{
  "abstract": "Traditional deep learning architectures relying on standard affine layers (WX +b) partition the activation space into unbounded polyhedral regions, which inherently introduce chronic training instabilities such as gradient vanishing and severe generalization decay. To resolve this structural vulnerability, we introduce an alternative “bounded-by-design” geometric framework that completely moves beyond traditional affine transformations. By replacing them entirely with ball coverings, we reformulate layer mechanics around the fundamental metric of a feature point’s proximity to a ball centered atW. Crucially, computing the formulation using direct dot products fully preserves GPU parallelization performance without altering external network components. Empirical validation demonstrates that our bounded formulation effectively precludes overfitting, maintains numerical stability, and exhibits superior testing generalization compared to unconstrained affine layers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Mengnien Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5bxk8ch12bm70.bib",
  "cited_by": 0,
  "doi": null,
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  "id": "5bxk8ch12bm70",
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  "landing_url": "https://hal.science/hal-05742801v1",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.info"
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    [
      "hal",
      "0.math"
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  "pdf_url": "https://hal.science/hal-05742801/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5bxk8ch12bm70.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:31Z",
      "native_id": "hal-05742801",
      "source": "hal",
      "url": "https://hal.science/hal-05742801v1"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Beyond Affine Layers: Bounded Ball Coverings to Preclude Gradient Vanishing",
  "title_text": "Beyond Affine Layers: Bounded Ball Coverings to Preclude Gradient Vanishing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:31Z",
  "url": "https://research.draconitic.com/paper/5bxk8ch12bm70",
  "venue": "HAL",
  "versions": []
}