Sampling a target probability distribution with an unknown normalization constant is a
fundamental challenge in computational science and engineering. Recent work shows that …

Sampling a probability distribution with an unknown normalization constant is a fundamental
problem in computational science and engineering. This task may be cast as an optimization …

As the problem of minimizing functionals on the Wasserstein space encompasses many
applications in machine learning, different optimization algorithms on $\mathbb {R}^ d …

Consensus-based optimization (CBO) is a versatile multi-particle optimization method for
performing nonconvex and nonsmooth global optimizations in high dimensions. Proofs of …

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 in …

A key numerical difficulty in compressible fluid dynamics is the formation of shock waves.
Shock waves feature jump discontinuities in the velocity and density of the fluid and thus …

Transformers, which are state-of-the-art in most machine learning tasks, represent the data
as sequences of vectors called tokens. This representation is then exploited by the attention …

This paper is concerned with the approximation of probability distributions known up to
normalization constants, with a focus on Bayesian inference for large-scale inverse …

The Wasserstein space of probability measures is known for its intricate Riemannian
structure, which underpins the Wasserstein geometry and enables gradient flow algorithms …