{
  "abstract": "An operational reference on oblique projections in deep learning and their instantiation, Recursive Oblique Projection Networks (ROPN). It contains: (i) the geometric foundations; (ii) the five block variants with verified PyTorch code -Dense, Dense-fast, LoRA, Circulant, auto-ROPN; (iii) a quantitative illustration of Theorem 2 through a targeted test executed; (iv) the detailed anisotropy sweep; (v) a synthesis sheet (properties, complexity, measured timings); (vi) the detailed operation of auto-ROPN; and (vii) usage examples. Central message, supported by the tests: the oblique map is the right geometry on anisotropic data and outperforms any model structurally unable to exploit the covariance; a multilayer perceptron (MLP) recovers it on its own when the data allow.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Olivier Caspary"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/50fvseaqs0axa.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "50fvseaqs0axa",
  "issns": [],
  "landing_url": "https://hal.science/hal-05851796v1",
  "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": [
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      "hal",
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    ],
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      "hal",
      "0.math"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05851796/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/50fvseaqs0axa.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:44Z",
      "native_id": "hal-05851796",
      "source": "hal",
      "url": "https://hal.science/hal-05851796v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:0.math",
      "subfield": "general"
    }
  ],
  "title": "Oblique Projection Networks (OPN) Reference guide - variants, code, tests, complexity, and the application scope of oblique projections",
  "title_text": "Oblique Projection Networks (OPN) Reference guide - variants, code, tests, complexity, and the application scope of oblique projections",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:44Z",
  "url": "https://research.draconitic.com/paper/50fvseaqs0axa",
  "venue": "HAL",
  "versions": []
}