train), _ = tf.keras.datasets.mnist.load_data()
dataset = tf.data.Dataset.from_tensor_slices(
    (x_train.reshape(60000, 784).astype("float32") / 255, y_train)
)
dataset = dataset.shuffle(buffer_size=1024).batch(64)

# Instantiate our linear layer (defined above) with 10 units.
linear_layer = Linear(10)

# Instantiate a logistic loss function that expects integer targets.
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)

# Instantiate an optimizer.
optimizer = tf.keras.optimizers.SGD(learning_rate=1e-3)

# Iterate over the batches of the dataset.
for step, (x, y) in enumerate(dataset):

    # Open a GradientTape.
    with tf.GradientTape() as tape:

        # Forward pass.
        logits = linear_layer(x)

        # Loss value for this batch.
        loss = loss_fn(y, logits)

    # Get gradients of weights wrt the loss.
    gradients = tape.gradient(loss, linear_layer.trainable_weights)

    # Update the weights of our linear layer.
    optimizer.apply_gradients(zip(gradients, linear_layer.trainable_weights))

    # Logging.
    if step % 100 == 0:
        print("Step:", step, "Loss:", float(loss))
``` Step: 0 Loss: 2.386174201965332 Step: 100 Loss: 2.22518253326416 Step: 200 Loss: 2.1162631511688232 Step: 300 Loss: 2.047822952270508 Step: 400 Loss: 2.025263547897339 Step: 500 Loss: 1.9544496536254883 Step: 600 Loss: 1.8216196298599243 Step: 700 Loss: 1.7630621194839478 Step: 800 Loss: 1.756800651550293 Step: 900 Loss: 1.6689152717590332 
</div>
---
## Trainable and non-trainable weights

Weights created by layers can be either trainable or non-trainable. They're
exposed in `trainable_weights` and `non_trainable_weights` respectively.
Here's a layer with a non-trainable weight:


```python

class ComputeSum(keras.layers.Layer):
    """Returns the sum of the inputs."""

    def __init__(self, input_dim):
        super(ComputeSum, self).__init__()
        # Create a non-trainable weight.
        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


my_sum = ComputeSum(2)
x = tf.ones((2, 2))

y = my_sum(x)
print(y.numpy())  # [2. 2.]

y = my_sum(x)
print(y.numpy())  # [4. 4.]

assert my_sum.weights == [my_sum.total]
assert my_sum.non_trainable_weights == [my_sum.total]
assert my_sum.trainable_weights == []
``` [2. 2.] [4. 4.] 
</div>
---
## Layers that own layers

Layers can be recursively nested to create bigger computation blocks.
Each layer will track the weights of its sublayers
(both trainable and non-trainable).


```python
# Let's reuse the Linear class
# with a `build` method that we defined above.


class MLP(keras.layers.Layer):
    """Simple stack of Linear layers."""

    def __init__(self):
        super(MLP, self).__init__()
        self.linear_1 = Linear(32)
        self.linear_2 = Linear(32)
        self.linear_3 = Linear(10)

    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 = MLP()

# The first call to the `mlp` object will create the weights.
y = mlp(tf.ones(shape=(3, 64)))

# Weights are recursively tracked.
assert len(mlp.weights) == 6

Note that our manually-created MLP above is equivalent to the following built-in option:

mlp = keras.Sequential(
    [
        keras.layers.Dense(32, activation=tf.nn.relu),
        keras.layers.Dense(32, activation=tf.nn.relu),
        keras.layers.Dense(10),
    ]
)

Tracking losses created by layers

Layers can create losses during the forward pass via the add_loss() method. This is especially useful for regularization losses. The losses created by sublayers are recursively tracked by the parent layers.

Here's a layer that creates an activity regularization loss:

class ActivityRegularization(keras.layers.Layer):
    """Layer that creates an activity sparsity regularization loss."""

    def __init__(self, rate=1e-2):
        super(ActivityRegularization, self).__init__()
        self.rate = rate

    def call(self, inputs):
        # We use `add_loss` to create a regularization loss
        # that depends on the inputs.
        self.add_loss(self.rate * tf.reduce_sum(inputs))
        return inputs

Any model incorporating this layer will track this regularization loss:

# Let's use the loss layer in a MLP block.


class SparseMLP(keras.layers.Layer):
    """Stack of Linear layers with a sparsity regularization loss."""

    def __init__(self):
        super(SparseMLP, self).__init__()
        self.linear_1 = Linear(32)
        self.regularization = ActivityRegularization(1e-2)
        self.linear_3 = Linear(10)

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


mlp = SparseMLP()
y = mlp(tf.ones((10, 10)))

print(mlp.losses)  # List containing one float32 scalar
``` [] 
</div>
These losses are cleared by the top-level layer at the start of each forward
pass -- they don't accumulate. `layer.losses` always contains only the losses
created during the last forward pass. You would typically use these losses by
summing them before computing your gradients when writing a training loop.


```python
# Losses correspond to the *last* forward pass.
mlp = SparseMLP()
mlp(tf.ones((10, 10)))
assert len(mlp.losses) == 1
mlp(tf.ones((10, 10)))
assert len(mlp.losses) == 1  # No accumulation.

# Let's demonstrate how to use these losses in a training loop.

# Prepare a dataset.
(x_train, y_train), _ = tf.keras.datasets.mnist.load_data()
dataset = tf.data.Dataset.from_tensor_slices(
    (x_train.reshape(60000, 784).astype("float32") / 255, y_train)
)
dataset = dataset.shuffle(buffer_size=1024).batch(64)

# A new MLP.
mlp = SparseMLP()

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

for step, (x, y) in enumerate(dataset):
    with tf.GradientTape() as tape:

        # Forward pass.
        logits = mlp(x)

        # External loss value for this batch.
        loss = loss_fn(y, logits)

        # Add the losses created during the forward pass.
        loss += sum(mlp.losses)

        # Get gradients of weights wrt the loss.
        gradients = tape.gradient(loss, mlp.trainable_weights)

    # Update the weights of our linear layer.
    optimizer.apply_gradients(zip(gradients, mlp.trainable_weights))

    # Logging.
    if step % 100 == 0:
        print("Step:", step, "Loss:", float(loss))
``` Step: 0 Loss: 6.238003730773926 Step: 100 Loss: 2.5299227237701416 Step: 200 Loss: 2.435337543487549 Step: 300 Loss: 2.3858678340911865 Step: 400 Loss: 2.3544323444366455 Step: 500 Loss: 2.3284459114074707 Step: 600 Loss: 2.3211910724639893 Step: 700 Loss: 2.3177292346954346 Step: 800 Loss: 2.322242259979248 Step: 900 Loss: 2.310494899749756 
</div>
---
## Keeping track of training metrics

Keras offers a broad range of built-in metrics, like `tf.keras.metrics.AUC`
or `tf.keras.metrics.PrecisionAtRecall`. It's also easy to create your
own metrics in a few lines of code.

To use a metric in a custom training loop, you would:

- Instantiate the metric object, e.g. `metric = tf.keras.metrics.AUC()`
- Call its `metric.udpate_state(targets, predictions)` method for each batch of data
- Query its result via `metric.result()`
- Reset the metric's state at the end of an epoch or at the start of an evaluation via
`metric.reset_states()`

Here's a simple example:


```python
# Instantiate a metric object
accuracy = tf.keras.metrics.SparseCategoricalAccuracy()

# Prepare our layer, loss, and optimizer.
model = keras.Sequential(
    [
        keras.layers.Dense(32, activation="relu"),
        keras.layers.Dense(32, activation="relu"),
        keras.layers.Dense(10),
    ]
)
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)

for epoch in range(2):
    # Iterate over the batches of a dataset.
    for step, (x, y) in enumerate(dataset):
        with tf.GradientTape() as tape:
            logits = model(x)
            # Compute the loss value for this batch.
            loss_value = loss_fn(y, logits)

        # Update the state of the `accuracy` metric.
        accuracy.update_state(y, logits)

        # Update the weights of the model to minimize the loss value.
        gradients = tape.gradient(loss_value, model.trainable_weights)
        optimizer.apply_gradients(zip(gradients, model.trainable_weights))

        # Logging the current accuracy value so far.
        if step % 200 == 0:
            print("Epoch:", epoch, "Step:", step)
            print("Total running accuracy so far: %.3f" % accuracy.result())

    # Reset the metric's state at the end of an epoch
    accuracy.reset_states()
``` Epoch: 0 Step: 0 Total running accuracy so far: 0.047 Epoch: 0 Step: 200 Total running accuracy so far: 0.755 Epoch: 0 Step: 400 Total running accuracy so far: 0.826 Epoch: 0 Step: 600 Total running accuracy so far: 0.855 Epoch: 0 Step: 800 Total running accuracy so far: 0.872 Epoch: 1 Step: 0 Total running accuracy so far: 0.938 Epoch: 1 Step: 200 Total running accuracy so far: 0.941 Epoch: 1 Step: 400 Total running accuracy so far: 0.943 Epoch: 1 Step: 600 Total running accuracy so far: 0.944 Epoch: 1 Step: 800 Total running accuracy so far: 0.943 
</div>
In addition to this, similarly to the `self.add_loss()` method, you have access
to an `self.add_metric()` method on layers. It tracks the average of
whatever quantity you pass to it. You can reset the value of these metrics
by calling `layer.reset_metrics()` on any layer or model.

---
## Compiled functions

Running eagerly is great for debugging, but you will get better performance by
compiling your computation into static graphs. Static graphs are a researcher's
best friends. You can compile any function by wrapping it in a `tf.function`
decorator.


```python
# Prepare our layer, loss, and optimizer.
model = keras.Sequential(
    [
        keras.layers.Dense(32, activation="relu"),
        keras.layers.Dense(32, activation="relu"),
        keras.layers.Dense(10),
    ]
)
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)

# Create a training step function.


@tf.function  # Make it fast.
def train_on_batch(x, y):
    with tf.GradientTape() as tape:
        logits = model(x)
        loss = loss_fn(y, logits)
        gradients = tape.gradient(loss, model.trainable_weights)
    optimizer.apply_gradients(zip(gradients, model.trainable_weights))
    return loss


# Prepare a dataset.
(x_train, y_train), _ = tf.keras.datasets.mnist.load_data()
dataset = tf.data.Dataset.from_tensor_slices(
    (x_train.reshape(60000, 784).astype("float32") / 255, y_train)
)
dataset = dataset.shuffle(buffer_size=1024).batch(64)

for step, (x, y) in enumerate(dataset):
    loss = train_on_batch(x, y)
    if step % 100 == 0:
        print("Step:", step, "Loss:", float(loss))
``` Step: 0 Loss: 2.307070016860962 Step: 100 Loss: 0.7121144533157349 Step: 200 Loss: 0.45566993951797485 Step: 300 Loss: 0.47507303953170776 Step: 400 Loss: 0.23864206671714783 Step: 500 Loss: 0.2954753041267395 Step: 600 Loss: 0.31291744112968445 Step: 700 Loss: 0.15316027402877808 Step: 800 Loss: 0.32832837104797363 Step: 900 Loss: 0.10866784304380417 
</div>
---
## Training mode & inference mode

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 modes.


```python

class Dropout(keras.layers.Layer):
    def __init__(self, rate):
        super(Dropout, self).__init__()
        self.rate = rate

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


class MLPWithDropout(keras.layers.Layer):
    def __init__(self):
        super(MLPWithDropout, self).__init__()
        self.linear_1 = Linear(32)
        self.dropout = Dropout(0.5)
        self.linear_3 = Linear(10)

    def call(self, inputs, training=None):
        x = self.linear_1(inputs)
        x = tf.nn.relu(x)
        x = self.dropout(x, training=training)
        return self.linear_3(x)


mlp = MLPWithDropout()
y_train = mlp(tf.ones((2, 2)), training=True)
y_test = mlp(tf.ones((2, 2)), training=False)

The Functional API for model-building

To build deep learning models, you don't have to use object-oriented programming all the time. All layers we've seen so far can also be composed functionally, like this (we call it the "Functional API"):

# We use an `Input` object to describe the shape and dtype of the inputs.
# This is the deep learning equivalent of *declaring a type*.
# The shape argument is per-sample; it does not include the batch size.
# The functional API focused on defining per-sample transformations.
# The model we create will automatically batch the per-sample transformations,
# so that it can be called on batches of data.
inputs = tf.keras.Input(shape=(16,), dtype="float32")

# We call layers on these "type" objects
# and they return updated types (new shapes/dtypes).
x = Linear(32)(inputs)  # We are reusing the Linear layer we defined earlier.
x = Dropout(0.5)(x)  # We are reusing the Dropout layer we defined earlier.
outputs = Linear(10)(x)

# A functional `Model` can be defined by specifying inputs and outputs.
# A model is itself a layer like any other.
model = tf.keras.Model(inputs, outputs)

# A functional model already has weights, before being called on any data.
# That's because we defined its input shape in advance (in `Input`).
assert len(model.weights) == 4

# Let's call our model on some data, for fun.
y = model(tf.ones((2, 16)))
assert y.shape == (2, 10)

# You can pass a `training` argument in `__call__`
# (it will get passed down to the Dropout layer).
y = model(tf.ones((2, 16)), training=True)

The Functional API tends to be more concise than subclassing, and provides a few other advantages (generally the same advantages that functional, typed languages provide over untyped OO development). However, it can only be used to define DAGs of layers -- recursive networks should be defined as Layer subclasses instead.

Learn more about the Functional API here.

In your research workflows, you may often find yourself mix-and-matching OO models and Functional models.

Note that the Model class also features built-in training & evaluation loops (fit() and evaluate()). You can always subclass the Model class (it works exactly like subclassing Layer) if you want to leverage these loops for your OO models.

End-to-end experiment example 1: variational autoencoders.

Here are some of the things you've learned so far:

  • A Layer encapsulates a state (created in __init__ or build) and some computation (defined in call).
  • Layers can be recursively nested to create new, bigger computation blocks.
  • You can easily write highly hackable training loops by opening a GradientTape, calling your model inside the tape's scope, then retrieving gradients and applying them via an optimizer.
  • You can speed up your training loops using the @tf.function decorator.
  • Layers can create and track losses (typically regularization losses) via self.add_loss().

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

Below is our model definition.

First, we have an Encoder class, which uses a Sampling layer to map a MNIST digit to a latent-space triplet (z_mean, z_log_var, z).

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, **kwargs):
        super(Encoder, self).__init__(**kwargs)
        self.dense_proj = layers.Dense(intermediate_dim, activation=tf.nn.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

Next, we have a Decoder class, which maps the probabilistic latent space coordinates back to a MNIST digit.

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

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

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

Finally, our VariationalAutoEncoder composes together an encoder and a decoder, and creates a KL divergence regularization loss via add_loss().

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

    def __init__(self, original_dim, intermediate_dim=64, latent_dim=32, **kwargs):
        super(VariationalAutoEncoder, self).__init__(**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

Now, let's write a training loop. Our training step is decorated with a @tf.function to compile into a super fast graph function.

# Our model.
vae = VariationalAutoEncoder(original_dim=784, intermediate_dim=64, latent_dim=32)

# Loss and optimizer.
loss_fn = tf.keras.losses.MeanSquaredError()
optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)

# Prepare a dataset.
(x_train, _), _ = tf.keras.datasets.mnist.load_data()
dataset = tf.data.Dataset.from_tensor_slices(
    x_train.reshape(60000, 784).astype("float32") / 255
)
dataset = dataset.shuffle(buffer_size=1024).batch(32)


@tf.function
def training_step(x):
    with tf.GradientTape() as tape:
        reconstructed = vae(x)  # Compute input reconstruction.
        # Compute loss.
        loss = loss_fn(x, reconstructed)
        loss += sum(vae.losses)  # Add KLD term.
    # Update the weights of the VAE.
    grads = tape.gradient(loss, vae.trainable_weights)
    optimizer.apply_gradients(zip(grads, vae.trainable_weights))
    return loss


losses = []  # Keep track of the losses over time.
for step, x in enumerate(dataset):
    loss = training_step(x)
    # Logging.
    losses.append(float(loss))
    if step % 100 == 0:
        print("Step:", step, "Loss:", sum(losses) / len(losses))

    # Stop after 1000 steps.
    # Training the model to convergence is left
    # as an exercise to the reader.
    if step >= 1000:
        break
``` Step: 0 Loss: 0.3283705711364746 Step: 100 Loss: 0.12607811022512982 Step: 200 Loss: 0.09977191104669476 Step: 300 Loss: 0.0897256354383654 Step: 400 Loss: 0.08479013259608549 Step: 500 Loss: 0.08158575140400799 Step: 600 Loss: 0.07913740716886997 Step: 700 Loss: 0.07780108796950753 Step: 800 Loss: 0.07658983394503593 Step: 900 Loss: 0.07564939806583057 Step: 1000 Loss: 0.0746984266928145 
</div>
As you can see, building and training this type of model in Keras
is quick and painless.

Now, you may find that the code above is somewhat verbose: we handle every little detail
on our own, by hand. This gives the most flexibility, but it's also a bit of work.

Let's take a look at what the Functional API version of
our VAE looks like:


```python
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)

Much more concise, right?

By the way, Keras also features built-in training & evaluation loops on its Model class (fit() and evaluate()). Check it out:

# Loss and optimizer.
loss_fn = tf.keras.losses.MeanSquaredError()
optimizer = tf.keras.optimizers.Adam(learning_rate=1e-3)

# Prepare a dataset.
(x_train, _), _ = tf.keras.datasets.mnist.load_data()
dataset = tf.data.Dataset.from_tensor_slices(
    x_train.reshape(60000, 784).astype("float32") / 255
)
dataset = dataset.map(lambda x: (x, x))  # Use x_train as both inputs & targets
dataset = dataset.shuffle(buffer_size=1024).batch(32)

# Configure the model for training.
vae.compile(optimizer, loss=loss_fn)

# Actually training the model.
vae.fit(dataset, epochs=1)
``` 1875/1875 [==============================] - 2s 999us/step - loss: 0.0838

<tensorflow.python.keras.callbacks.History at 0x1456bf250>

</div>
The use of the Functional API and `fit` reduces our example from 65 lines to 25 lines
(including model definition & training). The Keras philosophy is to offer you
productivity-boosting features like
these, while simultaneously empowering you to write everything yourself to gain absolute
control over every little detail. Like we did in the low-level training loop two
paragraphs earlier.

---
## End-to-end experiment example 2: hypernetworks.

Let's take a look at another kind of research experiment: hypernetworks.

A hypernetwork is a deep neural network whose weights are generated by another network
(usually smaller).

Let's implement a really trivial hypernetwork: we'll use a small 2-layer network  to
generate the weights of a larger 3-layer network.



```python
import numpy as np

input_dim = 784
classes = 10

# This is the model we'll actually use to predict labels (the hypernetwork).
outer_model = keras.Sequential(
    [keras.layers.Dense(64, activation=tf.nn.relu), keras.layers.Dense(classes),]
)

# It doesn't need to create its own weights, so let's mark its layers
# as already built. That way, calling `outer_model` won't create new variables.
for layer in outer_model.layers:
    layer.built = True

# This is the number of weight coefficients to generate. Each layer in the
# hypernetwork requires output_dim * input_dim + output_dim coefficients.
num_weights_to_generate = (classes * 64 + classes) + (64 * input_dim + 64)

# This is the model that generates the weights of the `outer_model` above.
inner_model = keras.Sequential(
    [
        keras.layers.Dense(16, activation=tf.nn.relu),
        keras.layers.Dense(num_weights_to_generate, activation=tf.nn.sigmoid),
    ]
)

This is our training loop. For each batch of data:

  • We use inner_model to generate an array of weight coefficients, weights_pred
  • We reshape these coefficients into kernel & bias tensors for the outer_model
  • We run the forward pass of the outer_model to compute the actual MNIST predictions
  • We run backprop through the weights of the inner_model to minimize the final classification loss
# Loss and optimizer.
loss_fn = tf.keras.losses.SparseCategoricalCrossentropy(from_logits=True)
optimizer = tf.keras.optimizers.Adam(learning_rate=1e-4)

# Prepare a dataset.
(x_train, y_train), _ = tf.keras.datasets.mnist.load_data()
dataset = tf.data.Dataset.from_tensor_slices(
    (x_train.reshape(60000, 784).astype("float32") / 255, y_train)
)

# We'll use a batch size of 1 for this experiment.
dataset = dataset.shuffle(buffer_size=1024).batch(1)


@tf.function
def train_step(x, y):
    with tf.GradientTape() as tape:
        # Predict weights for the outer model.
        weights_pred = inner_model(x)

        # Reshape them to the expected shapes for w and b for the outer model.
        # Layer 0 kernel.
        start_index = 0
        w0_shape = (input_dim, 64)
        w0_coeffs = weights_pred[:, start_index : start_index + np.prod(w0_shape)]
        w0 = tf.reshape(w0_coeffs, w0_shape)
        start_index += np.prod(w0_shape)
        # Layer 0 bias.
        b0_shape = (64,)
        b0_coeffs = weights_pred[:, start_index : start_index + np.prod(b0_shape)]
        b0 = tf.reshape(b0_coeffs, b0_shape)
        start_index += np.prod(b0_shape)
        # Layer 1 kernel.
        w1_shape = (64, classes)
        w1_coeffs = weights_pred[:, start_index : start_index + np.prod(w1_shape)]
        w1 = tf.reshape(w1_coeffs, w1_shape)
        start_index += np.prod(w1_shape)
        # Layer 1 bias.
        b1_shape = (classes,)
        b1_coeffs = weights_pred[:, start_index : start_index + np.prod(b1_shape)]
        b1 = tf.reshape(b1_coeffs, b1_shape)
        start_index += np.prod(b1_shape)

        # Set the weight predictions as the weight variables on the outer model.
        outer_model.layers[0].kernel = w0
        outer_model.layers[0].bias = b0
        outer_model.layers[1].kernel = w1
        outer_model.layers[1].bias = b1

        # Inference on the outer model.
        preds = outer_model(x)
        loss = loss_fn(y, preds)

    # Train only inner model.
    grads = tape.gradient(loss, inner_model.trainable_weights)
    optimizer.apply_gradients(zip(grads, inner_model.trainable_weights))
    return loss


losses = []  # Keep track of the losses over time.
for step, (x, y) in enumerate(dataset):
    loss = train_step(x, y)

    # Logging.
    losses.append(float(loss))
    if step % 100 == 0:
        print("Step:", step, "Loss:", sum(losses) / len(losses))

    # Stop after 1000 steps.
    # Training the model to convergence is left
    # as an exercise to the reader.
    if step >= 1000:
        break
``` Step: 0 Loss: 3.346794843673706 Step: 100 Loss: 2.5347713479901306 Step: 200 Loss: 2.3532673210943518 Step: 300 Loss: 2.105134464552208 Step: 400 Loss: 1.9224171297462687 Step: 500 Loss: 1.8143611295096513 Step: 600 Loss: 1.7148052298323655 Step: 700 Loss: 1.6695872197209294 Step: 800 Loss: 1.616796940164684 Step: 900 Loss: 1.5303113453757042 Step: 1000 Loss: 1.4919751342148413 
</div>
Implementing arbitrary research ideas with Keras is straightforward and highly
productive. Imagine trying out 25 ideas per day (20 minutes per experiment on average)!

Keras has been designed to go from idea to results as fast as possible, because we
believe this is
the key to doing great research.

We hope you enjoyed this quick introduction. Let us know what you build with Keras!