{"slug": "flashdiffusion-fused-tiled-kernel-spectral-decomposition", "title": "FlashDiffusion: Fused Tiled Kernel Spectral Decomposition", "summary": "Researchers submitted FlashDiffusion, a matrix-free method for diffusion maps and kernel spectral decomposition, to arXiv on 18 Sep 2026. FlashDiffusion evaluates dense Gaussian kernel blocks in fused GPU tiles and couples the eigensolver to an empirical β-flow that selects the finite-sample resolution scale, avoiding the O(N^2) memory cost of materializing dense Gaussian kernels at small bandwidth. A continuation over sample size and bandwidth warm-starts increasingly expensive spectral solves from coarser resolutions.", "body_md": "# Computer Science > Machine Learning\n\n  [Submitted on 18 Sep 2026]\n\n# Title:FlashDiffusion: Fused Tiled Kernel Spectral Decomposition\n\n[View PDF](https://arxiv.org/pdf/2609.38198)\n\n[HTML (experimental)](https://arxiv.org/html/2609.38198v1)\n\nAbstract: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.\n    \n\n### References & Citations\n\nLoading...\n\n# Bibliographic and Citation Tools\n\nBibliographic Explorer \n\n*(*[What is the Explorer?](https://info.arxiv.org/labs/showcase.html#arxiv-bibliographic-explorer))\nConnected Papers \n\n*(*[What is Connected Papers?](https://www.connectedpapers.com/about))\nLitmaps \n\n*(*[What is Litmaps?](https://www.litmaps.co/))\nscite Smart Citations \n\n*(*[What are Smart Citations?](https://www.scite.ai/))\n# Code, Data and Media Associated with this Article\n\nalphaXiv \n\n*(*[What is alphaXiv?](https://alphaxiv.org/))\nCatalyzeX Code Finder for Papers \n\n*(*[What is CatalyzeX?](https://www.catalyzex.com))\nDagsHub \n\n*(*[What is DagsHub?](https://dagshub.com/))\nGotit.pub \n\n*(*[What is GotitPub?](http://gotit.pub/faq))\nHugging Face \n\n*(*[What is Huggingface?](https://huggingface.co/huggingface))\nScienceCast \n\n*(*[What is ScienceCast?](https://sciencecast.org/welcome))\n# Demos\n\n# Recommenders and Search Tools\n\nInfluence Flower \n\n*(*[What are Influence Flowers?](https://influencemap.cmlab.dev/))\nCORE Recommender \n\n*(*[What is CORE?](https://core.ac.uk/services/recommender))\nIArxiv Recommender\n\n*(*[What is IArxiv?](https://iarxiv.org/about))\n# arXivLabs: experimental projects with community collaborators\n\narXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.\n\nBoth individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.\n\nHave an idea for a project that will add value for arXiv's community? [**Learn more about arXivLabs**](https://info.arxiv.org/labs/index.html).", "url": "https://wpnews.pro/news/flashdiffusion-fused-tiled-kernel-spectral-decomposition", "canonical_source": "https://arxiv.org/abs/2609.38198", "published_at": "2026-10-02 04:00:00+00:00", "updated_at": "2026-10-02 04:16:09.838889+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "ai-infrastructure"], "entities": ["FlashDiffusion", "arXiv"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/flashdiffusion-fused-tiled-kernel-spectral-decomposition", "markdown": "https://wpnews.pro/news/flashdiffusion-fused-tiled-kernel-spectral-decomposition.md", "text": "https://wpnews.pro/news/flashdiffusion-fused-tiled-kernel-spectral-decomposition.txt", "jsonld": "https://wpnews.pro/news/flashdiffusion-fused-tiled-kernel-spectral-decomposition.jsonld"}}