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
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)
Involved external institutions
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://dx.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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