Control of neural transport for normalizing flows

Understand

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.