LAPLEX: The FFT of Learnable Laplace Kernels

ArXi:2605.24584v1 Announce Type: cross Fast linear algebra in deep learning usually comes with a choice: fixed geometry and exact computation, as in the Fourier transform, or adaptive geometry paid for by dense parameters, random features, or low-rank surrogates. To move beyond this trade-off, we A LAPLEX layer is a typically full-rank dense matrix, implicitly defined by learnable coordinate anchors, with FFT-like scaling. Consequently, it s trainable matrix--vector operations at vector dimensions up to $10^9$ on modern GPUs.