no code implementations • 27 Nov 2023 • Teo Deveney, Jan Stanczuk, Lisa Maria Kreusser, Chris Budd, Carola-Bibiane Schönlieb
In this paper we rigorously describe the range of dynamics and approximations that arise when training score-based diffusion models, including the true SDE dynamics, the neural approximations, the various approximate particle dynamics that result, as well as their associated Fokker--Planck equations and the neural network approximations of these Fokker--Planck equations.
no code implementations • 17 Oct 2022 • David Alonso, Steffen Bauer, Markus Kirkilionis, Lisa Maria Kreusser, Luca Sbano
These rule-based approaches are motivated by chemical reaction rules which are traditionally solved numerically with the standard Gillespie algorithm proposed in the context of molecular dynamics.
no code implementations • 19 Jan 2022 • Oliver R. A. Dunbar, Charles M. Elliott, Lisa Maria Kreusser
We propose and unify classes of different models for information propagation over graphs.
no code implementations • 14 Nov 2021 • David Alonso, Steffen Bauer, Markus Kirkilionis, Lisa Maria Kreusser, Luca Sbano
Each single of our variety of models, called framework, is based on a mathematical formulation that we call a rule-based system.
no code implementations • 2 Mar 2021 • Jan Stanczuk, Christian Etmann, Lisa Maria Kreusser, Carola-Bibiane Schönlieb
Wasserstein GANs are based on the idea of minimising the Wasserstein distance between a real and a generated distribution.
no code implementations • 24 Jul 2020 • Lisa Maria Kreusser, Marie-Therese Wolfram
In many problems in data classification one wishes to assign labels to points in a point cloud with a certain number of them being already correctly labeled.
no code implementations • 21 Jan 2019 • Lisa Maria Kreusser, Stanley J. Osher, Bao Wang
First-order methods such as gradient descent are usually the methods of choice for training machine learning models.