Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime

Computer Science > Machine Learning [Submitted on 7 Oct 2025 (v1), last revised 29 May 2026 (this version, v3)] Title:Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime View PDF HTML (experimental)Abstract:This paper provides data-dependent bounds on the expected error of the Gibbs algorithm in the overparameterized interpolation regime, where low training errors are also obtained for impossible data, such as random labels in classification. The results show that generalization in the low-temperature regime is already signaled by small training errors in the noisier high-temperature regime. The bounds are stable under approximation with Langevin Monte Carlo algorithms. The analysis motivates the design of an algorithm to compute bounds, which on the MNIST, CIFAR-10, and SVHN datasets yield nontrivial, close predictions on the test error for true labeled data, while maintaining a correct upper bound on the test error for random labels. Submission history From: Erfan Mirzaei [view email][v1] Tue, 7 Oct 2025 15:25:56 UTC (3,684 KB) [v2] Thu, 12 Feb 2026 17:24:30 UTC (3,667 KB) [v3] Fri, 29 May 2026 20:25:59 UTC (4,222 KB) Current browse context: cs.LG References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) IArxiv Recommender (What is IArxiv?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both 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. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.