Reverse tangent categories

Geoffrey Cruttwell; Jean-Simon Pacaud Lemay

doi:10.4230/LIPIcs.CSL.2024.21

Reverse tangent categories

Geoffrey Cruttwell, Jean-Simon Pacaud Lemay^*

^*Corresponding author for this work

School of Mathematical and Physical Sciences

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

17 Downloads (Pure)

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.

Original language	English
Title of host publication	CSL 2024
Subtitle of host publication	32nd EACSL Annual Conference on Computer Science Logic
Editors	Aniello Murano, Alexandra Silva
Place of Publication	Naples, Italy
Publisher	Dagstuhl Publishing
Pages	21:1-21:21
Number of pages	21
ISBN (Electronic)	9783959773102
DOIs	https://doi.org/10.4230/LIPIcs.CSL.2024.21
Publication status	Published - Feb 2024
Event	32nd EACSL Annual Conference on Computer Science Logic, CSL 2024 - Naples, Italy Duration: 19 Feb 2024 → 23 Feb 2024

Publication series

Name	LIPIcs - Leibniz International Proceedings in Informatics
Volume	288
ISSN (Print)	1868-8969

Conference

Conference	32nd EACSL Annual Conference on Computer Science Logic, CSL 2024
Country/Territory	Italy
City	Naples
Period	19/02/24 → 23/02/24

Bibliographical note

© Geoffrey Cruttwell and Jean-Simon Pacaud Lemay. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

Keywords

Categorical Machine Learning
Reverse Differential Categories
Reverse Tangent Categories
Tangent Categories

Access to Document

10.4230/LIPIcs.CSL.2024.21Licence: CC BY

Publisher version (open access)Final published version, 917 KBLicence: CC BY

Cite this

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title = "Reverse tangent categories",

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.",

keywords = "Categorical Machine Learning, Reverse Differential Categories, Reverse Tangent Categories, Tangent Categories",

author = "Geoffrey Cruttwell and Lemay, {Jean-Simon Pacaud}",

note = "{\textcopyright} Geoffrey Cruttwell and Jean-Simon Pacaud Lemay. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.; 32nd EACSL Annual Conference on Computer Science Logic, CSL 2024 ; Conference date: 19-02-2024 Through 23-02-2024",

year = "2024",

month = feb,

doi = "10.4230/LIPIcs.CSL.2024.21",

language = "English",

series = "LIPIcs - Leibniz International Proceedings in Informatics",

publisher = "Dagstuhl Publishing",

pages = "21:1--21:21",

editor = "Aniello Murano and Alexandra Silva",

booktitle = "CSL 2024",

address = "Germany",

}

Cruttwell, G & Lemay, J-SP 2024, Reverse tangent categories. in A Murano & A Silva (eds), CSL 2024: 32nd EACSL Annual Conference on Computer Science Logic., 21, LIPIcs - Leibniz International Proceedings in Informatics, vol. 288, Dagstuhl Publishing, Naples, Italy, pp. 21:1-21:21, 32nd EACSL Annual Conference on Computer Science Logic, CSL 2024, Naples, Italy, 19/02/24. https://doi.org/10.4230/LIPIcs.CSL.2024.21

Reverse tangent categories. / Cruttwell, Geoffrey; Lemay, Jean-Simon Pacaud.
CSL 2024: 32nd EACSL Annual Conference on Computer Science Logic. ed. / Aniello Murano; Alexandra Silva. Naples, Italy: Dagstuhl Publishing, 2024. p. 21:1-21:21 21 (LIPIcs - Leibniz International Proceedings in Informatics; Vol. 288).

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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AU - Cruttwell, Geoffrey

AU - Lemay, Jean-Simon Pacaud

N1 - © Geoffrey Cruttwell and Jean-Simon Pacaud Lemay. Version archived for private and non-commercial use with the permission of the author/s and according to publisher conditions. For further rights please contact the publisher.

PY - 2024/2

Y1 - 2024/2

N2 - 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.

AB - 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.

KW - Categorical Machine Learning

KW - Reverse Differential Categories

KW - Reverse Tangent Categories

KW - Tangent Categories

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DO - 10.4230/LIPIcs.CSL.2024.21

M3 - Conference proceeding contribution

AN - SCOPUS:85185222317

T3 - LIPIcs - Leibniz International Proceedings in Informatics

SP - 21:1-21:21

BT - CSL 2024

A2 - Murano, Aniello

A2 - Silva, Alexandra

PB - Dagstuhl Publishing

CY - Naples, Italy

T2 - 32nd EACSL Annual Conference on Computer Science Logic, CSL 2024

Y2 - 19 February 2024 through 23 February 2024

ER -

Reverse tangent categories

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DE23: New Foundations for Algebraic Geometry

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Reverse tangent categories

Abstract

Publication series

Conference

Bibliographical note

Keywords

Access to Document

Other files and links

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DE23: New Foundations for Algebraic Geometry

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