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Variational and information flows in machine learning and optimal transport

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Variational and information flows in machine learning and optimal transport/ by Wuchen Li ... [et al.].
other author:	Li, Wuchen.
Published:	Cham :Springer Nature Switzerland : : 2025.,
Description:	xiv, 254 p. :ill. (some col.), digital ; : 24 cm.;
Contained By:	Springer Nature eBook
Subject:	Stochastic processes. -
Online resource:	https://doi.org/10.1007/978-3-031-92731-7
ISBN:	9783031927317

Variational and information flows in machine learning and optimal transport
Variational and information flows in machine learning and optimal transport[electronic resource] /by Wuchen Li ... [et al.]. - Cham :Springer Nature Switzerland :2025. - xiv, 254 p. :ill. (some col.), digital ;24 cm. - Oberwolfach seminars,v. 562296-5041 ;. - Oberwolfach seminars ;v.47..

- 1. A Dynamic Perspective of Optimal Transport -- 2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications -- 3. Wasserstein Dynamics in Mathematical Data Sciences -- 4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.

This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on "Computational Variational Flows in Machine Learning and Optimal Transport". Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.

ISBN: 9783031927317

Standard No.: 10.1007/978-3-031-92731-7doiSubjects--Topical Terms:

528256
Stochastic processes.

LC Class. No.: QA274

Dewey Class. No.: 519.23

Variational and information flows in machine learning and optimal transport
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505 0 $a - 1. A Dynamic Perspective of Optimal Transport -- 2. A Geometric Perspective on Diffeomorphic and Optimal Transport Flows and Their Applications -- 3. Wasserstein Dynamics in Mathematical Data Sciences -- 4. Flow Matching: Markov Kernels, Stochastic Processes and Transport Plans.
520 $a This book is based on lectures given at the Mathematisches Forschungsinstitut Oberwolfach on "Computational Variational Flows in Machine Learning and Optimal Transport". Variational and stochastic flows on measure spaces are ubiquitous in machine learning and generative modeling. Optimal transport and diffeomorphic flows provide powerful frameworks to analyze such trajectories of distributions with elegant notions from differential geometry, such as geodesics, gradient and Hamiltonian flows. Recently, mean field control and mean field games offered a general optimal control variational view on learning problems. The four independent chapters in this book address the question of how the presented tools lead us to better understanding and further development of machine learning and generative models.
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