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2019

Lenses and Learners

Fong, Brendan, Johnson, Michael

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Understand

Lenses are a well-established structure for modelling bidirectional transformations, such as the interactions between a database and a view of it.

Lenses may be symmetric or asymmetric, and may be composed, forming the morphisms of a monoidal category.
More recently, the notion of a learner has been proposed: these provide a compositional way of modelling supervised learning algorithms, and again form the morphisms of a monoidal category.
In this paper, we show that the two concepts are tightly linked.

Lenses and Learners · Around

Built on

Update semantics of relational views
Bancilhon, F. and Spyratos, N. (1981) · 1981
Earlier work this paper cites.
Lenses and view update translation. Preprint
Pierce, B. and Schmitt, A. (2003) · 2003
Earlier work this paper cites.
Combinators for bi-directional tree transformations: A linguistic approach to the view update problem
Foster, J., Greenwald, M., Moore, J., Pierce, B. and Schmitt, A. (2007) · 2007
Earlier work this paper cites.
From State- to Delta-Based Bidirectional Model Transformations: the Asymmetric Case
Diskin, Z., Xiong, Y. and Czarnecki, K. (2011) · 2011
Earlier work this paper cites.
Symmetric Lenses
Hofmann, M., Pierce, B., and Wagner, D. (2011) · 2011
Earlier work this paper cites.

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Then

Multiple model synchronization with multiary delta lenses
Diskin, Z., König, H. and Lawford, M. (2018) · 2018
Later among the works it cites.
Backprop as functor: a compositional perspective on supervised learning
Original
Fong, B., Spivak, D. I. and Tuyéras, R. (2019) · 2019
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An Invitation to Applied Category Theory: Seven Sketches in Compositionality ,
Fong, B., and Spivak, D. I. (2019) · 2019
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