{
  "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.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.27748",
  "author_total": 5,
  "authors": [
    {
      "name": "Halyun Jeong"
    },
    {
      "name": "Palle E. T. Jorgensen"
    },
    {
      "name": "Hyun-Kyoung Kwon"
    },
    {
      "name": "Myung-Sin Song"
    },
    {
      "name": "James Tian"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2r6p65pq85k5n.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.27748",
  "fulltext_url": null,
  "id": "2r6p65pq85k5n",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.27748",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.FA"
    ],
    [
      "arxiv",
      "stat.ML"
    ],
    [
      "openalex",
      "1702|Neural Networks and Applications"
    ]
  ],
  "openalex": "W7204761218",
  "pdf_url": "https://arxiv.org/pdf/2608.27748",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2r6p65pq85k5n.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:28Z",
      "native_id": "2608.27748",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.27748"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:stat.ML",
      "subfield": "statistics"
    }
  ],
  "title": "The role of parameter Jacobians in the stability of network outputs",
  "title_text": "The role of parameter Jacobians in the stability of network outputs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:34Z",
  "url": "https://research.draconitic.com/paper/2r6p65pq85k5n",
  "venue": "arXiv",
  "versions": []
}