the KL (Kullback-Leibler) divergence loss

KL divergence loss, also known as Kullback-Leibler divergence loss or relative entropy loss, is a measure of how different two probability distributions are from each other. It is often used in machine learning to train models to mimic a target distribution.

In the context of neural networks, KL divergence loss is commonly used in variational autoencoders (VAEs) to encourage the learned distribution to match a prior distribution, such as a Gaussian distribution. It is also used in generative adversarial networks (GANs) to measure the difference between the generated samples and the real samples.

The KL divergence loss is calculated as the sum of the logarithm of the ratio of the two probability distributions, multiplied by the probability of each input sample. It is not symmetric, which means that the KL divergence loss between probability distribution P and Q is not necessarily the same as the KL divergence loss between Q and P.