7 papers
Bernstein-Schur Kernels: Random Features by Sketched Modulation and Radial Randomization
Taha Bouhsine
Bernstein--Schur kernels are products of a finite-feature kernel and a completely monotone shift-invariant kernel: nonstationary kernels falling between the shift-invariant and dot…
In Defense of Cosine Similarity: Normalization Eliminates the Gauge Freedom
Taha Bouhsine
Steck, Ekanadham, and Kallus [arXiv:2403.05440] demonstrate that cosine similarity of learned embeddings from matrix factorization models can be rendered arbitrary by a diagonal ``…
A Universal Reproducing Kernel Hilbert Space from Polynomial Alignment and IMQ Distance
Taha Bouhsine
We introduce the Yat kernel $$k_{b,\varepsilon}(\mathbf{w},\mathbf{x})=\frac{(\mathbf{w}^\top\mathbf{x}+b)^2}{\|\mathbf{x}-\mathbf{w}\|^2+\varepsilon},\qquad b\ge 0,\ \varepsilon>0…
No More DeLuLu: Physics-Inspired Kernel Networks for Geometrically-Grounded Neural Computation
Taha Bouhsine
We introduce the yat-product, a kernel operator combining quadratic alignment with inverse-square proximity. We prove it is a Mercer kernel, analytic, Lipschitz on bounded domains,…
SLAY: Geometry-Aware Spherical Linearized Attention with Yat-Kernel
Jose Miguel Luna, Taha Bouhsine, Krzysztof Choromanski
We propose a new class of linear-time attention mechanisms based on a relaxed and computationally efficient formulation of the recently introduced E-Product, often referred to as t…
Deep Learning 2.0: Artificial Neurons That Matter -- Reject Correlation, Embrace Orthogonality
Taha Bouhsine
We introduce a yat-product-powered neural network, the Neural Matter Network (NMN), a breakthrough in deep learning that achieves non-linear pattern recognition without activation…