Deep learning has shown high performances in various types of tasks from visual
recognition to natural language processing, which indicates superior flexibility and adaptivity …

This book provides a systematic survey of classical and recent results on hyperbolic cross
approximation. Motivated by numerous applications, the last two decades have seen great …

Compressive sensing is a new type of sampling theory, which predicts that sparse signals
and images can be reconstructed from what was previously believed to be incomplete …

Using techniques developed recently in the field of compressed sensing we prove new
upper bounds for general (nonlinear) sampling numbers of (quasi-) Banach smoothness …

We introduce a new variational method for the numerical homogenization of divergence
form elliptic, parabolic and hyperbolic equations with arbitrary rough (L∞) coefficients. Our …

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In-context learning (ICL) of large language models has proven to be a surprisingly effective
method of learning a new task from only a few demonstrative examples. In this paper, we …

This book is a survey on multivariate approximation. The 20th century was a period of
transition from univariate problems to multivariate problems in a number of areas of …

Using tools from the theory of operator ideals and s-numbers, we develop a general
approach to transfer estimates for L 2-approximation of Sobolev functions into estimates for …

About a decade ago, a couple of groundbreaking articles revealed the possibility of faithfully
recovering high-dimensional signals from some seemingly incomplete information about …