Which measurements, and how few? Sampling signals generated by neural networks

Compressed sensing shows that a signal can be recovered from far fewer linear measurements than its dimension, provided it has low-dimensional structure. Much of the classical theory focuses on sparse signals and random measurements. More recently, deep generative models have emerged as a powerful way to capture the structure of natural signals, such as images: such signals can be modeled as lying near the range of a neural network with a low-dimensional input. For signals with this structure, which measurements work, and how few are needed?

I will discuss recent progress on both questions, moving beyond idealized random measurements towards structured ones, such as the Fourier measurements used in MRI. Although neural networks motivate these questions, much of the theory applies to arbitrary structured sets of signals. We'll see how the geometry of these sets determines how many measurements are needed, and how the measurements themselves can be chosen to exploit that geometry. This is based on joint work with several collaborators.

***** There will be coffee, tea and snacks at PIMS from 2:30 PM to 3 PM.

***** UBC Math Colloquium 2026-2027 Zoom info:

Meeting ID: 663 8015 7380

Passcode: 31415