Three lectures on Fourier analysis and learning theory

2024/09/17 by H. M. Zhang, Zhang, Haonan
Mathematics · Social Sciences · #History and Theory of Mathematics #Mathematics Education and Teaching Techniques

paper · pdf · doi:10.48550/arxiv.2409.10886

Abstract

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.

Related

• Quantum and classical low-degree learning via a dimension-free Remez inequality
• Tight bounds on the Fourier growth of bounded functions on the hypercube
• On the Fourier spectrum of functions on Boolean cubes
• A Discrete Fourier Transform on Lattices with Quantum Applications
• A Quantum Computational Learning Algorithm