{"slug": "why-not-to-use-the-gaussian-kernel", "title": "Why not to use the Gaussian kernel", "summary": "A new paper submitted to arXiv on August 27, 2026, argues that the Gaussian kernel, also known as the squared exponential or radial basis function kernel, should never be used as a default in Gaussian process regression because it is extremely brittle, leading to unrealistically small conditional variance and numerical ill-conditioning. The authors contend that analytic kernels in general are best avoided due to their unnatural smoothness.", "body_md": "# Statistics > Machine Learning\n\n[Submitted on 27 Aug 2026]\n\n# Title:Why not to use the Gaussian kernel\n\n[View PDF](/pdf/2608.26974)\n\nAbstract:Kernels measure similarity or correlation in tasks such as regression and classification. The Gaussian kernel, other names of which include squared exponential and radial basis function kernel, is one of the most popular in Gaussian process regression. We argue that the Gaussian kernel is best avoided and should never be used as a default. The argument rests on two results demonstrating that the Gaussian kernel is extremely brittle. First, the Gaussian kernel gives rise to a conditional variance that is unrealistically small. If the variance is used to quantify predictive uncertainty, catastrophic overconfidence is almost inevitable. Second, a small variance goes hand in hand with numerical ill-conditioning, so that to use the Gaussian kernel in practice requires tricks such as nugget terms that effectively modify the underlying regression or classification model. These problems are caused by the unnatural smoothness of the Gaussian kernel, a fact we are far from the first to take notice of. The problem is not the Gaussian form itself but the analyticity of the kernel: Our argument is more broadly that analytic kernels are best avoided. For stationary kernels analyticity is essentially equivalent to an exponential decay of the spectral density.\n\n### Current browse context:\n\nstat.ML\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/))# 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))# 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))# 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/why-not-to-use-the-gaussian-kernel", "canonical_source": "https://arxiv.org/abs/2608.26974", "published_at": "2026-08-29 00:59:03+00:00", "updated_at": "2026-08-29 01:18:15.939801+00:00", "lang": "en", "topics": ["machine-learning", "ai-research"], "entities": ["arXiv"], "alternates": {"html": "https://wpnews.pro/news/why-not-to-use-the-gaussian-kernel", "markdown": "https://wpnews.pro/news/why-not-to-use-the-gaussian-kernel.md", "text": "https://wpnews.pro/news/why-not-to-use-the-gaussian-kernel.txt", "jsonld": "https://wpnews.pro/news/why-not-to-use-the-gaussian-kernel.jsonld"}}