Optimal transport for generative models
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Publication:6606492
DOI10.1007/978-3-030-98661-2_105zbMATH Open1547.49035MaRDI QIDQ6606492
Na Lei, Xianfeng David Gu, Shing-Tung Yau
Publication date: 16 September 2024
Monge-Ampère equationoptimal transportmanifold learningconvex geometrygenerative adversarial networksexplainable deep learning
Artificial neural networks and deep learning (68T07) Computing methodologies for image processing (68U10) Image processing (compression, reconstruction, etc.) in information and communication theory (94A08) Monge-Ampère equations (35J96) Optimal transportation (49Q22)
Cites Work
- Variational principles for Minkowski type problems, discrete optimal transport, and discrete Monge-Ampère equations
- A geometric view of optimal transportation and generative model
- The refractor problem in reshaping light beams
- On a Monge-Ampère equation arising in geometric optics
- Area-preserving mesh parameterization for poly-annulus surfaces based on optimal mass transportation
- Surface parameterization based on polar factorization
- On the design of a reflector antenna. II
- Regularity of potential functions of the optimal transportation problem
- On a problem of Monge
- Convolutional Wasserstein distances: efficient optimal transportation on geometric domains
- Regularity Properties of Optimal Maps Between Nonconvex Domains in the Plane
- Polar factorization and monotone rearrangement of vector‐valued functions
- Some regularity properties of solutions of Monge Ampère equation
- Minimizing Flows for the Monge--Kantorovich Problem
- Earth mover's distances on discrete surfaces
- On the design of a reflector antenna
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