Variational autoencoder

As explained in Deep Learning with Python, Third Edition

A generative latent-variable model that learns an encoder-decoder structure and a probabilistic latent space for reconstructing and sampling data.

A variational autoencoder (VAE) learns a latent space from which new images can be sampled. It also reconstructs inputs: an encoder maps an image into the latent space, and a decoder maps a latent point back to an image. Unlike a classical autoencoder, a VAE is designed to make that space continuous and structured, which is useful for image editing and interpolation. section 17.1.2 section 17.4

A two-dimensional space of handwritten digits

For MNIST, an encoder maps each 28 × 28 digit to two vectors, z_mean and z_log_var. A sampling layer uses them to choose a latent point; a decoder turns that point into a reconstructed digit. After training, decoding a grid of points across the two-dimensional space produces a grid of digits. section 17.1.3

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

The diagram shows the crucial difference from a plain autoencoder: the encoder supplies parameters of a distribution, rather than one fixed code, before the decoder receives a sampled point. section 17.1.2

A practical Keras implementation has three parts:

• Encode images with a convolutional network that outputs z_mean and z_log_var. Strided convolutions preserve the location information needed for reconstruction. section 17.1.3
• Sample with a random epsilon using z_mean + exp(0.5 × z_log_var) × epsilon. section 17.1.3
• Decode the sampled vector into an image, and use custom training logic that tracks reconstruction and KL losses. Inputs themselves provide the reconstruction targets. section 17.1.3 section 17.1.2

Choose a VAE when reconstruction or control over a continuous latent space matters. For high-fidelity image generation, diffusion models are the stronger choice. section 17.1.2 section 17.4

How Deep Learning with Python, Third Edition covers it

How deep it goes

Works through a Keras encoder, sampling layer, decoder, custom loss, training, and visualization rather than a mathematical derivation.

Examples

Builds a Keras VAE for MNIST digits and decodes a grid of points in its two-dimensional latent space.

What it assumes

Introduces autoencoders before the VAE while drawing on convolutional networks and Keras model customization.

What you can do after

Build it from scratch with Keras to reconstruct MNIST digits and sample new digits from a two-dimensional latent space.

How it connects

Connects autoencoders, Bayesian inference, self-supervised reconstruction, latent-space interpolation, 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.

This explainer was generated by Manning's knowledge graph from the text of Deep Learning with Python, Third Edition. The section links point to the parts of the book it draws on.