How to Explore the GAN Latent Space When Generating Faces

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How to Use Interpolation and Vector Arithmetic to Explore the GAN Latent Space.

Generative Adversarial Networks, or GANs, are an architecture for training generative models, such as deep convolutional neural networks for generating images.

The generative model in the GAN architecture learns to map points in the latent space to generated images. The latent space has no meaning other than the meaning applied to it via the generative model. Yet, the latent space has structure that can be explored, such as by interpolating between points and performing vector arithmetic between points in latent space which have meaningful and targeted effects on the generated images.

In this tutorial, you will discover how to develop a generative adversarial network for face generation and explore the structure of latent space and the effect on generated faces.

After completing this tutorial, you will know:

  • How to develop a generative adversarial network for generating faces.
  • How to interpolate between points in latent space and generate images that morph from one face to another.
  • How to perform vector arithmetic in latent space and achieve targeted results in the resulting generated faces.

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  • Update Nov/2019: Updated for TensorFlow v2.0 and MTCNN v0.1.0.
How to Interpolate and Perform Vector Arithmetic With Faces Using a Generative Adversarial Network

How to Interpolate and Perform Vector Arithmetic With Faces Using a Generative Adversarial Network.
Photo by Intermountain Forest Service, some rights reserved.

Tutorial Overview

This tutorial is divided into five parts; they are:

  1. Vector Arithmetic in Latent Space
  2. Large-Scale CelebFaces Dataset (CelebA)
  3. How to Prepare CelebA Faces Dataset
  4. How to Develop a Generative Adversarial Network
  5. How to Explore the Latent Space for Generated Faces

Vector Arithmetic in Latent Space

The generator model in the GAN architecture takes a point from the latent space as input and generates a new image.

The latent space itself has no meaning. Typically it is a 100-dimensional hypersphere with each variable drawn from a Gaussian distribution with a mean of zero and a standard deviation of one. Through training, the generator learns to map points into the latent space with specific output images and this mapping will be different each time the model is trained.

The latent space has structure when interpreted by the generator model, and this structure can be queried and navigated for a given model.

Typically, new images are generated using random points in the latent space. Taken a step further, points in the latent space can be constructed (e.g. all 0s, all 0.5s, or all 1s) and used as input or a query to generate a specific image.

A series of points can be created on a linear path between two points in the latent space, such as two generated images. These points can be used to generate a series of images that show a transition between the two generated images.

Finally, the points in the latent space can be kept and used in simple vector arithmetic to create new points in the latent space that, in turn, can be used to generate images. This is an interesting idea, as it allows for the intuitive and targeted generation of images.

The important 2015 paper by Alec Radford, et al. titled “Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks” introduced a stable model configuration for training deep convolutional neural network models as part of the GAN architecture.

In the paper, the authors explored the latent space for GANs fit on a number of different training datasets, most notably a dataset of celebrity faces. They demonstrated two interesting aspects.

The first was the vector arithmetic with faces. For example, a face of a smiling woman minus the face of a neutral woman plus the face of a neutral man resulted in the face of a smiling man.

Specifically, the arithmetic was performed on the points in the latent space for the resulting faces. Actually on the average of multiple faces with a given characteristic, to provide a more robust result.

Example of Vector Arithmetic on Points in the Latent Space for Generating Faces with a GAN

Example of Vector Arithmetic on Points in the Latent Space for Generating Faces With a GAN.
Taken from Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks.

The second demonstration was the transition between two generated faces, specifically by creating a linear path through the latent dimension between the points that generated two faces and then generating all of the faces for the points along the path.

Example of Faces on a Path Between Two GAN Generated Faces

Example of Faces on a Path Between Two GAN Generated Faces.
Taken from Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks.

Exploring the structure of the latent space for a GAN model is both interesting for the problem domain and helps to develop an intuition for what has been learned by the generator model.

In this tutorial, we will develop a GAN for generating photos of faces, then explore the latent space for the model with vector arithmetic.

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Large-Scale CelebFaces Dataset (CelebA)

The first step is to select a dataset of faces.

In this tutorial, we will use the Large-scale CelebFaces Attributes Dataset, referred to as CelebA. This dataset was developed and published by Ziwei Liu, et al. for their 2015 paper titled “From Facial Parts Responses to Face Detection: A Deep Learning Approach.”

The dataset provides about 200,000 photographs of celebrity faces along with annotations for what appears in given photos, such as glasses, face shape, hats, hair type, etc. As part of the dataset, the authors provide a version of each photo centered on the face and cropped to the portrait with varying sizes around 150 pixels wide and 200 pixels tall. We will use this as the basis for developing our GAN model.

The dataset can be easily downloaded from the Kaggle webpage. Note: this may require an account with Kaggle.

Specifically, download the file “img_align_celeba.zip” which is about 1.3 gigabytes. To do this, click on the filename on the Kaggle website and then click the download icon.

The download might take a while depending on the speed of your internet connection.

After downloading, unzip the archive.

This will create a new directory named “img_align_celeba” that contains all of the images with filenames like 202599.jpg and 202598.jpg.

Next, we can look at preparing the raw images for modeling.

How to Prepare CelebA Faces Dataset

The first step is to develop code to load the images.

We can use the Pillow library to load a given image file, convert it to RGB format (if needed) and return an array of pixel data. The load_image() function below implements this.

Next, we can enumerate the directory of images, load each as an array of pixels in turn, and return an array with all of the images.

There are 200K images in the dataset, which is probably more than we need so we can also limit the number of images to load with an argument. The load_faces() function below implements this.

Finally, once the images are loaded, we can plot them using the imshow() function from the matplotlib library.

The plot_faces() function below does this, plotting images arranged into in a square.

Tying this together, the complete example is listed below.

Running the example loads a total of 25 images from the directory, then summarizes the size of the returned array.

Finally, the 25 images are plotted in a 5×5 square.

Plot of a Sample of 25 Faces from the Celebrity Faces Dataset

Plot of a Sample of 25 Faces from the Celebrity Faces Dataset

When working with a GAN, it is easier to model a dataset if all of the images are small and square in shape.

Further, as we are only interested in the face in each photo, and not the background, we can perform face detection and extract only the face before resizing the result to a fixed size.

There are many ways to perform face detection. In this case, we will use a pre-trained Multi-Task Cascaded Convolutional Neural Network, or MTCNN. This is a state-of-the-art deep learning model for face detection, described in the 2016 paper titled “Joint Face Detection and Alignment Using Multitask Cascaded Convolutional Networks.”

We will use the implementation provided by Iván de Paz Centeno in the ipazc/mtcnn project. This library can be installed via pip as follows:

We can confirm that the library was installed correctly by importing the library and printing the version; for example:

Running the example prints the current version of the library.

The MTCNN model is very easy to use.

First, an instance of the MTCNN model is created, then the detect_faces() function can be called passing in the pixel data for one image. The result is a list of detected faces, with a bounding box defined in pixel offset values.

We can update our example to extract the face from each loaded photo and resize the extracted face pixels to a fixed size. In this case, we will use the square shape of 80×80 pixels.

The extract_face() function below implements this, taking the MTCNN model and pixel values for a single photograph as arguments and returning an 80x80x3 array of pixel values with just the face, or None if no face was detected (which can happen rarely).

We can now update the load_faces() function to extract the face from the loaded photo and store that in the list of faces returned.

Tying this together, the complete example is listed below.

In this case, we increase the total number of loaded faces to 50,000 to provide a good training dataset for our GAN model.

Running the example may take a few minutes given the larger number of faces to be loaded.

At the end of the run, the array of extracted and resized faces is saved as a compressed NumPy array with the filename ‘img_align_celeba.npz‘.

The prepared dataset can then be loaded any time, as follows.

Loading the dataset summarizes the shape of the array, showing 50K images with the size of 80×80 pixels and three color channels.

We are now ready to develop a GAN model to generate faces using this dataset.

How to Develop a Generative Adversarial Network

In this section, we will develop a GAN for the faces dataset that we have prepared.

The first step is to define the models.

The discriminator model takes as input one 80×80 color image an outputs a binary prediction as to whether the image is real (class=1) or fake (class=0). It is implemented as a modest convolutional neural network using best practices for GAN design such as using the LeakyReLU activation function with a slope of 0.2, using a 2×2 stride to downsample, and the adam version of stochastic gradient descent with a learning rate of 0.0002 and a momentum of 0.5

The define_discriminator() function below implements this, defining and compiling the discriminator model and returning it. The input shape of the image is parameterized as a default function argument in case you want to re-use the function for your own image data later.

The generator model takes as input a point in the latent space and outputs a single 80×80 color image.

This is achieved by using a fully connected layer to interpret the point in the latent space and provide sufficient activations that can be reshaped into many copies (in this case 128) of a low-resolution version of the output image (e.g. 5×5). This is then upsampled four times, doubling the size and quadrupling the area of the activations each time using transpose convolutional layers. The model uses best practices such as the LeakyReLU activation, a kernel size that is a factor of the stride size, and a hyperbolic tangent (tanh) activation function in the output layer.

The define_generator() function below defines the generator model but intentionally does not compile it as it is not trained directly, then returns the model. The size of the latent space is parameterized as a function argument.

Next, a GAN model can be defined that combines both the generator model and the discriminator model into one larger model. This larger model will be used to train the model weights in the generator, using the output and error calculated by the discriminator model. The discriminator model is trained separately, and as such, the model weights are marked as not trainable in this larger GAN model to ensure that only the weights of the generator model are updated. This change to the trainability of the discriminator weights only has an effect when training the combined GAN model, not when training the discriminator standalone.

This larger GAN model takes as input a point in the latent space, uses the generator model to generate an image, which is fed as input to the discriminator model, then output or classified as real or fake.

The define_gan() function below implements this, taking the already-defined generator and discriminator models as input.

Now that we have defined the GAN model, we need to train it. But, before we can train the model, we require input data.

The first step is to load and scale the pre-processed faces dataset. The saved NumPy array can be loaded, as we did in the previous section, then the pixel values must be scaled to the range [-1,1] to match the output of the generator model.

The load_real_samples() function below implements this, returning the loaded and scaled image data ready for modeling.

We will require one batch (or a half) batch of real images from the dataset each update to the GAN model. A simple way to achieve this is to select a random sample of images from the dataset each time.

The generate_real_samples() function below implements this, taking the prepared dataset as an argument, selecting and returning a random sample of face images and their corresponding class label for the discriminator, specifically class=1, indicating that they are real images.

Next, we need inputs for the generator model. These are random points from the latent space, specifically Gaussian distributed random variables.

The generate_latent_points() function implements this, taking the size of the latent space as an argument and the number of points required and returning them as a batch of input samples for the generator model.

Next, we need to use the points in the latent space as input to the generator in order to generate new images.

The generate_fake_samples() function below implements this, taking the generator model and size of the latent space as arguments, then generating points in the latent space and using them as input to the generator model. The function returns the generated images and their corresponding class label for the discriminator model, specifically class=0 to indicate they are fake or generated.

We are now ready to fit the GAN models.

The model is fit for 100 training epochs, which is arbitrary, as the model begins generating plausible faces after perhaps the first few epochs. A batch size of 128 samples is used, and each training epoch involves 50,000/128 or about 390 batches of real and fake samples and updates to the model.

First, the discriminator model is updated for a half batch of real samples, then a half batch of fake samples, together forming one batch of weight updates. The generator is then updated via the combined GAN model. Importantly, the class label is set to 1 or real for the fake samples. This has the effect of updating the generator toward getting better at generating real samples on the next batch.

The train() function below implements this, taking the defined models, dataset, and size of the latent dimension as arguments and parameterizing the number of epochs and batch size with default arguments.

You will note that every 10 training epochs, the summarize_performance() function is called.

There is currently no reliable way to automatically evaluate the quality of generated images. Therefore, we must generate images periodically during training and save the model at these times. This both provides a check-point that we can later load and use to generate images, and a way to safeguard against the training process failing, which can happen.

Below defines the summarize_performance() and save_plot() functions.

The summarize_performance() function generates samples and evaluates the performance of the discriminator on real and fake samples. The classification accuracy is reported and might provide insight into model performance. The save_plot() is called to create and save a plot of the generated images, and then the model is saved to a file.

We can then define the size of the latent space, define all three models, and train them on the loaded face dataset.

Tying all of this together, the complete example is listed below.

Running the example may take a long time on modest hardware.

I recommend running the example on GPU hardware. If you need help, you can get started quickly by using an AWS EC2 instance to train the model. See the tutorial:

The loss for the discriminator on real and fake samples, as well as the loss for the generator, is reported after each batch.

Your specific results will vary given the stochastic nature of the learning algorithm.

The discriminator loss may crash down to values of 0.0 for real and generated samples.

If this happens, it is an example of a training failure from which the model is likely to not recover and you should restart the training process.

Review the generated plots and select a model based on the best quality images.

The model should begin to generate faces after about 30 training epochs.

The faces are not completely clear, but it is obvious that they are faces, with all the right things (hair, eyes, nose, mouth) in roughly the right places.

Example of Celebrity Faces Generated by a Generative Adversarial Network

Example of Celebrity Faces Generated by a Generative Adversarial Network

How to Explore the Latent Space for Generated Faces

In this section, we will use our trained GAN model as the basis for exploring the latent space.

How to Load Model and Generate Faces

The first step is to load the saved model and confirm that it can generate plausible faces.

The model can be loaded using the load_model() function in the Keras API. We can then generate a number of random points in the latent space and use them as input to the loaded model to generate new faces. The faces can then be plotted.

The complete example is listed below.

Running the example first loads the saved model.

Then, 25 random points in the 100-dimensional latent space are created, provided to the generator model to create 25 images of faces, which are then plotted in a 5×5 grid.

Plot of Randomly Generated Faces Using the Loaded GAN Model

Plot of Randomly Generated Faces Using the Loaded GAN Model

How to Interpolate Between Generated Faces

Next, we can create an interpolation path between two points in the latent space and generate faces along this path.

The simplest interpolation we can use is a linear or uniform interpolation between two points in the latent space. We can achieve this using the linspace() NumPy function to calculate ratios of the contribution from two points, then enumerate these ratios and construct a vector for each ratio.

The interpolate_points() function below implements this and returns a series of linearly interpolated vectors between two points in latent space, including the first and last point.

We can then generate two points in the latent space, perform the interpolation, then generate an image for each interpolated vector.

The result will be a series of images that transition between the two original images. The example below demonstrates this for two faces.

Running the example calculates the interpolation path between the two points in latent space, generates images for each, and plots the result.

You can see the clear linear progression in ten steps from the first face on the left to the final face on the right.

Plot Showing the Linear Interpolation Between Two GAN Generated Faces

Plot Showing the Linear Interpolation Between Two GAN Generated Faces

We can update the example to repeat this process multiple times so we can see the transition between multiple generated faces on a single plot.

The complete example is listed below.

Running the example creates 10 different face starting points and 10 matching face endpoints, and the linear interpolation between each.

Plot Showing Multiple Linear Interpolations Between Two GAN Generated Faces

Plot Showing Multiple Linear Interpolations Between Two GAN Generated Faces

In these cases, we have performed a linear interpolation which assumes that the latent space is uniformly distributed hypercube. Technically, our chosen latent space is a 100-dimension hypersphere or multimodal Gaussian distribution.

There is a mathematical function called the spherical linear interpolation function, or ‘Slerp,’ that should be used when interpolating this space to ensure the curving of the space is taken into account. For more details, I recommend reading the Issue on Linear Interpolation in Soumith Chintala’s dcgan.torch project. In that project, an implementation of the Slerp function for Python is provided that we can use as the basis for our own Slerp function, provided below:

This function can be called from our interpolate_points() function instead of performing the manual linear interpolation.

The complete example with this change is listed below.

The result is 10 more transitions between generated faces, this time using the correct Slerp interpolation method.

The difference is subtle but somehow visually more correct.

Plot Showing Multiple Seraphically Linear Interpolation Between Two GAN Generated Faces

Plot Showing Multiple Seraphically Linear Interpolation Between Two GAN Generated Faces

How to Perform Vector Arithmetic With Faces

Finally, we can explore the latent space by performing vector arithmetic with the generated faces

First, we must generate a large number of faces and save both the faces and their corresponding latent vectors. We can then review the plot of generated faces and select faces with features we’re interested in, note their index (number), and retrieve their latent space vectors for manipulation.

The example below will load the GAN model and use it to generate 100 random faces.

Running the example loads the model, generates faces, and saves the latent vectors and generated faces.

The latent vectors are saved to a compressed NumPy array with the filename ‘latent_points.npz‘. The 100 generated faces are plotted in a 10×10 grid and saved in a file named ‘generated_faces.png‘.

In this case, we have a good collection of faces to work with. Each face has an index that we can use to retrieve the latent vector. For example, the first face is 1, which corresponds to the first vector in the saved array (index 0).

We will perform the operation:

Therefore, we need three faces for each of smiling woman, neutral woman, and neutral man.

In this case, we will use the following indexes in the image:

  • Smiling Woman: 92, 98, 99
  • Neutral Woman: 9, 21, 79
  • Neutral Man: 10, 30, 45
Plot of 100 Generated Faces Used as the Basis for Vector Arithmetic with Faces

Plot of 100 Generated Faces Used as the Basis for Vector Arithmetic with Faces

Now that we have latent vectors to work with and a target arithmetic, we can get started.

First, we can specify our preferred images and load the saved NumPy array of latent points.

Next, we can retrieve each vector and calculate the average for each vector type (e.g. smiling woman). We could perform vector arithmetic with single images directly, but we will get a more robust result if we work with an average of a few faces with the desired property.

The average_points() function below takes the loaded array of latent space points, retrieves each, calculates the average, and returns all of the vectors.

We can now use this function to retrieve all of the required points in latent space and generate images.

Finally, we can use the average vectors to perform vector arithmetic in latent space and plot the result.

Tying this together, the complete example is listed below.

Running the example first loads the points in latent space for our specific images, calculates the average of the points, and generates the faces for the points.

We can see that, indeed, our selected faces were retrieved correctly and that the average of the points in the vector space captures the salient feature we are going for on each line (e.g. smiling woman, neutral woman, etc.).

Plot of Selected Generated Faces and the Average Generated Face for Each Row

Plot of Selected Generated Faces and the Average Generated Face for Each Row

Next, vector arithmetic is performed and the result is a smiling man, as we would expect.

Plot of the Resulting Generated Face Based on Vector Arithmetic in Latent Space

Plot of the Resulting Generated Face Based on Vector Arithmetic in Latent Space

Extensions

This section lists some ideas for extending the tutorial that you may wish to explore.

  • Additional Arithmetic. Try arithmetic with different image features or different arithmetic and review the results of the generated faces.
  • Additional Interpolation. Try interpolating between three or more points in latent space and review the results of the generated faces.
  • Tune Model. Update the GAN model configuration so that training is more stable and better quality faces can be generated.

If you explore any of these extensions, I’d love to know.
Post your findings in the comments below.

Further Reading

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

Books

Papers

API

Articles

Summary

In this tutorial, you discovered how to develop a generative adversarial network for face generation and explore the structure of latent space and the effect on generated faces.

Specifically, you learned:

  • How to develop a generative adversarial network for generating faces.
  • How to interpolate between points in latent space and generate images that morph from one face to another.
  • How to perform vector arithmetic in latent space and achieve targeted results in the resulting generated faces.

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

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16 Responses to How to Explore the GAN Latent Space When Generating Faces

  1. Mankaran Singh July 5, 2019 at 5:15 pm #

    Excellently detailed post ! Eagerly waiting for your book on GANs.

    • Jason Brownlee July 6, 2019 at 8:26 am #

      Thanks!

      Yes, this was a really fun tutorial to write 🙂

      The new book should be ready in a week or two. I’m really excited about it.

  2. Minel July 19, 2019 at 1:55 am #

    Hello Jason

    I met some troubles using MTCNN after doing a pip install . I got the message “no module named cv2”
    I had to install it by typing :
    python -m pip install opencv-python
    best

  3. Shubhesh August 1, 2019 at 12:28 am #

    I am getting this value
    Loaded: (50000, 218, 178, 3)
    what might be the problem?

    • Jason Brownlee August 1, 2019 at 6:53 am #

      Is it possible that you skipped a step?

      • Shubhesh August 2, 2019 at 5:40 am #

        Yes, it was silly mistake in one of the function. It’s fine now. Thanks.

  4. Ryan August 11, 2019 at 12:48 am #

    Thank you for this amazing tutorial , I wonder how to do the same with Cycle Gans while generating faces , i.e creating angry face , smiling face, …

    • Jason Brownlee August 11, 2019 at 6:00 am #

      It may not make sense with a cyclegan as it for image translation, not generating new images, like faces.

  5. D. Uys August 15, 2019 at 2:04 am #

    Thank you for this.
    I have such a hard time wrapping my mind around what latent space is? I have gone through a few of your GAN tutorials as well as other tutorials. I feel that I have a good empirical understanding of what latent space is, and why it is used, but I have no idea how one decides on the shape. Why is it that in DCGAN the latent space is a 100D vector? WHy not 50D or 20D or 1000D?

    This also stems from another tutorial you have where you use a GAN network for simple 1D function modeling, there you use a 5D latent space. I also read in some of the comments in your other article, that you said it becomes arbitrary to choose a different latent space shape? I hope I am asking the right question here.

    If you could please give an ELI5 version, I would greatly appreciate it! Thanks

    • Jason Brownlee August 15, 2019 at 8:24 am #

      The size/shape is arbitrary. Larger may give more freedom, too large or too small may lead to an unstable model.

      It is not a real thing, instead the model learns to apply meaning to it – to draw inspiration if you will, but in a consistent way so that it is ordered and different parts of the space map to different specific outputs – although it is a different structure/mapping each time the model is trained.

      It is a crazy thing to understand. You’re not alone 🙂

      I think I gave a good intro to “latent space” in this post:
      https://machinelearningmastery.com/what-are-generative-adversarial-networks-gans/

  6. Jun October 4, 2019 at 3:58 am #

    Hello, I am quite a new to this field and your articles are being really helpful.
    However, since it is difficult to understand fully, May I ask a few specific questions?

    First, I know train on batch function makes gan_model to improve its performance.
    But, I do not get that why generating latent_points always use randn function to make random noise.
    I am guessing that value of noise is not important because the gan model generates image are making better images as training process keeps going on even though the noise is always random.
    Is that right..?

    Second, Can you briefly tell me what is ‘arr_0’ in every process of loading npz files such as points = data[‘arr_0′]?

    Third, vector arithmetic parts comes real hard to me and cannot figure out what is going on in this part.
    ”’
    # average vectors
    smiling_woman = average_points(points, smiling_woman_ix)
    neutral_woman = average_points(points, neutral_woman_ix)
    neutral_man = average_points(points, neutral_man_ix)
    # combine all vectors
    all_vectors = vstack((smiling_woman, neutral_woman, neutral_man))

    # smiling woman – neutral woman + neutral man = smiling man
    result_vector = smiling_woman[-1] – neutral_woman[-1] + neutral_man[-1]
    ”’
    Could you please tell us a little more details? I understand ‘average_points’ are making averages between vectors of dif images but cannot understand the inner part of average_point function and why the last element of vectors make the result_vector.

    Thank you always for your articles.

  7. Dant. October 5, 2019 at 6:26 pm #

    Why isn’t it classified as DCGAN even though it contains CNN in both discriminator and generator model?

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