这篇开创性研究通过将深度神经网络（DNN）视为输入变量与参数变量的二元函数，首次构建了基于再生核Banach空间（RKBS）的深度学习假设空间。作者证明了该空间的弱*闭包性质，并构造了显式再生核，为DNN学习模型（包括正则化学习和最小范数插值问题）建立 ...

Banach spaces, as complete normed vector spaces, have long served as a fundamental framework for analysing linear operators. Operator theory within these spaces investigates the properties and ...

Banach space theory is a central branch of modern functional analysis concerned with the properties of complete normed vector spaces. This area of mathematics encompasses the study of geometric ...

For every well-founded tree 𝒯 having a unique root such that every non-maximal node of it has countable infinitely many immediate successors, we construct a ℒ∞-space X𝒯. We prove that, for each such ...

We obtain a Bernstein-type inequality for sums of Banach-valued random variables satisfying a weak dependence assumption of general type and under certain smoothness ...

Friday’s Google Doodle was dedicated to the “invaluable contribution” of influential 20th century mathematician Stefan Banach to the study. Banach was an original member of the Lwów School of ...

From reproductive rights to climate change to Big Tech, The Independent is on the ground when the story is developing. Whether it's investigating the financials of Elon Musk's pro-Trump PAC or ...