Which of these exists when the outputs of one unit or group become the inputs for another?

Setup

import tensorflow as tf
from tensorflow import keras
from tensorflow.keras import layers

When to use a Sequential model

A Sequential model is appropriate for a plain stack of layers where each layer has exactly one input tensor and one output tensor.

Schematically, the following Sequential model:

# Define Sequential model with 3 layers
model = keras.Sequential(
    [
        layers.Dense(2, activation="relu", name="layer1"),
        layers.Dense(3, activation="relu", name="layer2"),
        layers.Dense(4, name="layer3"),
    ]
)
# Call model on a test input
x = tf.ones((3, 3))
y = model(x)

is equivalent to this function:

# Create 3 layers
layer1 = layers.Dense(2, activation="relu", name="layer1")
layer2 = layers.Dense(3, activation="relu", name="layer2")
layer3 = layers.Dense(4, name="layer3")

# Call layers on a test input
x = tf.ones((3, 3))
y = layer3(layer2(layer1(x)))

A Sequential model is not appropriate when:

• Your model has multiple inputs or multiple outputs
• Any of your layers has multiple inputs or multiple outputs
• You need to do layer sharing
• You want non-linear topology (e.g. a residual connection, a multi-branch model)

Creating a Sequential model

You can create a Sequential model by passing a list of layers to the Sequential constructor:

model = keras.Sequential(
    [
        layers.Dense(2, activation="relu"),
        layers.Dense(3, activation="relu"),
        layers.Dense(4),
    ]
)

Its layers are accessible via the layers attribute:

model.layers

[<keras.layers.core.Dense at 0x7fdc784478d0>,
 <keras.layers.core.Dense at 0x7fdbbc3c4650>,
 <keras.layers.core.Dense at 0x7fdbbc3c4a10>]

You can also create a Sequential model incrementally via the add() method:

model = keras.Sequential()
model.add(layers.Dense(2, activation="relu"))
model.add(layers.Dense(3, activation="relu"))
model.add(layers.Dense(4))

Note that there's also a corresponding pop() method to remove layers: a Sequential model behaves very much like a list of layers.

model.pop()
print(len(model.layers))  # 2

2

Also note that the Sequential constructor accepts a name argument, just like any layer or model in Keras. This is useful to annotate TensorBoard graphs with semantically meaningful names.

model = keras.Sequential(name="my_sequential")
model.add(layers.Dense(2, activation="relu", name="layer1"))
model.add(layers.Dense(3, activation="relu", name="layer2"))
model.add(layers.Dense(4, name="layer3"))

Specifying the input shape in advance

Generally, all layers in Keras need to know the shape of their inputs in order to be able to create their weights. So when you create a layer like this, initially, it has no weights:

layer = layers.Dense(3)
layer.weights  # Empty

[]

It creates its weights the first time it is called on an input, since the shape of the weights depends on the shape of the inputs:

# Call layer on a test input
x = tf.ones((1, 4))
y = layer(x)
layer.weights  # Now it has weights, of shape (4, 3) and (3,)

[<tf.Variable 'dense_6/kernel:0' shape=(4, 3) dtype=float32, numpy=
 array([[ 0.5319189 , -0.8767905 , -0.63919735],
        [-0.6276014 ,  0.1689707 , -0.57695866],
        [ 0.6710613 ,  0.5354214 , -0.00893992],
        [ 0.15670097, -0.15280598,  0.8865864 ]], dtype=float32)>,
 <tf.Variable 'dense_6/bias:0' shape=(3,) dtype=float32, numpy=array([0., 0., 0.], dtype=float32)>]

Naturally, this also applies to Sequential models. When you instantiate a Sequential model without an input shape, it isn't "built": it has no weights (and calling model.weights results in an error stating just this). The weights are created when the model first sees some input data:

model = keras.Sequential(
    [
        layers.Dense(2, activation="relu"),
        layers.Dense(3, activation="relu"),
        layers.Dense(4),
    ]
)  # No weights at this stage!

# At this point, you can't do this:
# model.weights

# You also can't do this:
# model.summary()

# Call the model on a test input
x = tf.ones((1, 4))
y = model(x)
print("Number of weights after calling the model:", len(model.weights))  # 6

Number of weights after calling the model: 6

Once a model is "built", you can call its summary() method to display its contents:

model.summary()

Model: "sequential_3"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_7 (Dense)              (1, 2)                    10        
_________________________________________________________________
dense_8 (Dense)              (1, 3)                    9         
_________________________________________________________________
dense_9 (Dense)              (1, 4)                    16        
=================================================================
Total params: 35
Trainable params: 35
Non-trainable params: 0
_________________________________________________________________

However, it can be very useful when building a Sequential model incrementally to be able to display the summary of the model so far, including the current output shape. In this case, you should start your model by passing an Input object to your model, so that it knows its input shape from the start:

model = keras.Sequential()
model.add(keras.Input(shape=(4,)))
model.add(layers.Dense(2, activation="relu"))

model.summary()

Model: "sequential_4"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_10 (Dense)             (None, 2)                 10        
=================================================================
Total params: 10
Trainable params: 10
Non-trainable params: 0
_________________________________________________________________

Note that the Input object is not displayed as part of model.layers, since it isn't a layer:

model.layers

[<keras.layers.core.Dense at 0x7fdbbc37c390>]

A simple alternative is to just pass an input_shape argument to your first layer:

model = keras.Sequential()
model.add(layers.Dense(2, activation="relu", input_shape=(4,)))

model.summary()

Model: "sequential_5"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
dense_11 (Dense)             (None, 2)                 10        
=================================================================
Total params: 10
Trainable params: 10
Non-trainable params: 0
_________________________________________________________________

Models built with a predefined input shape like this always have weights (even before seeing any data) and always have a defined output shape.

In general, it's a recommended best practice to always specify the input shape of a Sequential model in advance if you know what it is.

A common debugging workflow: add() + summary()

When building a new Sequential architecture, it's useful to incrementally stack layers with add() and frequently print model summaries. For instance, this enables you to monitor how a stack of Conv2D and MaxPooling2D layers is downsampling image feature maps:

model = keras.Sequential()
model.add(keras.Input(shape=(250, 250, 3)))  # 250x250 RGB images
model.add(layers.Conv2D(32, 5, strides=2, activation="relu"))
model.add(layers.Conv2D(32, 3, activation="relu"))
model.add(layers.MaxPooling2D(3))

# Can you guess what the current output shape is at this point? Probably not.
# Let's just print it:
model.summary()

# The answer was: (40, 40, 32), so we can keep downsampling...

model.add(layers.Conv2D(32, 3, activation="relu"))
model.add(layers.Conv2D(32, 3, activation="relu"))
model.add(layers.MaxPooling2D(3))
model.add(layers.Conv2D(32, 3, activation="relu"))
model.add(layers.Conv2D(32, 3, activation="relu"))
model.add(layers.MaxPooling2D(2))

# And now?
model.summary()

# Now that we have 4x4 feature maps, time to apply global max pooling.
model.add(layers.GlobalMaxPooling2D())

# Finally, we add a classification layer.
model.add(layers.Dense(10))

Model: "sequential_6"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d (Conv2D)              (None, 123, 123, 32)      2432      
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 121, 121, 32)      9248      
_________________________________________________________________
max_pooling2d (MaxPooling2D) (None, 40, 40, 32)        0         
=================================================================
Total params: 11,680
Trainable params: 11,680
Non-trainable params: 0
_________________________________________________________________
Model: "sequential_6"
_________________________________________________________________
Layer (type)                 Output Shape              Param #   
=================================================================
conv2d (Conv2D)              (None, 123, 123, 32)      2432      
_________________________________________________________________
conv2d_1 (Conv2D)            (None, 121, 121, 32)      9248      
_________________________________________________________________
max_pooling2d (MaxPooling2D) (None, 40, 40, 32)        0         
_________________________________________________________________
conv2d_2 (Conv2D)            (None, 38, 38, 32)        9248      
_________________________________________________________________
conv2d_3 (Conv2D)            (None, 36, 36, 32)        9248      
_________________________________________________________________
max_pooling2d_1 (MaxPooling2 (None, 12, 12, 32)        0         
_________________________________________________________________
conv2d_4 (Conv2D)            (None, 10, 10, 32)        9248      
_________________________________________________________________
conv2d_5 (Conv2D)            (None, 8, 8, 32)          9248      
_________________________________________________________________
max_pooling2d_2 (MaxPooling2 (None, 4, 4, 32)          0         
=================================================================
Total params: 48,672
Trainable params: 48,672
Non-trainable params: 0
_________________________________________________________________

Very practical, right?

What to do once you have a model

Once your model architecture is ready, you will want to:

• Train your model, evaluate it, and run inference. See our guide to training & evaluation with the built-in loops
• Save your model to disk and restore it. See our guide to serialization & saving.
• Speed up model training by leveraging multiple GPUs. See our guide to multi-GPU and distributed training.

Once a Sequential model has been built, it behaves like a Functional API model. This means that every layer has an input and output attribute. These attributes can be used to do neat things, like quickly creating a model that extracts the outputs of all intermediate layers in a Sequential model:

initial_model = keras.Sequential(
    [
        keras.Input(shape=(250, 250, 3)),
        layers.Conv2D(32, 5, strides=2, activation="relu"),
        layers.Conv2D(32, 3, activation="relu"),
        layers.Conv2D(32, 3, activation="relu"),
    ]
)
feature_extractor = keras.Model(
    inputs=initial_model.inputs,
    outputs=[layer.output for layer in initial_model.layers],
)

# Call feature extractor on test input.
x = tf.ones((1, 250, 250, 3))
features = feature_extractor(x)

Here's a similar example that only extract features from one layer:

initial_model = keras.Sequential(
    [
        keras.Input(shape=(250, 250, 3)),
        layers.Conv2D(32, 5, strides=2, activation="relu"),
        layers.Conv2D(32, 3, activation="relu", name="my_intermediate_layer"),
        layers.Conv2D(32, 3, activation="relu"),
    ]
)
feature_extractor = keras.Model(
    inputs=initial_model.inputs,
    outputs=initial_model.get_layer(name="my_intermediate_layer").output,
)
# Call feature extractor on test input.
x = tf.ones((1, 250, 250, 3))
features = feature_extractor(x)

Transfer learning with a Sequential model

Transfer learning consists of freezing the bottom layers in a model and only training the top layers. If you aren't familiar with it, make sure to read our guide to transfer learning.

Here are two common transfer learning blueprint involving Sequential models.

First, let's say that you have a Sequential model, and you want to freeze all layers except the last one. In this case, you would simply iterate over model.layers and set layer.trainable = False on each layer, except the last one. Like this:

model = keras.Sequential([
    keras.Input(shape=(784)),
    layers.Dense(32, activation='relu'),
    layers.Dense(32, activation='relu'),
    layers.Dense(32, activation='relu'),
    layers.Dense(10),
])

# Presumably you would want to first load pre-trained weights.
model.load_weights(...)

# Freeze all layers except the last one.
for layer in model.layers[:-1]:
  layer.trainable = False

# Recompile and train (this will only update the weights of the last layer).
model.compile(...)
model.fit(...)

Another common blueprint is to use a Sequential model to stack a pre-trained model and some freshly initialized classification layers. Like this:

# Load a convolutional base with pre-trained weights
base_model = keras.applications.Xception(
    weights='imagenet',
    include_top=False,
    pooling='avg')

# Freeze the base model
base_model.trainable = False

# Use a Sequential model to add a trainable classifier on top
model = keras.Sequential([
    base_model,
    layers.Dense(1000),
])

# Compile & train
model.compile(...)
model.fit(...)

If you do transfer learning, you will probably find yourself frequently using these two patterns.

That's about all you need to know about Sequential models!

To find out more about building models in Keras, see:

• Guide to the Functional API
• Guide to making new Layers & Models via subclassing

In which form of interdependence does the output of one unit become the input for another in a successive fashion?

When the output of one department becomes the input of the other department and vice versa it is classified as?

During which stage in group development group members come to accept fellow members and develop a unity of purpose that binds them?

What exists when activities flow both ways between units?