2 Search Results for "MacAdam, Benjamin"

Document
DOI: 10.4230/LIPIcs.FSCD.2025.26
Functorial Models of Differential Linear Logic

Authors: Marie Kerjean, Valentin Maestracci, and Morgan Rogers

Published in: LIPIcs, Volume 337, 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)

Abstract
Differentiation in logic has several sources of inspiration. The most recent is differentiable programming, models of which demand functoriality and good typing properties. More historical is reverse denotational semantics, taking inspiration from models of Linear Logic to differentiate proofs and λ-terms. In this paper, we take advantage of the rich structure of categorical models of Linear Logic to give a new functorial presentation of differentiation. We define differentiation as a functor from a coslice of the category of smooth maps to the category of linear maps. Extending linear-non-linear adjunction models of Linear Logic, this produces models of Differential Linear Logic. We use these functorial presentations to shed new light on integration in differential categories.
Cite as

Marie Kerjean, Valentin Maestracci, and Morgan Rogers. Functorial Models of Differential Linear Logic. In 10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 337, pp. 26:1-26:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{kerjean_et_al:LIPIcs.FSCD.2025.26,
  author =	{Kerjean, Marie and Maestracci, Valentin and Rogers, Morgan},
  title =	{{Functorial Models of Differential Linear Logic}},
  booktitle =	{10th International Conference on Formal Structures for Computation and Deduction (FSCD 2025)},
  pages =	{26:1--26:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-374-4},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{337},
  editor =	{Fern\'{a}ndez, Maribel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2025.26},
  URN =		{urn:nbn:de:0030-drops-236419},
  doi =		{10.4230/LIPIcs.FSCD.2025.26},
  annote =	{Keywords: Categorical semantics, Differential Programming, Linear Logic}
}
Document
DOI: 10.4230/LIPIcs.CSL.2020.18
Reverse Derivative Categories

Authors: Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher, Jean-Simon Pacaud Lemay, Benjamin MacAdam, Gordon Plotkin, and Dorette Pronk

Published in: LIPIcs, Volume 152, 28th EACSL Annual Conference on Computer Science Logic (CSL 2020)

Abstract
The reverse derivative is a fundamental operation in machine learning and automatic differentiation [Martín Abadi et al., 2015; Griewank, 2012]. This paper gives a direct axiomatization of a category with a reverse derivative operation, in a similar style to that given by [Blute et al., 2009] for a forward derivative. Intriguingly, a category with a reverse derivative also has a forward derivative, but the converse is not true. In fact, we show explicitly what a forward derivative is missing: a reverse derivative is equivalent to a forward derivative with a dagger structure on its subcategory of linear maps. Furthermore, we show that these linear maps form an additively enriched category with dagger biproducts.
Cite as

Robin Cockett, Geoffrey Cruttwell, Jonathan Gallagher, Jean-Simon Pacaud Lemay, Benjamin MacAdam, Gordon Plotkin, and Dorette Pronk. Reverse Derivative Categories. In 28th EACSL Annual Conference on Computer Science Logic (CSL 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 152, pp. 18:1-18:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{cockett_et_al:LIPIcs.CSL.2020.18,
  author =	{Cockett, Robin and Cruttwell, Geoffrey and Gallagher, Jonathan and Lemay, Jean-Simon Pacaud and MacAdam, Benjamin and Plotkin, Gordon and Pronk, Dorette},
  title =	{{Reverse Derivative Categories}},
  booktitle =	{28th EACSL Annual Conference on Computer Science Logic (CSL 2020)},
  pages =	{18:1--18:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-132-0},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{152},
  editor =	{Fern\'{a}ndez, Maribel and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2020.18},
  URN =		{urn:nbn:de:0030-drops-116611},
  doi =		{10.4230/LIPIcs.CSL.2020.18},
  annote =	{Keywords: Reverse Derivatives, Cartesian Reverse Differential Categories, Categorical Semantics, Cartesian Differential Categories, Dagger Categories, Automatic Differentiation}
}
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