关于傅立叶分析和学习理论的三场讲座

arXiv - MATH - Mathematical Physics Pub Date : 2024-09-17 DOI:arxiv-2409.10886

Haonan Zhang

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引用次数: 0

摘要

离散超立方$\{-1,1\}^n$上的傅立叶分析在学习理论中有着大量的应用。最近的一个突破是在学习低度布尔函数的背景下使用了傅里叶分析的经典结果，即 Bohnenblust--Hille 不等式。在这些讲座笔记中，我们探讨了这一研究方向，并讨论了离散量子系统和经典傅立叶分析的最新进展。

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Three lectures on Fourier analysis and learning theory

Fourier analysis on the discrete hypercubes $\{-1,1\}^n$ has found numerous applications in learning theory. A recent breakthrough involves the use of a classical result from Fourier analysis, the Bohnenblust--Hille inequality, in the context of learning low-degree Boolean functions. In these lecture notes, we explore this line of research and discuss recent progress in discrete quantum systems and classical Fourier analysis.

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arXiv - MATH - Mathematical Physics

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