Relational lenses

Bohannon, Aaron; Pierce, Benjamin C.; Vaughan, Jeffrey A.

doi:10.1145/1142351.1142399

Cited by 144 publications

(17 citation statements)

References 9 publications

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“…A third way to understand the request function is by analogy with other compositional structures: the request function plays an analogous role to the put function in an asymmetric lens [3] and the coplay function in an open game [11].…”

Section: The Category Of Learnersmentioning

confidence: 99%

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Backprop as Functor: A compositional perspective on supervised learning

Fong

Spivak

Tuyéras

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

130

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A supervised learning algorithm searches over a set of functions A → B parametrised by a space P to find the best approximation to some ideal function f : A → B. It does this by taking examples (a, f (a)) ∈ A × B, and updating the parameter according to some rule. We define a category where these update rules may be composed, and show that gradient descent-with respect to a fixed step size and an error function satisfying a certain property-defines a monoidal functor from a category of parametrised functions to this category of update rules. A key contribution is the notion of request function. This provides a structural perspective on backpropagation, giving a broad generalisation of neural networks and linking it with structures from bidirectional programming and open games.

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Section: The Category Of Learnersmentioning

confidence: 99%

“…This novel category Learn, synthesised from the above analysis of learning algorithms, nonetheless curiously resembles and is closely related to lenses [3] and open games [11], two well-known structures that also model compositional, bidirectional exchange information between interacting systems. We return to this briefly in Section VII.…”

Section: Introductionmentioning

confidence: 99%

Backprop as Functor: A compositional perspective on supervised learning

Fong

Spivak

Tuyéras

2019

2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)

130

View full text Add to dashboard Cite

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“…There are well-known languages and techniques (e.g. [6,7,27,29]) that provide concrete tools for realizing a BX. However, due to inherent complexity, it is difficult to determine when a BX does the "right thing".…”

Section: On Bi-and Multidirectional Synchronizationsmentioning

confidence: 99%

Controllable and decomposable multidirectional synchronizations

Bergmann

2021

Softw Syst Model

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Studying large-scale collaborative systems engineering projects across teams with differing intellectual property clearances, or healthcare solutions where sensitive patient data needs to be partially shared, or similar multi-user information systems over databases, all boils down to a common mathematical framework. Updateable views (lenses) and more generally bidirectional transformations are abstractions to study the challenge of exchanging information between participants with different read access privileges. The view provided to each participant must be different due to access control or other limitations, yet also consistent in a certain sense, to enable collaboration towards common goals. A collaboration system must apply bidirectional synchronization to ensure that after a participant modifies their view, the views of other participants are updated so that they are consistent again. While bidirectional transformations (synchronizations) have been extensively studied, there are new challenges that are unique to the multidirectional case. If complex consistency constraints have to be maintained, synchronizations that work fine in isolation may not compose well. We demonstrate and characterize a failure mode of the emergent behaviour, where a consistency restoration mechanism undoes the work of other participants. On the other end of the spectrum, we study the case where synchronizations work especially well together: we characterize very well-behaved multidirectional transformations, a non-trivial generalization from the bidirectional case. For the former challenge, we introduce a novel concept of controllability, while for the latter one, we propose a novel formal notion of faithful decomposition. Additionally, the paper proposes several novel properties of multidirectional transformations.

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“…How to keep two corresponding data structures synchronized is related both to the view-update problem [Kel85] and lenses [BPV06,FPP08,HPW11,WGW11]. We need in our approach to define a pair of transformations to map the source to the view, and the view to the source.…”

Section: Development Effortmentioning

confidence: 99%

Incremental Dynamic Updates with First-class Contexts.

Wernli¹,

Lungu²,

Nierstrasz³

2013

JOT

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Highly available software systems occasionally need to be updated while avoiding downtime. Dynamic software updates reduce downtime, but still require the system to reach a quiescent state in which a global update can be performed. This can be difficult for multi-threaded systems. We present a novel approach to dynamic updates using first-class contexts, called Theseus. First-class contexts make global updates unnecessary: existing threads run to termination in an old context, while new threads start in a new, updated context; consistency between contexts is ensured with the help of bidirectional transformations. We show that for multi-threaded systems with coherent memory, first-class contexts offer a practical and flexible approach to dynamic updates, with acceptable overhead.

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Relational lenses

Cited by 144 publications

References 9 publications

Backprop as Functor: A compositional perspective on supervised learning

Backprop as Functor: A compositional perspective on supervised learning

Controllable and decomposable multidirectional synchronizations

Incremental Dynamic Updates with First-class Contexts.

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