Control of neural transport for normalising flows

Ruiz-Balet D, Zuazua Iriondo E (2024)

Publication Language: English

Publication Status: Submitted

Publication Type: Journal article, Original article

Future Publication Type: Journal article

Publication year: 2024

Journal

Journal De Mathematiques Pures Et Appliquees Elsevier

Book Volume: 181

Pages Range: 58-90

DOI: 10.1016/j.matpur.2023.10.005

Open Access Link: https://arxiv.org/abs/2307.07817

Abstract

Inspired by normalizing flows, we analyze the bilinear control of neural transport equations by means of time-dependent velocity fields restricted to fulfill, at any time instance, a simple neural network ansatz. The L^1 approximate controllability property is proved, showing that any probability density can be driven arbitrarily close to any other one in any time horizon. The control vector fields are built explicitly and inductively and this provides quantitative estimates on their complexity and amplitude. This also leads to statistical error bounds when only random samples of the target probability density are available.

Authors with CRIS profile

Enrique Zuazua Iriondo Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Additional Organisation(s)

Lehrstuhl für Dynamics, Control, Machine Learning and Numerics (Alexander von Humboldt-Professur)

Involved external institutions

Imperial College London / The Imperial College of Science, Technology and Medicine GB United Kingdom (GB)

How to cite

APA:

Ruiz-Balet, D., & Zuazua Iriondo, E. (2024). Control of neural transport for normalising flows. Journal De Mathematiques Pures Et Appliquees, 181, 58-90. https://doi.org/10.1016/j.matpur.2023.10.005

MLA:

Ruiz-Balet, Domènec, and Enrique Zuazua Iriondo. "Control of neural transport for normalising flows." Journal De Mathematiques Pures Et Appliquees 181 (2024): 58-90.

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