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5 When a feature has a bell-shaped normal distribution (also called a Gaussian distribution), which is very com‐ mon, the "68-95-99.7" rule applies: about 68% of the values fall within 1σ of the mean, 95% within 2σ, and 99.7% within 3σ.
The actual coding is then sampled randomly from a Gaussian distribution with mean μ and standard devi‐ ation σ.
As you can see on the diagram, although the inputs may have a very convoluted dis‐ tribution, a variational autoencoder tends to produce codings that look as though they were sampled from a simple Gaussian distribution:6 during training, the cost function (discussed next) pushes the codings to gradually migrate within the coding space (also called the latent space) to occupy a roughly (hyper)spherical region that looks like a cloud of Gaussian points.
6 Variational autoencoders are actually more general; the codings are not limited to Gaussian distributions.
variational autoencoder, you can very easily generate a new instance: just sample a random coding from the Gaussian distribution, decode it, and voilà!
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