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Reverse Tangent Categories

Authors Geoffrey Cruttwell , Jean-Simon Pacaud Lemay

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Author Details

Geoffrey Cruttwell
  • Mount Allison University, Sackville, Canada
Jean-Simon Pacaud Lemay
  • Macquarie University, Sydney, Australia

Funding

  • Cruttwell, Geoffrey: Partially funded by an NSERC Discovery Grant.
  • Lemay, Jean-Simon Pacaud: For this research, this author was funded by an NSERC PDF (456414649), an ARC DECRA (DE230100303), & an AFOSR Research Grant (FA9550-24-1-0008).

Acknowledgements

The authors would like to thank Bryce Clark for pointing out [Philip J. Higgins and Kirril C. H. Mackenzie, 1993], which ties in nicely with the story of this paper, as well as Geoff Vooys for useful discussions, answering questions, and helping find references regarding Example 31.

Cite As Get BibTex

Geoffrey Cruttwell and Jean-Simon Pacaud Lemay. Reverse Tangent Categories. In 32nd EACSL Annual Conference on Computer Science Logic (CSL 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 288, pp. 21:1-21:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CSL.2024.21

Abstract

Previous work has shown that reverse differential categories give an abstract setting for gradient-based learning of functions between Euclidean spaces. However, reverse differential categories are not suited to handle gradient-based learning for functions between more general spaces such as smooth manifolds. In this paper, we propose a setting to handle this, which we call reverse tangent categories: tangent categories with an involution operation for their differential bundles.

Subject Classification

ACM Subject Classification
  • Theory of computation → Categorical semantics
Keywords
  • Tangent Categories
  • Reverse Tangent Categories
  • Reverse Differential Categories
  • Categorical Machine Learning

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References

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