6 papers
1-Lipschitz Neural Networks on Hadamard Manifolds
Davide Murari, Marta Ghirardelli, Ben Adcock +4
Controlling the Lipschitz constant of a neural network is a standard way to promote robustness and stability. Most existing constraining strategies are designed for Euclidean space…
Hybrid least squares for learning functions from highly noisy data
Ben Adcock, Bernhard Hientzsch, Akil Narayan +1
Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods…
Christoffel-DPS: Optimal sensor placement in diffusion posterior sampling for arbitrary distributions
James Rowbottom, Nick Huang, Carola-Bibiane Schönlieb +1
State estimation is a critical task in scientific, engineering and control applications. Since the reliability of reconstructions depends on the number and position of sensors, opt…
GRIFDIR: Graph Resolution-Invariant FEM Diffusion Models in Function Spaces over Irregular Domains
James Rowbottom, Elizabeth L. Baker, Nick Huang +3
Score-based diffusion models in infinite-dimensional function spaces provide a mathematically principled framework for modelling function-valued data, offering key advantages such…
Refinement-based Christoffel sampling for least squares approximation in non-orthogonal bases
Astrid Herremans, Ben Adcock
We introduce a refinement-based Christoffel sampling (RCS) algorithm for least squares approximation in the span of a given, generally non-orthogonal set of functions $Φ_n = \{Ï_…
How many measurements are enough? Bayesian recovery in inverse problems with general distributions
Ben Adcock, Nick Huang
We study the sample complexity of Bayesian recovery for solving inverse problems with general prior, forward operator and noise distributions. We consider posterior sampling accord…