Readings

References for the course. The Peyré-Cuturi monograph is the single best starting point; the papers below are organized by the section they're first discussed in.

Primary references

• Peyré, G. & Cuturi, M. (2019). Computational Optimal Transport: With Applications to Data Science. Foundations and Trends in Machine Learning. arXiv:1803.00567.
• Villani, C. (2009). Optimal Transport: Old and New. Springer. (Mathematical reference.)
• Santambrogio, F. (2015). Optimal Transport for Applied Mathematicians. Birkhäuser.

§I Fundamentals

• Monge, G. (1781). Mémoire sur la théorie des déblais et des remblais.
• Kantorovich, L. (1942). On the translocation of masses.
• Brenier, Y. (1991). Polar factorization and monotone rearrangement of vector-valued functions.

§II Computation

• Cuturi, M. (2013). Sinkhorn distances: Lightspeed computation of optimal transport. NeurIPS.
• Feydy, J. et al. (2019). Interpolating between optimal transport and MMD using Sinkhorn divergences. AISTATS.
• Benamou, J.-D. & Brenier, Y. (2000). A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem.
• Jordan, R., Kinderlehrer, D. & Otto, F. (1998). The variational formulation of the Fokker-Planck equation.

§III Generalizations

• Rabin, J., Peyré, G., Delon, J. & Bernot, M. (2011). Wasserstein barycenter and its application to texture mixing.
• Bonneel, N. et al. (2015). Sliced and Radon Wasserstein barycenters of measures.
• Mémoli, F. (2011). Gromov–Wasserstein distances and the metric approach to object matching.
• Chizat, L. et al. (2018). Unbalanced optimal transport.

§IV ML Applications

• Arjovsky, M., Chintala, S. & Bottou, L. (2017). Wasserstein generative adversarial networks. ICML.
• Courty, N. et al. (2017). Optimal transport for domain adaptation. IEEE PAMI.
• Alvarez-Melis, D. & Jaakkola, T. (2018). Gromov-Wasserstein alignment of word embedding spaces. EMNLP.
• Lipman, Y. et al. (2023). Flow matching for generative modeling. ICLR.
• Melnyk, I. et al. (2024). Distributional preference alignment of LLMs via optimal transport.

Course tutorials and lecture notes

• Cuturi, M. & Solomon, J. (2020). A Primer on Optimal Transport. NeurIPS tutorial.
• Peyré, G. (various). Numerical Optimal Transport — undergraduate course notes.
• Flamary, R. & Courty, N. (various). POT: Python Optimal Transport. pythonot.github.io.