Kullback–Leibler divergence

As explained in Deep Learning with R, Third Edition

Kullback–Leibler divergence is a measure of how one probability distribution differs from a reference probability distribution.

Kullback–Leibler divergence measures how an encoder’s probability distribution differs from a reference distribution. In a variational autoencoder, it acts as a regularization loss alongside reconstruction loss. section 17.1.2

The regularization term nudges the encoder output toward a well-rounded normal distribution centered around zero, producing a more structured latent space and reducing overfitting. section 17.1.2

VAE latent-space workflow

An encoder produces z_mean and z_log_var, which define a latent probability distribution. A sampled latent point z is passed to the decoder, while reconstruction and regularization losses train the model. section 17.1.2

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.

Shows how a VAE maps an image to z_mean and z_log_var, defines a latent distribution, samples a latent point, and decodes it. section 17.1.2

How Deep Learning with R, Third Edition covers it

How deep it goes

Defines the training role and intended distributional effect, but does not derive the divergence mathematically.

Examples

Uses z_mean, z_log_var, latent sampling, decoding, reconstruction loss, and regularization loss as the working example.

What you can do after

Understand how distributional regularization shapes a variational autoencoder’s latent space.

How it connects

Connects variational autoencoders with latent spaces, encoder distributions, reconstruction loss, and regularization loss.

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Also explained in

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  Reinforcement Learning from Human FeedbackForward KL divergence is KL divergence from a target distribution to an approximating distribution, with expectation taken under the target distribution.
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  Math and Architectures of Deep LearningA loss term based on Kullback-Leibler divergence that penalizes differences between probability distributions, such as an encoder's latent distribution and a chosen prior.
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  Learn Generative AI with PyTorchA divergence measure used as a regularization term to encourage a latent-variable distribution to resemble a normal distribution.
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  Build a Reasoning Model (From Scratch)A measure of how different two probability distributions are, used here for soft distillation.
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  Machine Learning Algorithms in DepthKullback-Leibler divergence is a nonnegative measure of the discrepancy between two probability distributions.
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  Evolutionary Deep Learning: Genetic algorithms and neural networksA divergence-based measure comparing probability distributions through differences in their information content.
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  Causal AIKullback–Leibler divergence quantifies the difference between two probability distributions.
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  Data Without LabelsKullback-Leibler divergence is a directed measure of the difference between two probability distributions based on their relative information content.
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  Bayesian Optimization in ActionKullback–Leibler divergence is a nonnegative statistical divergence that quantifies how one probability distribution differs from another.
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  Optimization Algorithms: AI techniques for design, planning, and control problemsKullback–Leibler divergence is a metric quantifying the dissimilarity between two probability distributions.

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Related concepts

• Group Relative Policy Optimizationpart of · Group Relative Policy Optimization is a reinforcement-learning algorithm that updates a policy using relative rewards or advantages estimated from groups of sampled outputs or actions.
• t-SNEused by · t-SNE is a nonlinear dimensionality-reduction technique that maps high-dimensional data to a lower-dimensional space while emphasizing local similarities or neighborhood relationships.
• variational inferenceused by · Variational inference is an approximate inference technique that optimizes a tractable family of probability distributions to approximate a target distribution, often a posterior.
• variational Gaussian processused by · A variational Gaussian process is a scalable approximation to a Gaussian process whose posterior is represented through variational inference over a finite set of inducing points.

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