Corpus ID: 73728981

Lenses and Learners

@inproceedings{Fong2019LensesAL,
  title={Lenses and Learners},
  author={B. Fong and Michael Johnson},
  booktitle={Bx@PLW},
  year={2019}
}
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… Expand

Paper Mentions

Supervised categorical learning as change propagation with delta lenses
  • Z. Diskin
  • Computer Science, Mathematics
  • ArXiv
  • 2019
TLDR
A notion of an asymmetric learning delta lens with amendment is defined, and how ala-lens can be organized into a symmetric monoidal category is shown, showing that sequential and parallel composition of well-behaved alA-lenses are also wb so that wb ala -lenses constitute a full sm-subcategory of ala. Expand
Backprop as Functor: A compositional perspective on supervised learning
TLDR
A key contribution is the notion of request function, which provides a structural perspective on backpropagation, giving a broad generalisation of neural networks and linking it with structures from bidirectional programming and open games. Expand
Multicategories of Multiary Lenses
TLDR
A class of asymmetric amendment lenses called spg-lenses (stable putget lenses) is introduced which is more general than well-behaved amendment lenses, but is closed under composition, and it is shown how to use spg -lenses to capture a wide class of mutidirectional transformations which compose well and form a well-known and long-standing structure, a multicategory — a multicategories of multiary lenses. Expand
L G ] 2 M ar 2 02 1 Categorical Foundations of Gradient-Based Learning
We propose a categorical foundation of gradientbased machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories. This foundation provides a powerfulExpand
Profunctor optics and traversals
TLDR
It is shown that a refinement of the notion of optic is required in order to model it faithfully in Haskell programming, and two different approaches to composition between profunctor optics of different families are given: using distributive laws between the monads defining them, and using coproducts of monads. Expand
Profunctor optics, a categorical update
TLDR
This work generalizes a classic result by Pastro and Street on Tambara theory and uses it to describe mixed V-enriched profunctor optics and to endow them with V-category structure. Expand
Category Theory in Machine Learning
TLDR
This work aims to document the motivations, goals and common themes across these applications of category theory in machine learning, touching on gradient-based learning, probability, and equivariant learning. Expand
Categorical Foundations of Gradient-Based Learning
TLDR
A categorical foundation of gradientbased machine learning algorithms in terms of lenses, parametrised maps, and reverse derivative categories is proposed, which encompasses a variety of gradient descent algorithms such as ADAM, AdaGrad, and Nesterov momentum. Expand
Mathematical background for statistical games 2 . 1 . Compositional probability , concretely and abstractly
  • 2021
Operads for complex system design specification, analysis and synthesis
TLDR
It is argued that operads provide an effective knowledge representation to address scalability challenges for complex system design and recent progress in effective modelling is described. Expand
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A key contribution is the notion of request function, which provides a structural perspective on backpropagation, giving a broad generalisation of neural networks and linking it with structures from bidirectional programming and open games. Expand
Multicategories of Multiary Lenses
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A class of asymmetric amendment lenses called spg-lenses (stable putget lenses) is introduced which is more general than well-behaved amendment lenses, but is closed under composition, and it is shown how to use spg -lenses to capture a wide class of mutidirectional transformations which compose well and form a well-known and long-standing structure, a multicategory — a multicategories of multiary lenses. Expand
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