Prime Fourier Embeddings: A Principled Basis for Modular Arithmetic

Excerpt

arXiv:2606.23044v3 Announce Type: replace Abstract: Numbers have algebraic structure that standard neural embeddings often fail to expose. We introduce Prime Fourier Embeddings (PFE), which encode integers as prime-indexed (cos, sin) pairs derived from the harmonic analysis of Q, providing a pre-structured representation in which modular arithmetic reduces to selecting the relevant prime channel rather than discovering algebraic structure from scratch. We prove that any linear map equivariant wi