How to Use the Keras Functional API for Deep Learning

The Keras Python library makes creating deep learning models fast and easy.

The sequential API allows you to create models layer-by-layer for most problems. It is limited in that it does not allow you to create models that share layers or have multiple inputs or outputs.

The functional API in Keras is an alternate way of creating models that offers a lot more flexibility, including creating more complex models.

In this tutorial, you will discover how to use the more flexible functional API in Keras to define deep learning models.

After completing this tutorial, you will know:

  • The difference between the Sequential and Functional APIs.
  • How to define simple Multilayer Perceptron, Convolutional Neural Network, and Recurrent Neural Network models using the functional API.
  • How to define more complex models with shared layers and multiple inputs and outputs.

Let’s get started.

  • Update Nov/2017: Update note about hanging dimension for input layers only affecting 1D input, thanks Joe.

Tutorial Overview

This tutorial is divided into 6 parts; they are:

  1. Keras Sequential Models
  2. Keras Functional Models
  3. Standard Network Models
  4. Shared Layers Model
  5. Multiple Input and Output Models
  6. Best Practices

1. Keras Sequential Models

As a review, Keras provides a Sequential model API.

This is a way of creating deep learning models where an instance of the Sequential class is created and model layers are created and added to it.

For example, the layers can be defined and passed to the Sequential as an array:

Layers can also be added piecewise:

The Sequential model API is great for developing deep learning models in most situations, but it also has some limitations.

For example, it is not straightforward to define models that may have multiple different input sources, produce multiple output destinations or models that re-use layers.

2. Keras Functional Models

The Keras functional API provides a more flexible way for defining models.

It specifically allows you to define multiple input or output models as well as models that share layers. More than that, it allows you to define ad hoc acyclic network graphs.

Models are defined by creating instances of layers and connecting them directly to each other in pairs, then defining a Model that specifies the layers to act as the input and output to the model.

Let’s look at the three unique aspects of Keras functional API in turn:

1. Defining Input

Unlike the Sequential model, you must create and define a standalone Input layer that specifies the shape of input data.

The input layer takes a shape argument that is a tuple that indicates the dimensionality of the input data.

When input data is one-dimensional, such as for a multilayer Perceptron, the shape must explicitly leave room for the shape of the mini-batch size used when splitting the data when training the network. Therefore, the shape tuple is always defined with a hanging last dimension when the input is one-dimensional (2,), for example:

2. Connecting Layers

The layers in the model are connected pairwise.

This is done by specifying where the input comes from when defining each new layer. A bracket notation is used, such that after the layer is created, the layer from which the input to the current layer comes from is specified.

Let’s make this clear with a short example. We can create the input layer as above, then create a hidden layer as a Dense that receives input only from the input layer.

Note the (visible) after the creation of the Dense layer that connects the input layer output as the input to the dense hidden layer.

It is this way of connecting layers piece by piece that gives the functional API its flexibility. For example, you can see how easy it would be to start defining ad hoc graphs of layers.

3. Creating the Model

After creating all of your model layers and connecting them together, you must define the model.

As with the Sequential API, the model is the thing you can summarize, fit, evaluate, and use to make predictions.

Keras provides a Model class that you can use to create a model from your created layers. It requires that you only specify the input and output layers. For example:

Now that we know all of the key pieces of the Keras functional API, let’s work through defining a suite of different models and build up some practice with it.

Each example is executable and prints the structure and creates a diagram of the graph. I recommend doing this for your own models to make it clear what exactly you have defined.

My hope is that these examples provide templates for you when you want to define your own models using the functional API in the future.

3. Standard Network Models

When getting started with the functional API, it is a good idea to see how some standard neural network models are defined.

In this section, we will look at defining a simple multilayer Perceptron, convolutional neural network, and recurrent neural network.

These examples will provide a foundation for understanding the more elaborate examples later.

Multilayer Perceptron

In this section, we define a multilayer Perceptron model for binary classification.

The model has 10 inputs, 3 hidden layers with 10, 20, and 10 neurons, and an output layer with 1 output. Rectified linear activation functions are used in each hidden layer and a sigmoid activation function is used in the output layer, for binary classification.

Running the example prints the structure of the network.

A plot of the model graph is also created and saved to file.

Multilayer Perceptron Network Graph

Multilayer Perceptron Network Graph

Convolutional Neural Network

In this section, we will define a convolutional neural network for image classification.

The model receives black and white 64×64 images as input, then has a sequence of two convolutional and pooling layers as feature extractors, followed by a fully connected layer to interpret the features and an output layer with a sigmoid activation for two-class predictions.

Running the example summarizes the model layers.

A plot of the model graph is also created and saved to file.

Convolutional Neural Network Graph

Convolutional Neural Network Graph

Recurrent Neural Network

In this section, we will define a long short-term memory recurrent neural network for sequence classification.

The model expects 100 time steps of one feature as input. The model has a single LSTM hidden layer to extract features from the sequence, followed by a fully connected layer to interpret the LSTM output, followed by an output layer for making binary predictions.

Running the example summarizes the model layers.

A plot of the model graph is also created and saved to file.

Recurrent Neural Network Graph

Recurrent Neural Network Graph

4. Shared Layers Model

Multiple layers can share the output from one layer.

For example, there may be multiple different feature extraction layers from an input, or multiple layers used to interpret the output from a feature extraction layer.

Let’s look at both of these examples.

Shared Input Layer

In this section, we define multiple convolutional layers with differently sized kernels to interpret an image input.

The model takes black and white images with the size 64×64 pixels. There are two CNN feature extraction submodels that share this input; the first has a kernel size of 4 and the second a kernel size of 8. The outputs from these feature extraction submodels are flattened into vectors and concatenated into one long vector and passed on to a fully connected layer for interpretation before a final output layer makes a binary classification.

Running the example summarizes the model layers.

A plot of the model graph is also created and saved to file.

Neural Network Graph With Shared Inputs

Neural Network Graph With Shared Inputs

Shared Feature Extraction Layer

In this section, we will two parallel submodels to interpret the output of an LSTM feature extractor for sequence classification.

The input to the model is 100 time steps of 1 feature. An LSTM layer with 10 memory cells interprets this sequence. The first interpretation model is a shallow single fully connected layer, the second is a deep 3 layer model. The output of both interpretation models are concatenated into one long vector that is passed to the output layer used to make a binary prediction.

Running the example summarizes the model layers.

A plot of the model graph is also created and saved to file.

Neural Network Graph With Shared Feature Extraction Layer

Neural Network Graph With Shared Feature Extraction Layer

5. Multiple Input and Output Models

The functional API can also be used to develop more complex models with multiple inputs, possibly with different modalities. It can also be used to develop models that produce multiple outputs.

We will look at examples of each in this section.

Multiple Input Model

We will develop an image classification model that takes two versions of the image as input, each of a different size. Specifically a black and white 64×64 version and a color 32×32 version. Separate feature extraction CNN models operate on each, then the results from both models are concatenated for interpretation and ultimate prediction.

Note that in the creation of the Model() instance, that we define the two input layers as an array. Specifically:

The complete example is listed below.

Running the example summarizes the model layers.

A plot of the model graph is also created and saved to file.

Neural Network Graph With Multiple Inputs

Neural Network Graph With Multiple Inputs

Multiple Output Model

In this section, we will develop a model that makes two different types of predictions. Given an input sequence of 100 time steps of one feature, the model will both classify the sequence and output a new sequence with the same length.

An LSTM layer interprets the input sequence and returns the hidden state for each time step. The first output model creates a stacked LSTM, interprets the features, and makes a binary prediction. The second output model uses the same output layer to make a real-valued prediction for each input time step.

Running the example summarizes the model layers.

A plot of the model graph is also created and saved to file.

Neural Network Graph With Multiple Outputs

Neural Network Graph With Multiple Outputs

6. Best Practices

In this section, I want to give you some tips to get the most out of the functional API when you are defining your own models.

  • Consistent Variable Names. Use the same variable name for the input (visible) and output layers (output) and perhaps even the hidden layers (hidden1, hidden2). It will help to connect things together correctly.
  • Review Layer Summary. Always print the model summary and review the layer outputs to ensure that the model was connected together as you expected.
  • Review Graph Plots. Always create a plot of the model graph and review it to ensure that everything was put together as you intended.
  • Name the layers. You can assign names to layers that are used when reviewing summaries and plots of the model graph. For example: Dense(1, name=’hidden1′).
  • Separate Submodels. Consider separating out the development of submodels and combine the submodels together at the end.

Do you have your own best practice tips when using the functional API?
Let me know in the comments.

Further Reading

This section provides more resources on the topic if you are looking go deeper.

Summary

In this tutorial, you discovered how to use the functional API in Keras for defining simple and complex deep learning models.

Specifically, you learned:

  • The difference between the Sequential and Functional APIs.
  • How to define simple Multilayer Perceptron, Convolutional Neural Network, and Recurrent Neural Network models using the functional API.
  • How to define more complex models with shared layers and multiple inputs and outputs.

Do you have any questions?
Ask your questions in the comments below and I will do my best to answer.

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65 Responses to How to Use the Keras Functional API for Deep Learning

  1. Salameh October 27, 2017 at 5:36 am #

    Thank you
    I have been waiting fir this tutorial

  2. Thabet Ali October 27, 2017 at 7:21 am #

    You’re awesome Jason!

    I just can’t wait to see more from you on this wonderful blog, where did you hide all of this 😉
    Can you please write a book where you implement more of the functional API?
    I’m sure the book will be a real success

    Best regards
    Thabet

    • Tom October 27, 2017 at 12:18 pm #

      I agree with Thabet Ali, need a book on advance functional API part.

      • Jason Brownlee October 27, 2017 at 2:57 pm #

        What aspects of the functional API do you need more help with Tom?

    • Jason Brownlee October 27, 2017 at 2:54 pm #

      Thanks!

      What problems are you having with the functional API?

      • Thabet October 27, 2017 at 7:00 pm #

        I would like to know more on how to implement autoencoders on multi input time series signals with a single output categorical classification, using the functional API

      • Franco April 19, 2018 at 5:34 am #

        Hi Jason, are you asking for a wish list? 🙂
        – Autoencoders / Anomaly detection with Keras’s API

        Thanks!

    • Franco April 19, 2018 at 5:32 am #

      Yes, totally agree.

  3. Alexander October 27, 2017 at 6:50 pm #

    Jason, thank you for very interest blog. Beautiful article which can open new doors.

  4. Leon October 28, 2017 at 5:28 pm #

    Dr. Brownlee,
    How do you study mathematics behind so many algorithms that you implement?
    regards
    Leon

  5. Alex November 4, 2017 at 5:32 am #

    Can I consider the initial_state of an LSTM layer as an input branch of the architecture? Say that for each data I have a sequence s1, s2, s3 and a context feature X. I define an LSTM with 128 neurons, for each batch I want to map X to a 128 dimensional feature through a Dense(128) layer and set the initial_state for that batch training, meanwhile the sequence s1, s2,s3 is fed to the LSTM as the input sequence.

    • Jason Brownlee November 4, 2017 at 5:34 am #

      Sorry Alex, I’m not sure I follow. If you have some ideas, perhaps design an experiment to test them?

  6. Jithu R Jacob November 6, 2017 at 8:38 pm #

    Thank you for the awesome tutorial.

    For anyone wants to directly visualize in Jupyter Notebooks use the following lines.

    from IPython.display import SVG
    from keras.utils.vis_utils import model_to_dot

    SVG(model_to_dot(model).create(prog=’dot’, format=’svg’))

  7. Luis November 7, 2017 at 2:09 am #

    Thanks for this blog. It is really helpful and well explained.

    • Jason Brownlee November 7, 2017 at 9:51 am #

      Thanks Luis, I’m glad to hear that. I appreciate your support!

  8. Cal Almodovar November 11, 2017 at 8:52 am #

    Hi Jason – I am wondering if the code should be:

    visible = Input(image_file, shape=( height, width, color channels))

    if not, I wonder how the code references the image in question….

    Surprised no one else asked this…

    YOU ROCK JASON!

  9. joe November 25, 2017 at 5:32 am #

    In section 1 you write that “the shape tuple is always defined with a hanging last dimension”, but when you define the convolutional network, you define it as such:

    visible = Input(shape=(64,64,1))

    without any hanging last dimension. Am I missing something here?

    • Jason Brownlee November 25, 2017 at 10:23 am #

      Yes, I was incorrect. This is only the case for 1D input. I have updated the post, thanks.

  10. Franek December 1, 2017 at 9:14 pm #

    Jason, I’ve been reading about keras and AI for some time and I always find your articles more clear and straightforward than all the other stuff on the net 🙂
    Thanks!

  11. Franek December 1, 2017 at 9:17 pm #

    Jason, for some reasons I need to know the output tensors of the layers in my model. I’ve tried to experiment with the layer.get_output, get_output_et etc following the keras documentation, but I always fail to get anything sensible.

    I tried to look for this subject on your blog, but I couldn’t find anything. Are you planning to write a post on this? 🙂 That would really help!

  12. Nicola December 2, 2017 at 12:32 am #

    Hi Jason, yet another great post.
    Using one of your past posts I created an LSTM that, using multiple time series, predicts several step ahead of a specific time series. Currently I have this structure:

    where:
    – x_tr has (440, 7, 6) dimensions (440 samples, 7 past time steps, 6 variables/time series)
    – y_tr has (440, 21) dimensions, that is 440 samples and 21 ahead predicted values.

    Now, I’d like to extend my network so that it predicts the (multi-step ahead) values of two time series. I tried this code:

    where y1 and y2 both have (440, 21) dimensions, but I have this error:

    “Error when checking target: expected dense_4 to have 3 dimensions, but got array with shape (440, 21)”.

    How should I reshape y1 and y2 so that they fit with the network?

    • Jason Brownlee December 2, 2017 at 9:03 am #

      Sorry, I cannot debug your code for you, perhaps post to stack overflow?

  13. Davor December 22, 2017 at 3:12 am #

    Great tutorial, it really helped me understand Model API better! THANKS!

  14. Debarati Bhattacharjee January 5, 2018 at 2:27 am #

    Hii Jason, this was a great post, specially for beginners to learn the Functional API. Would you mind to write a post to explain the code for a image segmentation problem step by step for beginners?

  15. Harminder January 6, 2018 at 10:10 pm #

    Hi Jason, thank you for such a great post. It helped me a lot to understand functional API’s in keras.
    Could you please explain how we define the model.compile statement in multiple output case where each sub-model has a different objective function. For example, one output might be regression and the other classification as you mentioned in this post.

    • Jason Brownlee January 7, 2018 at 5:06 am #

      I believe you must have one objective function for the whole model.

  16. Harry Garrison January 23, 2018 at 7:57 pm #

    Splendid tutorial as always!

    Do you think you could make a tutorial about siamese neural nets in the future? It would be particularly interesting to see how a triplet loss model can be created in keras, one that recognizes faces, for example. The functional API must be the way to go, but I can’t imagine exactly how the layers should be connected.

  17. Akhtar Ali January 27, 2018 at 8:20 pm #

    Good tutorial
    Thanks alot

  18. Paul the Student February 2, 2018 at 2:49 am #

    Thank you very much for your tutorial! He helped me a lot!

    I have a question about cost functions. I have one request and several documents: 1 relevant and 4 irrelevant. I would like a cost function that both maximizes SCORE(Q, D+) and minimizes SCORE(Q, D-). So, I could have Delta = SUM{ Score(Q,D+) – Score(Q,Di-) } for i in (1..4)
    Using the Hinge Loss cost function, I have L = max(0, 4 – Delta)

    I wanted to know if taking the 4 documents, calculating their score with the NN and sending everything in the cost function is a good practice?

  19. Joseph February 15, 2018 at 3:42 am #

    I was wondering if was possible to have two separate layers as inputs to the output layer, without concatenating them in a new layer and then having the concatenated layer project to the output layer. If you can’t do this with Keras, could you suggest another library that allows you to do this? I am new to neural networks, so would prefer a library that is suitable for newbies.

    • Jason Brownlee February 15, 2018 at 8:50 am #

      There are a host of merge layers to choose from besides concat.

      Does that help?

  20. vinayakumar r February 16, 2018 at 12:16 am #

    I have two images, first image and its label is good, second images and its label is bad. I want to pass both images at a time to deep learning model for training. While testing I will have two images (unlabelled) and I want to detect which one is good and which one is bad. Could you please tell how to do it?

    • Jason Brownlee February 16, 2018 at 8:34 am #

      You will need a model with two inputs, one for each image.

  21. vinayakumar r February 24, 2018 at 5:57 pm #

    Any examples you have to give two inputs to a model

  22. John February 25, 2018 at 7:28 am #

    Thanks so much for the tutorial! It is much appreciated.

    Where I am confused is for a model with multiple inputs and multiple outputs. To make it simple, lets say we have two input layers, some shared layers, and two output layers. I was able to build this in Keras and get a model printout that looks as expected, but when I go to fit the model Keras complains: ValueError: All input arrays (x) should have the same number of samples

    Is it not possible to feed in inputs of different sizes?

    • Jason Brownlee February 25, 2018 at 7:47 am #

      Correct. Inputs must be padded to the same length.

  23. saira March 8, 2018 at 6:54 am #

    Hi,

    In the start of the post, you talked about hanging dimension to entertain the mini batch size. Could you kindly explain this a little.
    My feature Matrix is a numpy N-d Array, in one -hot -encoded form: (6000,200) , and my batch size = 150.

    Does this mean, I should give shape=(200,) ?

    • saira March 8, 2018 at 6:55 am #

      * batch size = 50.

      Thanks!

    • Jason Brownlee March 8, 2018 at 2:53 pm #

      Sorry, it means a numpy array where there is really only 1D of data with the second dimension not specified.

      For example:

      Results in:

      It’s 1D, but looks confusing to beginners.

      • saira March 8, 2018 at 5:09 pm #

        This means I should use shape(200,).

        Thanks a lot for the prompt reply !!!

  24. H Hua March 9, 2018 at 1:32 am #

    how to do a case with multi-input and multi-output cases

    • Jason Brownlee March 9, 2018 at 6:24 am #

      Simply combine some of the examples from this post.

  25. Kieu My March 9, 2018 at 5:18 am #

    Hi Jason,
    Thank you very much for your blog, it’s easy to understand via some examples, I recognize that learning from some example is one of the fast way to learn new things.
    In your post, I have a little confuse that in case multi input. If you have 1 image but you want get RGB 32x32x3 version and 64x64x1 gray-scale version for each Conv branch. How can the network know that. Because when we define the network we only said the input_shape, we don’t say which kind of image we want to led into the Conv in branch 1 or branch 2? In fit method we also have to said input and output, not give the detail. And if I want in the gray-scale version is: 32x32x3 (3 because I want to channel-wise, triple gray-scale version). And how can the network recognize the first branch is for gray-scale. Sorry for my question if is there any easy thing I don’t know. Thanks again for your post. I always follow your post.

    • Jason Brownlee March 9, 2018 at 6:28 am #

      You could run all images through one input and pad the smaller image to the dimensions of the larger image. Or you can use a multiple input model and define two separate input shapes.

  26. saira March 9, 2018 at 5:32 pm #

    Hi,

    When I run this functional API in model for k fold cross validation, the numbers in the naming the dense layer is increasing in the return fitted model of each fold.
    Like in first fold it’s “dense_2_acc”, then in 2nd fold its “dense_5_acc”.

    By my model summary shows my model is correct. Could you kindly tell why is it changing the names in the fitted model “history” object of each fold?

    regards,

  27. Jane March 16, 2018 at 4:33 pm #

    This was a fantastic and concise beginner tutorial for building neural networks with Keras. Great job !

  28. HARISANKAR HARIDAS March 19, 2018 at 10:44 pm #

    Thanks for the tutorial.

    “When input data is one-dimensional, such as for a multilayer Perceptron, the shape must explicitly leave room for the shape of the mini-batch size used when splitting the data when training the network.

    Therefore, the shape tuple is always defined with a hanging last dimension when the input is one-dimensional (2,)


    visible = Input(shape=(2,))

    I was a bit confused at first after reading these 2 sentences.

    regarding trailing comma: A trailing comma is always required when we have a tuple with a single element. Otherwise (2) returns only the value 2, not a tuple with the value 2. https://docs.python.org/3/reference/expressions.html#expression-lists

    As the shape parameter for Input should be a tuple ( https://keras.io/layers/core/#input ), we do not have any option other than to add a comma when we have a single element to be passed.

    So, I’m not able to get the meaning implied in “the shape must explicitly leave room for the shape of the mini-batch size … Therefore, the shape tuple is always defined with a hanging last dimension”

  29. Jeremy March 27, 2018 at 2:50 am #

    Hi Jason,

    Thanks so much for such a great post.

    So, in your case in shared input layers section, you have the same CNN models for feature extraction, and the output can be concated since both features produced binary classification result.

    But what if we have separate categorical classification model (for sequence classification) and regression model (for time series) which relies on the same input data. So is it possible to concate categorical classification model (which produces more than two classes) with a regression model, and the final result after model concatenation is binary classification?

    Your opinion, in this case, is much appreciated.

    Thank you.

    • Jason Brownlee March 27, 2018 at 6:39 am #

      Not sure I follow. Perhaps try it and as many variations as you can think of, and see.

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