LAPLEX: The FFT of Learnable Laplace Kernels
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 introduce LAPLEX, a class of exact, trainable (phased) Laplace-kernel operators. A LAPLEX layer is a typically full-rank dense matrix, implicitly defined by learnable coordinate anchors, with FFT-like scaling. Consequently, it supports trainable matrix--vector operations at vector dimensions up to $10^9$ on modern GPUs. As a neural layer, it yields compact projections and classification heads interpretable as soft, trainable routing m...
| Authors | Łukasz Struski, Hanna Blazhko, Piotr Kubaty et al. |
|---|---|
| Primary category | cs.LG |
| Published | 23 May 2026 |
| Last updated at source | 23 May 2026 |
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