LAPLEX: Fast Trainable Laplace Kernels with FFT Scaling
A new class of exact, trainable Laplace-kernel operators called LAPLEX has been introduced by researchers. These operators provide FFT-like scaling while accommodating adaptive geometry. A LAPLEX layer consists of a full-rank dense matrix characterized by learnable coordinate anchors, which allows for trainable matrix-vector operations on vectors with dimensions reaching up to 10^9 on contemporary GPUs. Functioning as a neural layer, it produces compact projections and interpretable classification heads. Additionally, it acts as an efficient Gram operator for high-dimensional covariance models applied to images with dimensions of 3·10^6, maintaining spatial structure without introducing convolutional bias. This research is available on arXiv, referenced as 2605.24584.
Key facts
- LAPLEX stands for Learnable Laplace Kernels with FFT-like scaling.
- It supports trainable matrix-vector operations at vector dimensions up to 10^9 on modern GPUs.
- The layer is a full-rank dense matrix implicitly defined by learnable coordinate anchors.
- It yields compact projections and classification heads interpretable as soft, trainable routing models.
- It serves as an efficient Gram operator for high-dimensional covariance models.
- It can process flattened images of dimension 3·10^6 without convolutional bias.
- The approach moves beyond the trade-off between fixed geometry and adaptive geometry.
- The paper is available on arXiv with ID 2605.24584.
Entities
Institutions
- arXiv