The role of parameter Jacobians in the stability of network outputs

[2608.27748] The role of parameter Jacobians in the stability of network outputs Skip to main content Search Submit Donate Log in Mathematics > Functional Analysis arXiv:2608.27748 (math) [Submitted on 27 Aug 2026] Title: The role of parameter Jacobians in the stability of network outputs Authors: Halyun Jeong , Palle E. T. Jorgensen , Hyun-Kyoung Kwon , Myung-Sin Song , James Tian View PDF HTML (experimental) Abstract: In the framework of network dynamics, learning models, and neural tangent kernels (NTK), we show that the corresponding linearized dynamics leads naturally to a semigroup formulation. More precisely, in our analysis of input/output models, the time-dynamics is presented via special semigroups of linear operators on Hilbert spaces, together with an associated class of semigroup perturbations. In this context, we then present new and explicit a priori perturbation-bound results: for the fixed-kernel linearization constructions arising in the NTK setting, we prove norm-bounds on the corresponding semigroup perturbations, in the form of explicit finite-time perturbation estimates. We further present refinements on prescribed task spaces, Cesàro-averaged (ergodic) comparisons estimates, and versions in which the lower spectral edge assumption is replaced by a spectral-distribution condition. We also extend the comparison to nonautonomous NTK evolutions through piecewise-frozen approximations, record a corresponding discrete Euler specialization, and offer worked examples in order to illustrate our perturbation-bound estimates. Subjects: Functional Analysis (math.FA) ; Machine Learning (stat.ML) MSC classes: 68T07, 62M10, 47A63 Cite as: arXiv:2608.27748 [math.FA] (or arXiv:2608.27748v1 [math.FA] for this version) https://doi.org/10.48550/arXiv.2608.27748 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Halyun Jeong [ view email ] [v1] Thu, 27 Aug 2026 22:21:10 UTC (42 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.FA < prev | next > new | recent | 2026-08 Change to browse by: math stat stat.ML References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs 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 . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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