This book presents optimal transport as a working language for machine learning. It starts from finite assignments and transport plans, builds the Monge and Kantorovich theories, develops Sinkhorn algorithms and generalized distances, and then uses this geometry to study gradient flows, learning dynamics, and transportation-based generative models.
How to cite
Gabriel Peyré. Optimal Transport for Machine Learners. arXiv:2505.06589 [stat.ML], submitted May 10, 2025; cross-listed in cs.AI and math.OC. DOI: 10.48550/arXiv.2505.06589.
Focus survey
A long survey of PDE tools for machine learning, written with an optimal-transport bias. It reorganizes the OT4ML material most relevant to dynamic OT, Wasserstein gradient flows, particle limits, diffusion models, flow matching, mean-field training, and transportation views of modern architectures.
The web version follows the manuscript and places interactive panels beside the mathematical figures, so the reading flow stays centered on the book.
The figure gallery is a searchable database: filter by concept or book section, inspect thumbnails, open notebooks on GitHub, and launch them in Colab.
Self-contained notebooks for classroom use and quick experimentation. Each can be opened in GitHub or launched directly in Colab.
Four slide decks provide a lecture-oriented route through the computational OT material.
Each letter is a small live visualization of one construction used in the book. Its two sliders expose complementary geometric and numerical parameters of the corresponding method.