Advanced Deep Learning with Keras

Variational Autoencoders (VAEs)
Figure 8.1.6 shows the continuous space of latent vector after 50 epochs using plot_
results(). For simplicity, the function is not shown here but can be found in the
rest of the code of vae-mlp-mnist-8.1.1.py. The function plots two images, the
test dataset labels (Figure 8.1.6) and the sample generated digits (Figure 8.1.7) both
as a function of z. Both plots demonstrate how the latent vector determines the
attributes of the generated digits.
Navigating through the continuous space will always result in an output that bears
a resemblance to the MNIST digits. For example, the region of digit 9 is close to
the region of digit 7. Moving from 9 near the center to the left morphs the digit
to 7. Moving from the center downward changes the generated digits from 3 to 8
and finally to 1. The morphing of the digits is more evident in Figure 8.1.7 which
is another way of interpreting Figure 8.1.6.
In Figure 8.1.7, instead of colorbar, the generator output is displayed. The
distribution of digits in the latent space is shown. It can be observed that all the
digits are represented. Since the distribution is dense near the center, the change is
rapid in the middle and slow as the mean values get bigger. We need to remember
that Figure 8.1.7 is a reflection of Figure 8.1.6. For example, digit 0 is on the top right
quadrant on both figures while digit 1 is on the lower right quadrant.
There are some unrecognizable digits in Figure 8.1.7, especially on the top left
quadrant. From the following figure, it can be observed that this region is mostly
empty and far away from the center:
Figure 8.1.6: The latent vector mean values for the test dataset (VAE MLP). The colorbar shows the
corresponding MNIST digit as a function of z. Color images can be found on the book GitHub repository:
https://github.com/PacktPublishing/Advanced-Deep-Learning-with-Keras/tree/master/chapter8-vae.
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