9 papers
Gradient Descent on Point Clouds and Applications in Learned Operator Correction
Andreas Hauptmann, Yury Korolev, Matthew Thorpe
We consider the problem of minimising an energy over an unknown manifold that is given implicitly by a point cloud. For a known manifold one can define a gradient descent scheme an…
Approximation of Maximally Monotone Operators : A Graph Convergence Perspective
Takashi Furuya, Yury Korolev, Takaharu Yaguchi
Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-includ…
Large Data Limits of Laplace Learning for Gaussian Measure Data in Infinite Dimensions
Zhengang Zhong, Yury Korolev, Matthew Thorpe
Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The…
A Lipschitz spaces view of infinitely wide shallow neural networks
Francesca Bartolucci, Marcello Carioni, José A. Iglesias +3
We revisit the mean field parametrization of shallow neural networks, using signed measures on unbounded parameter spaces and duality pairings that take into account the regularity…
Introduction to Nonlinear Spectral Analysis
Leon Bungert, Yury Korolev
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding no…
Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization
Martin Burger, Samira Kabri, Yury Korolev +2
The aim of this paper is to provide a mathematical analysis of transformer architectures using a self-attention mechanism with layer normalization. In particular, observed patterns…