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Backprop as Functor: A compositional perspective on supervised learning

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

Backpropagation gives

doi:10.1109/lics.2019.8785665
dblp:conf/lics/FongST19
fatcat:g7btwbi5frfjliyghc4bkiaakq
*a*way*to*compute the derivative of*a*function via message passing on*a*network, significantly*speeding**up*learning. ... This request function allows us*to*construct training*data**for*all sub-parts of*a*composite learning*algorithm*from training*data**for*just the input and output of the composite*algorithm*. ...##
###
Backprop as Functor: A compositional perspective on supervised learning
[article]

2019
*
arXiv
*
pre-print

*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. ... 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 ... quicker

*to*compute

*for*lower dimensional spaces, expresses the

*speed*

*up*in learning provided by backpropagation. ...

##
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CLASSIFYING PROCESSES: AN ESSAY IN APPLIED ONTOLOGY

2012
*
Ratio
*

the first steps of

doi:10.1111/j.1467-9329.2012.00557.x
pmid:23888086
pmcid:PMC3718480
fatcat:ecgsa3rf6jbfpdk6rbrijz6lmq
*an*approach*to*the classification of such processes within the BFO framework. 1 ... BFO is*a**bicategorial*ontology, embracing both three-dimensionalist (continuant) and four-dimensionalist (occurrent) perspectives within*a*single framework. ... First*Approximation**to**a*Solution of the Problem of Process Measurement*Data*How, then, do we respond*to*the need on the part of the users of BFO*to*annotate*data*deriving from measurements which have ...##
###
Classifying Processes: An Essay in Applied Ontology
[chapter]

2013
*
Classifying Reality
*

First

doi:10.1002/9781118627747.ch6
fatcat:f72xdelfvzab5e4hvccyozzvhy
*Approximation**to**a*Solution of the Problem of Process Measurement*Data*How, then, do we respond*to*the need on the part of the users of BFO*to*annotate*data*deriving from measurements which have ... when we talk,*for*example, of the*speed*of light, or the*speed*of the earth, or the*speed*of*a*billiard ball. ...##
###
Lenses and Learners
[article]

2019
*
arXiv
*
pre-print

Lenses are

arXiv:1903.03671v2
fatcat:ot2vkmpognabpgrqci2helzg4e
*a*well-established*structure**for*modelling bidirectional transformations, such as the interactions between*a*database and*a*view of it. ... 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. ... BF thanks Jules Hedges*for*first bringing the contents of Remark 4.7*to*his attention. ...##
###
Programs: Improvements, Complexity, and Meanings (Dagstuhl Seminar 98231)

1998

The organizers wish

doi:10.4230/dagsemrep.213
fatcat:j3wgtbf5ufb6flypjmweaswdsu
*to*thank all the participants, as well has the Dagstuhl staff,*for*making this*a*successful meeting. ...*A*considerable amount of bridge building took place, but there were clearly some chasms no one yet knows how*to*cross (e.g., how*to*deal*with*all the issues involved in rigorous complexity analyses of ... We present*a*new*application*of Berry and Curien's intensional semantics of sequential*algorithms*on concrete*data**structures*and its related programming language, CDS0. ...##
###
Seven Sketches in Compositionality: An Invitation to Applied Category Theory
[article]

2018
*
arXiv
*
pre-print

The tour takes place over seven sketches, each pairing

arXiv:1803.05316v3
fatcat:mpg54meyrngepe3ohm7i2h5pt4
*an*evocative*application*, such as databases, electric circuits, or dynamical systems,*with*the exploration of*a*categorical*structure*, such as adjoint ... This book is*an*invitation*to*discover advanced topics in category theory through concrete, real-world examples. It aims*to*give*a*tour:*a*gentle, quick introduction*to*guide later exploration. ... We want*to*draw the graph corresponding*to*the instance I : G → Set shown below: Email sent_by received_by Em_1 Bob Grace Em_2 Grace Pat Em_3 Bob Emory Em_4 Sue Doug Em_5 Doug Sue Em_6 Bob Bob ...##
###
Short Steps in Noncommutative Geometry
[article]

2019
*
arXiv
*
pre-print

*A*noncommutative algebra is

*an*associative algebra in which the multiplication is not commutative, that is,

*for*which xy does not always equal yx; or more generally

*an*algebraic

*structure*in which one ... Noncommutative geometry (NCG) is

*a*branch of mathematics concerned

*with*

*a*geometric approach

*to*noncommutative algebras, and

*with*the construction of spaces that are locally presented by noncommutative ...

*up*

*to*

*a*2-isomorphism. ...

##
###
This Week's Finds in Mathematical Physics (1-50)
[article]

2022
*
arXiv
*
pre-print

These issues focus on quantum gravity, topological quantum field theory, knot theory, and

arXiv:2101.04168v3
fatcat:kh5eurusrjevbkttpuq24p3s4q
*applications*of n-categories*to*these subjects. ... These are the first 50 issues of This Week's Finds of Mathematical Physics, from January 19, 1993*to*March 12, 1995. ... We introduce*a*path-dependent hamiltonian representation (the path representation)*for*SU (2)*with*fermions in 3 + 1 dimensions. ...##
###
This Week's Finds in Mathematical Physics (51-100)
[article]

2022
*
arXiv
*
pre-print

These are the second 50 issues of This Week's Finds of Mathematical Physics, from April 23, 1995

arXiv:2203.02631v1
fatcat:mhrjnnmee5a7nljvh4jt4qyou4
*to*March 23, 1997. ... But now suppose one wanted*to*build*a*computer language that could not only deal*with*all sorts of*data*types corresponding*to*different "sets*with*essentially algebraic*structure*", but also various "categories ... Mathematically sophisticated computer scientists want*to*be able define*data*types corresponding*to*arbitrary sorts of sets*with*essentially algebraic*structure*, and*to*play around*with*them easily. ...##
###
Behavioral Congruences and Verification of Graph Transformation Systems with Applications to Model Refactoring
[article]

2008

This

doi:10.14279/depositonce-2032
fatcat:xjkmz7g575gyfegfsja3gmn6bq
*algorithm*forms the core of*a*tool support which will enable us*to*come*up**with*behavior analysi [...] ... The concept of borrowed contexts has opened*up*graph transformations*to*the notion of*an*external "observer" where graphs (specifying systems) may interact*with**an*environment in order*to*evolve. ... Proof Techniques*for*DPO-BC*with*NACs We introduce here some proof techniques*to**speed**up*the bisimulation checking procedure. ...