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


Book Volume: 181

Pages Range: 58-90

DOI: 10.1016/j.matpur.2023.10.005

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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.

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Ruiz-Balet, D., & Zuazua Iriondo, E. (2024). Control of neural transport for normalising flows. Journal De Mathematiques Pures Et Appliquees, 181, 58-90.


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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