Posts tagged “bochner-theorem”

2 posts found

Bochner's Theorem and the Kernel–Fourier Bridge

For continuous stationary positive-definite kernels, Bochner’s theorem turns kernel design into a choice of spectral measure. We derive random Fourier features, connect positional rotations to frequency, and explain where the bridge to attention and spectral transformers needs extra assumptions.

Sep 27, 2026•28 min read

ai-tutorialstutorialfourier-transform

The Frequency Domain: How Fourier Transforms Secretly Powered Everything We Built

A practitioner-level synthesis of twelve weeks of tutorials through one lens — spectral bias, Fourier features, FFT-based token mixing, Bochner's theorem, and neural operators — showing that positional encodings, kernels, state-space models and diffusion schedules are the same idea in different clothes.

Sep 17, 2026•82 min read