Variational autoencoder

As explained in Deep Learning with R, Third Edition

A variational autoencoder is a probabilistic autoencoder whose encoder represents inputs as parameters of a latent probability distribution and whose decoder reconstructs or generates data from sampled latent points.

A variational autoencoder (VAE) learns to reconstruct images while shaping a latent space from which new images can be generated. Unlike a classical autoencoder, which encodes an image as a vector, its encoder produces two vectors describing a probability distribution. A point sampled from that distribution goes to the decoder, which produces an image. section 17.1.2 section 17.1.3

Figure 17.4 A VAE maps an image to two vectors, z_mean and z_log_var, which define a probability distribution over the latent space, used to sample a latent point to decode.

Follow the image through the encoder’s mean and log-variance outputs, the sampled latent point, and the decoder. section 17.1.2

Generate handwritten digits

A Keras VAE for MNIST uses 28 × 28 digit images and a two-dimensional latent space. Its convolutional encoder outputs z_mean and z_log_var. A sampling layer draws random noise and computes z_mean + exp(0.5 × z_log_var) × noise; the decoder turns the resulting point into a 28 × 28 image. After training on normalized digits, pass a grid of two-dimensional points to the decoder to see how the generated digits vary across the space. section 17.1.3

The implementation has three practical parts:

• Encode with strided convolutions and produce separate mean and log-variance vectors. Strides preserve the location information needed to reconstruct an image. section 17.1.3
• Sample a latent point using the mean, log variance, and random noise. section 17.1.3
• Decode by reshaping the latent point and using convolutional layers to recover the input image dimensions. A custom compute_loss() handles training with the input image as the reconstruction target. section 17.1.3

The resulting continuous, structured latent space is useful for image editing and smooth transitions between images. VAEs also support reconstruction, but diffusion models are the stronger choice here for high-fidelity image generation. section 17.1.2 section 17.4

How Deep Learning with R, Third Edition covers it

How deep it goes

Works through an encoder, sampling layer, decoder, custom loss, training, and visualization, without a formal probabilistic derivation.

Examples

Builds a Keras VAE for MNIST digits and displays images decoded from a two-dimensional latent grid.

What it assumes

Assumes familiarity with convolutional networks and Keras workflows while introducing the autoencoder and its self-supervised training setup.

What you can do after

Build it from scratch in R/Keras to reconstruct MNIST digits and generate images by decoding latent points.

How it connects

Connects VAEs to autoencoders, latent spaces, self-supervised learning, Bayesian inference, and diffusion models.

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Related concepts

• encoderhas part · An encoder is a component that transforms input data into an encoded representation for subsequent processing, reconstruction, comparison, or transmission.
• autoencoderkind of · An autoencoder is a neural network that encodes input data into an internal representation and decodes it to reconstruct the input or an approximation.
• decodehas part · Decoding is the process of transforming an encoded or internal representation into an interpretable or target-form output.
• generationkind of · Generation is the computational production of outputs from supplied inputs or context, often by applying a model to produce predictions or new content.
• reconstruction lossuses · Reconstruction loss is a measure of the discrepancy between an input or observation and the output a model reconstructs from it or its representation.
• image generationuses · Image generation is the computational creation of new images from learned models, input data, or specified conditions.

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