8 papers · 1 filter
Sparse entropic quadrature for moment equations
Georgii Oblapenko, Michael Herty, Manuel Torrilhon
In the present work, we study the properties of the sparse entropic quadrature method, a recently proposed method for the closure of systems of moment equations in rarefied gas dyn…
A Mean-Field Theory of Transformers: Well-Posedness of the Coupled Data--Parameter Dynamics and Global Convergence of Training
Michael Herty, Hailiang Liu
We develop a rigorous mean-field theory for transformer networks that captures two large-scale limits inherent in the architecture: the number of tokens in the input s…
Convergence of time-discrete finite particle consensus based optimization in Hilbert spaces
Michael Herty, Hui Huang, Hicham Kouhkouh
We study a time-discrete, finite-particle Consensus-Based Optimization (CBO) algorithm in a separable Hilbert space. Our analysis provides convergence guarantees directly for the c…
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…
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. A central limitation of its continuous-time dynamics is premature…
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 CBO method that incorporates jumps driven by an -stable stochastic process within a kinetic framework. This approach naturally induces nonlocal sto…