The Sequential model

Complete guide to the Sequential model.

Setup

library(tensorflow)
library(keras)

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_model_sequential() %>%
  layer_dense(2, activation = "relu", name = "layer1") %>%
  layer_dense(3, activation = "relu", name = "layer2") %>%
  layer_dense(4, name = "layer3")
Loaded Tensorflow version 2.9.1
# Call model on a test input
x <- tf$ones(shape(3, 3))
y <- model(x)

is equivalent to this function:

# Create 3 layers
layer1 <- layer_dense(units = 2, activation = "relu", name = "layer1")
layer2 <- layer_dense(units = 3, activation = "relu", name = "layer2")
layer3 <- layer_dense(units = 4, name = "layer3")

# Call layers on a test input
x <- tf$ones(shape(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 piping a model through a series layers.

model <- keras_model_sequential() %>%
  layer_dense(2, activation = "relu") %>%
  layer_dense(3, activation = "relu") %>%
  layer_dense(4)

Its layers are accessible via the layers attribute:

model$layers
[[1]]
<keras.layers.core.dense.Dense object at 0x7fc370086b50>

[[2]]
<keras.layers.core.dense.Dense object at 0x7fc3700bbe20>

[[3]]
<keras.layers.core.dense.Dense object at 0x7fc37111e520>

You can also create a Sequential model incrementally:

model <- keras_model_sequential()
model %>% layer_dense(2, activation = "relu")
model %>% layer_dense(3, activation = "relu")
model %>% layer_dense(4)

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

model %>% pop_layer()
length(model$layers)  # 2
[1] 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_model_sequential(name = "my_sequential")
model %>% layer_dense(2, activation = "relu", name = "layer1")
model %>% layer_dense(3, activation = "relu", name = "layer2")
model %>% layer_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 <- layer_dense(units = 3)
layer$weights  # Empty
list()

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$ones(shape(1, 4))
y <- layer(x)
layer$weights  # Now it has weights, of shape (4, 3) and (3,)
[[1]]
<tf.Variable 'dense_6/kernel:0' shape=(4, 3) dtype=float32, numpy=
array([[ 0.04102254,  0.4609574 ,  0.2932011 ],
       [-0.8724068 ,  0.4684844 ,  0.3217095 ],
       [-0.3895173 , -0.25451916, -0.8876987 ],
       [-0.22169489, -0.0800401 ,  0.8842974 ]], dtype=float32)>

[[2]]
<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_model_sequential() %>%
        layer_dense(2, activation = "relu") %>%
        layer_dense(3, activation = "relu") %>%
        layer_dense(4)

# No weights at this stage!
# At this point, you can't do this:

try(model$weights)
Error in py_get_attr_impl(x, name, silent) : 
  ValueError: Weights for model sequential_3 have not yet been created. Weights are created when the Model is first called on inputs or `build()` is called with an `input_shape`.
# The model summary is also not available:
summary(model)
Model: <no summary available, model was not built>
# Call the model on a test input
x <- tf$ones(shape(1, 4))
y <- model(x)
cat("Number of weights after calling the model:", length(model$weights), "\n")  # 6
Number of weights after calling the model: 6 

Once a model is “built”, you can call its summary() method to display its contents (the summary() method is also called by the default print() method:

summary(model)
Model: "sequential_3"
____________________________________________________________________________
 Layer (type)                     Output Shape                  Param #     
============================================================================
 dense_9 (Dense)                  (1, 2)                        10          
 dense_8 (Dense)                  (1, 3)                        9           
 dense_7 (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_shape argument to your model, so that it knows its input shape from the start:

model <- keras_model_sequential(input_shape = c(4))
model %>% layer_dense(2, activation = "relu")

model
Model: "sequential_4"
____________________________________________________________________________
 Layer (type)                     Output Shape                  Param #     
============================================================================
 dense_10 (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: %>% + summary()

When building a new Sequential architecture, it’s useful to incrementally stack layers and 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_model_sequential(input_shape = c(250, 250, 3)) # 250x250 RGB images

model %>%
  layer_conv_2d(32, 5, strides = 2, activation = "relu") %>%
  layer_conv_2d(32, 3, activation = "relu") %>%
  layer_max_pooling_2d(3)

# Can you guess what the current output shape is at this point? Probably not.
# Let's just print it:
model
Model: "sequential_5"
____________________________________________________________________________
 Layer (type)                     Output Shape                  Param #     
============================================================================
 conv2d_1 (Conv2D)                (None, 123, 123, 32)          2432        
 conv2d (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
____________________________________________________________________________
# The answer was: (40, 40, 32), so we can keep downsampling...
model %>%
  layer_conv_2d(32, 3, activation = "relu") %>%
  layer_conv_2d(32, 3, activation = "relu") %>%
  layer_max_pooling_2d(3) %>%
  layer_conv_2d(32, 3, activation = "relu") %>%
  layer_conv_2d(32, 3, activation = "relu") %>%
  layer_max_pooling_2d(2)

# And now?
model
Model: "sequential_5"
____________________________________________________________________________
 Layer (type)                     Output Shape                  Param #     
============================================================================
 conv2d_1 (Conv2D)                (None, 123, 123, 32)          2432        
 conv2d (Conv2D)                  (None, 121, 121, 32)          9248        
 max_pooling2d (MaxPooling2D)     (None, 40, 40, 32)            0           
 conv2d_5 (Conv2D)                (None, 38, 38, 32)            9248        
 conv2d_4 (Conv2D)                (None, 36, 36, 32)            9248        
 max_pooling2d_2 (MaxPooling2D)   (None, 12, 12, 32)            0           
 conv2d_3 (Conv2D)                (None, 10, 10, 32)            9248        
 conv2d_2 (Conv2D)                (None, 8, 8, 32)              9248        
 max_pooling2d_1 (MaxPooling2D)   (None, 4, 4, 32)              0           
============================================================================
Total params: 48,672
Trainable params: 48,672
Non-trainable params: 0
____________________________________________________________________________
# Now that we have 4x4 feature maps, time to apply global max pooling.
model %>% layer_global_max_pooling_2d()

# Finally, we add a classification layer.
model %>% layer_dense(10)

Very practical, right?

What to do once you have a model

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

Feature extraction with a Sequential model

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_model_sequential(input_shape = c(250, 250, 3)) %>%
  layer_conv_2d(32, 5, strides = 2, activation = "relu") %>%
  layer_conv_2d(32, 3, activation = "relu") %>%
  layer_conv_2d(32, 3, activation = "relu")

feature_extractor <- keras_model(
  inputs = initial_model$inputs,
  outputs = lapply(initial_model$layers, \(layer) layer$output)
)

# Call feature extractor on test input.

x <- tf$ones(shape(1, 250, 250, 3))
features <- feature_extractor(x)

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

initial_model <-
  keras_model_sequential(input_shape = c(250, 250, 3)) %>%
  layer_conv_2d(32, 5, strides = 2, activation = "relu") %>%
  layer_conv_2d(32, 3, activation = "relu", name = "my_intermediate_layer") %>%
  layer_conv_2d(32, 3, activation = "relu")

feature_extractor <- keras_model(
  inputs = initial_model$inputs,
  outputs =  get_layer(initial_model, name = "my_intermediate_layer")$output
)

# Call feature extractor on test input.
x <- tf$ones(shape(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_model_sequential(input_shape = c(784)) %>%
  layer_dense(32, activation = 'relu') %>%
  layer_dense(32, activation = 'relu') %>%
  layer_dense(32, activation = 'relu') %>%
  layer_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 head(model$layers, -1))
  layer$trainable <- FALSE

# can also just call: freeze_weights(model, to = -2)

# 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 <- application_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_model_sequential() %>%
  base_model() %>%
  layer_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:

Environment Details

tensorflow::tf_config()
TensorFlow v2.9.1 (~/.virtualenvs/r-tensorflow-site/lib/python3.9/site-packages/tensorflow)
Python v3.9 (~/.virtualenvs/r-tensorflow-site/bin/python)
sessionInfo()
R version 4.2.1 (2022-06-23)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Ubuntu 20.04.4 LTS

Matrix products: default
BLAS/LAPACK: /usr/lib/x86_64-linux-gnu/libmkl_rt.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] keras_2.9.0.9000      tensorflow_2.9.0.9000

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.9           knitr_1.39           whisker_0.4         
 [4] magrittr_2.0.3       here_1.0.1           lattice_0.20-45     
 [7] R6_2.5.1             rlang_1.0.4          fastmap_1.1.0       
[10] stringr_1.4.0        tools_4.2.1          grid_4.2.1          
[13] xfun_0.31            png_0.1-7            cli_3.3.0           
[16] htmltools_0.5.2      tfruns_1.5.0         rprojroot_2.0.3     
[19] yaml_2.3.5           digest_0.6.29        Matrix_1.4-1        
[22] base64enc_0.1-3      htmlwidgets_1.5.4    zeallot_0.1.0       
[25] evaluate_0.15        rmarkdown_2.14       stringi_1.7.8       
[28] compiler_4.2.1       generics_0.1.3       reticulate_1.25-9000
[31] jsonlite_1.8.0      
system2(reticulate::py_exe(), c("-m pip freeze"), stdout = TRUE) |> writeLines()
absl-py==1.1.0
asttokens==2.0.5
astunparse==1.6.3
backcall==0.2.0
beautifulsoup4==4.11.1
cachetools==5.2.0
certifi==2022.6.15
cffi==1.15.1
charset-normalizer==2.1.0
decorator==5.1.1
dill==0.3.5.1
etils==0.6.0
executing==0.8.3
filelock==3.7.1
flatbuffers==1.12
gast==0.4.0
gdown==4.5.1
google-auth==2.9.0
google-auth-oauthlib==0.4.6
google-pasta==0.2.0
googleapis-common-protos==1.56.4
grpcio==1.47.0
h5py==3.7.0
idna==3.3
importlib-metadata==4.12.0
importlib-resources==5.8.0
ipython==8.4.0
jedi==0.18.1
Jinja2==3.1.2
keras==2.9.0
Keras-Preprocessing==1.1.2
keras-tuner==1.1.2
kt-legacy==1.0.4
libclang==14.0.1
Markdown==3.3.7
MarkupSafe==2.1.1
matplotlib-inline==0.1.3
numpy==1.23.1
oauthlib==3.2.0
opt-einsum==3.3.0
packaging==21.3
pandas==1.4.3
parso==0.8.3
pexpect==4.8.0
pickleshare==0.7.5
Pillow==9.2.0
promise==2.3
prompt-toolkit==3.0.30
protobuf==3.19.4
ptyprocess==0.7.0
pure-eval==0.2.2
pyasn1==0.4.8
pyasn1-modules==0.2.8
pycparser==2.21
pydot==1.4.2
Pygments==2.12.0
pyparsing==3.0.9
PySocks==1.7.1
python-dateutil==2.8.2
pytz==2022.1
pytz-deprecation-shim==0.1.0.post0
PyYAML==6.0
requests==2.28.1
requests-oauthlib==1.3.1
rpy2==3.5.2
rsa==4.8
scipy==1.8.1
six==1.16.0
soupsieve==2.3.2.post1
stack-data==0.3.0
tensorboard==2.9.1
tensorboard-data-server==0.6.1
tensorboard-plugin-wit==1.8.1
tensorflow==2.9.1
tensorflow-datasets==4.6.0
tensorflow-estimator==2.9.0
tensorflow-hub==0.12.0
tensorflow-io-gcs-filesystem==0.26.0
tensorflow-metadata==1.9.0
termcolor==1.1.0
toml==0.10.2
tqdm==4.64.0
traitlets==5.3.0
typing_extensions==4.3.0
tzdata==2022.1
tzlocal==4.2
urllib3==1.26.10
wcwidth==0.2.5
Werkzeug==2.1.2
wrapt==1.14.1
zipp==3.8.1
TF Devices:
-  PhysicalDevice(name='/physical_device:CPU:0', device_type='CPU') 
-  PhysicalDevice(name='/physical_device:GPU:0', device_type='GPU') 
CPU cores: 12 
Date rendered: 2022-07-21 
Page render time: 5 seconds