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Why It Matters
Estimating integrals of black-box, high-dimensional functions, from expectations and kernel mean embeddings to the softmax kernel in self-attention, is a basic subroutine in machine learning.
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Discovered via ArXiv and published by ArXiv.
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Original description
Estimating integrals of black-box, high-dimensional functions, from expectations and kernel mean embeddings to the softmax kernel in self-attention, is a basic subroutine in machine learning. Rank-1 lattice rules suit this setting: they query the integrand only at a fixed point set and need no gradients. When the $n$ points serve as a design matrix $X\in\mathbb{R}^{n\times d}$ for a feature map, however, computing $Ψ(X)^\top v$ or $Ψ(X)w$ for an elementwise nonlinearity $Ψ$ costs $O(nd)$ time and memory for any standard quasi-Monte Carlo point set. We study subgroup rank-1 lattices, whose Koro...
Discovered via ArXiv
Research papers and preprints from arXiv.
Publisher: arxiv.org
ID: http://arxiv.org/abs/2609.35177v1 · Indexed 44 minutes ago