arXiv:2605.24584v1 Announce Type: new Abstract: 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
The continuous drive for more efficient and scalable machine learning algorithms, particularly in deep learning, necessitates innovations that overcome current computational bottlenecks.
This research outlines a method to significantly improve the efficiency of linear algebra operations in deep learning, potentially making large-scale models more feasible and less resource-intensive.
The introduction of LAPLEX could enable powerful, full-rank dense matrices with FFT-like scaling, offering an alternative to current trade-offs between computational exactness and adaptive geometry.
- · AI researchers
- · Deep learning practitioners
- · Cloud computing providers
- · Data scientists
- · Developers reliant on less efficient linear algebra techniques
Deep learning models could process larger datasets and achieve higher complexity without prohibitive computational costs.
This efficiency gain could accelerate the development of more sophisticated AI applications across various industries.
Reduced compute requirements might democratize access to advanced AI research and development, potentially fostering more innovation beyond well-resourced labs.
This signal links to a primary source. Continuum Brief monitors and indexes it as part of the live intelligence stream — we do not republish source content.
Read at arXiv cs.LG