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PreprintCC BY 4.0HAL

Oblique Projection Networks (OPN) Reference guide - variants, code, tests, complexity, and the application scope of oblique projections

  • Olivier Caspary
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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.

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Cite

BibTeXRIS
BibTeX
@misc{caspary2026oblique,
  title = {{Oblique Projection Networks (OPN) Reference guide - variants, code, tests, complexity, and the application scope of oblique projections}},
  author = {Olivier Caspary},
  howpublished = {HAL},
  year = {2026},
  month = nov,
  url = {https://hal.science/hal-05851796v1},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Oblique Projection Networks (OPN) Reference guide - variants, code, tests, complexity, and the application scope of oblique projections
AU  - Olivier Caspary
PY  - 2026
DA  - 2026/11/04
PB  - HAL
UR  - https://hal.science/hal-05851796v1
AB  - 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.
ER  -