arXiv：cs.LG（机器学习，全量分类）· Julio Candanedo·· 5 小时前AI 评分31
FlashDiffusion：融合分块核谱分解
FlashDiffusion: Fused Tiled Kernel Spectral Decomposition
AI 导读
FlashDiffusion 是一种无矩阵方法，通过在融合 GPU 分块中计算稠密高斯核块，避免 O(N²) 内存开销，并将特征求解器与经验 β-flow 耦合以选择有限样本分辨率尺度。该方法还对样本量和带宽做延拓，用粗分辨率热启动越来越昂贵的谱求解。
正文
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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.38198 [cs.LG] |
| (or arXiv:2609.38198v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.38198 arXiv-issued DOI via DataCite |
Submission history
From: Julio Candanedo [view email]
[v1]
Fri, 18 Sep 2026 22:27:09 UTC (2,292 KB)
来源：arXiv：cs.LG（机器学习，全量分类） · arxiv.org