Normalizing Flows are used in deep learning to learn probability distributions by sampling, encoding them inside a neural network. Here, we train an invertible neural network to map a normal Gaussian distribution into a spiral-shaped distribution of data points in 2D, by learning a coordinate transformation (the transformed original coordinate grid is displayed in the background). The probability density generated by the neural network is indicated in yellow, while a few sample data points from the spiral-shaped target distribution are shown as well. Training proceeds by sampling from the data points and maximizing the model's average log-likelihood on the data points.
2021 by Florian Marquardt. Watch https://www.youtube.com/watch?v=dR5xlOnzrpc for the full explanation behind this!
This animation is part of the online lecture series "Advanced Machine Learning for Physics, Science, and Artificial Scientific Discovery". See the website https://pad.gwdg.de/s/2021_AdvancedMachineLearningForScience# and the channel with the full lecture videos: https://www.youtube.com/playlist?list=PLemsnf33Vij4-kv-JTjDthaGUYUnQbbws.
