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FlashDiffusion addresses the prohibitive memory costs of dense Gaussian kernels in geometric learning by introducing a matrix-free approach that leverages fused GPU tiles and spectral decomposition. This method efficiently scales to large datasets by coupling eigensolvers with an empirical flow to select optimal resolution scales, avoiding the $O(N^2)$ memory bottleneck typical of standard kernel implementations.
FlashDiffusion: Fused Tiled Kernel Spectral Decomposition
arXiv:2609.38198v1 Announce Type: new Abstract: Diffusion maps, and kernel methods more generally, provide an interpretable nonlinear spectral representation basis for geometric learning. In the geometric limit, small bandwidth, these matrices tend to be high rank and thus require materializing dense Gaussian kernels requires $O(N^2)$ memory. We introduce FlashDiffusion, a matrix-free method that evaluates dense Gaussian kernel blocks in fused GPU tiles and couples the eigensolver to an empirical $\beta$-flow that selects the finite-sample resolution scale. A continuation over sample size and bandwidth warm-starts increasingly expensive spectral solves from coarser resolutions.
Abstract:Diffusion maps, and kernel methods more generally, provide an interpretable nonlinear spectral representation basis for geometric learning. In the geometric limit, small bandwidth, these matrices tend to be high rank and thus require materializing dense Gaussian kernels requires $O(N^2)$ memory. We introduce FlashDiffusion, a matrix-free method that evaluates dense Gaussian kernel blocks in fused GPU tiles and couples the eigensolver to an empirical $\beta$-flow that selects the finite-sample resolution scale. A continuation over sample size and bandwidth warm-starts increasingly expensive spectral solves from coarser resolutions.
Machine Learning (cs.LG)
arXiv:2609.38198 [cs.LG]
(or arXiv:2609.38198v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.38198 Focus to learn more arXiv-issued DOI via DataCite
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