10 papers
A PDE-Based Framework for Generative Modeling Beyond Classical Score-Based Diffusion
Horacio Tettamanti, Michael Herty
We introduce an alternative generative framework based on a nonlinear modification of the classical Ornstein--Uhlenbeck dynamics. The proposed dynamics admits both a microscopic de…
Mean-Field Model for Two-Layer Neural Networks Trained with Consensus-Based Optimization
William De Deyn, Michael Herty, Giovanni Samaey
We study Consensus-Based Optimization (CBO) for two-layer neural network training. We compare the performance of CBO against Adam on two test cases and demonstrate how a hybrid app…
Ensemble Kalman Inversion as an Inertial Interacting Particle System
Michael Herty, Pierpaolo Porretta, Giuseppe Visconti
Ensemble Kalman Inversion (EKI) is a derivative-free, ensemble-based method for inverse and optimization problems. Its continuous-time formulation can be interpreted as an interact…
Sparse and low-rank kinetic distribution estimation
Georgii Oblapenko, Lambert Theisen, Rostislav-Paul Wilhelm +2
In this paper, we consider methods that allow for memory-efficient storage of high-dimensional distributions and retain certain key features thereof, specifically in a kinetic theo…
Computation of entanglement for quantum states by a Consensus-Based Optimization method
Michael Herty, Yijia Tang, Yizhou Zhou
The computation of quantum entanglement can be formulated as a high-dimensional nonconvex optimization problem with orthogonality constraints. In this work, we propose structure-pr…
Consensus-based optimization with -stable jump processes
Pedro Aceves-Sanchez, Giacomo Albi, Federica Ferrarese +1
In this paper, we introduce a novel variant of the CBO method that incorporates jumps according to an -stable stochastic process in a kinetic framework. This extension gives ri…