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Generative Modeling and Stochastic Control as Dynamics on Probability Distributions.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Generative Modeling and Stochastic Control as Dynamics on Probability Distributions./
Author:	Domingo i Enrich, Carles.
Description:	1 online resource (231 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-12, Section: B.
Contained By:	Dissertations Abstracts International85-12B.
Subject:	Computer science. -
Online resource:	click for full text (PQDT)
ISBN:	9798383161418

Generative Modeling and Stochastic Control as Dynamics on Probability Distributions.
Domingo i Enrich, Carles.

Generative Modeling and Stochastic Control as Dynamics on Probability Distributions. - 1 online resource (231 pages)

Source: Dissertations Abstracts International, Volume: 85-12, Section: B.

Thesis (Ph.D.)--New York University, 2024.

Includes bibliographical references

Several modern machine learning algorithms can be studied from the perspective of evolution dynamics on the space of probability measures. Gradient descent-ascent algorithms that are used to solve minimax problems such as the ones arising in generative adversarial networks (GANs) can be interpreted as a joint evolution of two measures: one over the space of parameters of the generator, and one over the space of parameters of the discriminator. In chapter 2, we study systems of this form, and we provide convergence guarantees when possible. Diffusion models, which are another generative modeling technique, are also based on dynamics on probability measures, in this case over the space of samples. The dynamics are simulated at inference time; the starting distribution is a Gaussian, and the final distribution is meant to be the target data distribution. Diffusion models were generalized by the Flow Matching framework, which allows to construct different paths between the Gaussian noise distribution and the data distribution. In chapter 3, we introduce Multisample Flow Matching, which is a generalization of Flow Matching with intimate connections to optimal transport. Stochastic optimal control is a third problem where dynamics on measures play a critical role. The goal is to learn a vector field (the control) in order to drive the behavior of the solutions of a stochastic differential equation. In chapter 4, we present Stochastic Optimal Control Matching, a least-squares loss that is based on the same principles that are used to formulate diffusion model losses, and which achieves errors that are an order of magnitude lower than for existing methods.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798383161418Subjects--Topical Terms:

573171
Computer science.
Subjects--Index Terms:

Diffusion modelsIndex Terms--Genre/Form:

554714
Electronic books.

Generative Modeling and Stochastic Control as Dynamics on Probability Distributions.
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