Approximation by superpositions of a sigmoidal function View Full Text


Ontology type: schema:ScholarlyArticle      Open Access: True


Article Info

DATE

1989-12

AUTHORS

G. Cybenko

ABSTRACT

In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks. More... »

PAGES

303-314

References to SciGraph publications

Journal

Identifiers

URI

http://scigraph.springernature.com/pub.10.1007/bf02551274

DOI

http://dx.doi.org/10.1007/bf02551274

DIMENSIONS

https://app.dimensions.ai/details/publication/pub.1023250347


Indexing Status Check whether this publication has been indexed by Scopus and Web Of Science using the SN Indexing Status Tool
Incoming Citations Browse incoming citations for this publication using opencitations.net

JSON-LD is the canonical representation for SciGraph data.

TIP: You can open this SciGraph record using an external JSON-LD service: JSON-LD Playground Google SDTT

[
  {
    "@context": "https://springernature.github.io/scigraph/jsonld/sgcontext.json", 
    "about": [
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/01", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mathematical Sciences", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/09", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0102", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Applied Mathematics", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0906", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Electrical and Electronic Engineering", 
        "type": "DefinedTerm"
      }, 
      {
        "id": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/0913", 
        "inDefinedTermSet": "http://purl.org/au-research/vocabulary/anzsrc-for/2008/", 
        "name": "Mechanical Engineering", 
        "type": "DefinedTerm"
      }
    ], 
    "author": [
      {
        "affiliation": {
          "alternateName": "Center for Supercomputing Research and Development and Department of Electrical and Computer Engineering, University of Illinois, 61801, Urbana, Illinois, USA", 
          "id": "http://www.grid.ac/institutes/grid.35403.31", 
          "name": [
            "Center for Supercomputing Research and Development and Department of Electrical and Computer Engineering, University of Illinois, 61801, Urbana, Illinois, USA"
          ], 
          "type": "Organization"
        }, 
        "familyName": "Cybenko", 
        "givenName": "G.", 
        "id": "sg:person.011441523233.54", 
        "sameAs": [
          "https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011441523233.54"
        ], 
        "type": "Person"
      }
    ], 
    "citation": [
      {
        "id": "sg:pub.10.1007/bf00336857", 
        "sameAs": [
          "https://app.dimensions.ai/details/publication/pub.1040529426", 
          "https://doi.org/10.1007/bf00336857"
        ], 
        "type": "CreativeWork"
      }
    ], 
    "datePublished": "1989-12", 
    "datePublishedReg": "1989-12-01", 
    "description": "In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks.", 
    "genre": "article", 
    "id": "sg:pub.10.1007/bf02551274", 
    "isAccessibleForFree": true, 
    "isPartOf": [
      {
        "id": "sg:journal.1135855", 
        "issn": [
          "0932-4194", 
          "1435-568X"
        ], 
        "name": "Mathematics of Control, Signals, and Systems", 
        "publisher": "Springer Nature", 
        "type": "Periodical"
      }, 
      {
        "issueNumber": "4", 
        "type": "PublicationIssue"
      }, 
      {
        "type": "PublicationVolume", 
        "volumeNumber": "2"
      }
    ], 
    "keywords": [
      "finite linear combination", 
      "approximation properties", 
      "single hidden layer neural network", 
      "univariate functions", 
      "continuous functions", 
      "hidden layer neural network", 
      "unit hypercube", 
      "feedforward neural network", 
      "neural network", 
      "linear combination", 
      "affine functionals", 
      "real variables", 
      "layer neural network", 
      "sigmoidal nonlinearity", 
      "arbitrary decision regions", 
      "possible types", 
      "nonlinearity", 
      "sigmoidal function", 
      "decision regions", 
      "artificial neural network", 
      "hidden layer", 
      "open question", 
      "approximation", 
      "functionals", 
      "hypercube", 
      "representability", 
      "network", 
      "function", 
      "superposition", 
      "class", 
      "set", 
      "variables", 
      "properties", 
      "mild conditions", 
      "layer", 
      "conditions", 
      "results", 
      "types", 
      "region", 
      "combination", 
      "questions", 
      "composition", 
      "support", 
      "paper"
    ], 
    "name": "Approximation by superpositions of a sigmoidal function", 
    "pagination": "303-314", 
    "productId": [
      {
        "name": "dimensions_id", 
        "type": "PropertyValue", 
        "value": [
          "pub.1023250347"
        ]
      }, 
      {
        "name": "doi", 
        "type": "PropertyValue", 
        "value": [
          "10.1007/bf02551274"
        ]
      }
    ], 
    "sameAs": [
      "https://doi.org/10.1007/bf02551274", 
      "https://app.dimensions.ai/details/publication/pub.1023250347"
    ], 
    "sdDataset": "articles", 
    "sdDatePublished": "2022-10-01T06:27", 
    "sdLicense": "https://scigraph.springernature.com/explorer/license/", 
    "sdPublisher": {
      "name": "Springer Nature - SN SciGraph project", 
      "type": "Organization"
    }, 
    "sdSource": "s3://com-springernature-scigraph/baseset/20221001/entities/gbq_results/article/article_197.jsonl", 
    "type": "ScholarlyArticle", 
    "url": "https://doi.org/10.1007/bf02551274"
  }
]
 

Download the RDF metadata as:  json-ld nt turtle xml License info

HOW TO GET THIS DATA PROGRAMMATICALLY:

JSON-LD is a popular format for linked data which is fully compatible with JSON.

curl -H 'Accept: application/ld+json' 'https://scigraph.springernature.com/pub.10.1007/bf02551274'

N-Triples is a line-based linked data format ideal for batch operations.

curl -H 'Accept: application/n-triples' 'https://scigraph.springernature.com/pub.10.1007/bf02551274'

Turtle is a human-readable linked data format.

curl -H 'Accept: text/turtle' 'https://scigraph.springernature.com/pub.10.1007/bf02551274'

RDF/XML is a standard XML format for linked data.

curl -H 'Accept: application/rdf+xml' 'https://scigraph.springernature.com/pub.10.1007/bf02551274'


 

This table displays all metadata directly associated to this object as RDF triples.

117 TRIPLES      21 PREDICATES      73 URIs      61 LITERALS      6 BLANK NODES

Subject Predicate Object
1 sg:pub.10.1007/bf02551274 schema:about anzsrc-for:01
2 anzsrc-for:0102
3 anzsrc-for:09
4 anzsrc-for:0906
5 anzsrc-for:0913
6 schema:author Nc4fbdc6031b54816a7723678a65722da
7 schema:citation sg:pub.10.1007/bf00336857
8 schema:datePublished 1989-12
9 schema:datePublishedReg 1989-12-01
10 schema:description In this paper we demonstrate that finite linear combinations of compositions of a fixed, univariate function and a set of affine functionals can uniformly approximate any continuous function ofn real variables with support in the unit hypercube; only mild conditions are imposed on the univariate function. Our results settle an open question about representability in the class of single hidden layer neural networks. In particular, we show that arbitrary decision regions can be arbitrarily well approximated by continuous feedforward neural networks with only a single internal, hidden layer and any continuous sigmoidal nonlinearity. The paper discusses approximation properties of other possible types of nonlinearities that might be implemented by artificial neural networks.
11 schema:genre article
12 schema:isAccessibleForFree true
13 schema:isPartOf N0104f39e06f9482cb2c25f2bc4f2dd84
14 Nc7d9ba220bdb42908370d42f8d83e66e
15 sg:journal.1135855
16 schema:keywords affine functionals
17 approximation
18 approximation properties
19 arbitrary decision regions
20 artificial neural network
21 class
22 combination
23 composition
24 conditions
25 continuous functions
26 decision regions
27 feedforward neural network
28 finite linear combination
29 function
30 functionals
31 hidden layer
32 hidden layer neural network
33 hypercube
34 layer
35 layer neural network
36 linear combination
37 mild conditions
38 network
39 neural network
40 nonlinearity
41 open question
42 paper
43 possible types
44 properties
45 questions
46 real variables
47 region
48 representability
49 results
50 set
51 sigmoidal function
52 sigmoidal nonlinearity
53 single hidden layer neural network
54 superposition
55 support
56 types
57 unit hypercube
58 univariate functions
59 variables
60 schema:name Approximation by superpositions of a sigmoidal function
61 schema:pagination 303-314
62 schema:productId N91b716ca23054310af7c16962795a783
63 Ncc06cf305fd14b3b9ed80a275d8f9e9f
64 schema:sameAs https://app.dimensions.ai/details/publication/pub.1023250347
65 https://doi.org/10.1007/bf02551274
66 schema:sdDatePublished 2022-10-01T06:27
67 schema:sdLicense https://scigraph.springernature.com/explorer/license/
68 schema:sdPublisher N465aa7bb92ee4d26aacb2796bbf74dc9
69 schema:url https://doi.org/10.1007/bf02551274
70 sgo:license sg:explorer/license/
71 sgo:sdDataset articles
72 rdf:type schema:ScholarlyArticle
73 N0104f39e06f9482cb2c25f2bc4f2dd84 schema:issueNumber 4
74 rdf:type schema:PublicationIssue
75 N465aa7bb92ee4d26aacb2796bbf74dc9 schema:name Springer Nature - SN SciGraph project
76 rdf:type schema:Organization
77 N91b716ca23054310af7c16962795a783 schema:name dimensions_id
78 schema:value pub.1023250347
79 rdf:type schema:PropertyValue
80 Nc4fbdc6031b54816a7723678a65722da rdf:first sg:person.011441523233.54
81 rdf:rest rdf:nil
82 Nc7d9ba220bdb42908370d42f8d83e66e schema:volumeNumber 2
83 rdf:type schema:PublicationVolume
84 Ncc06cf305fd14b3b9ed80a275d8f9e9f schema:name doi
85 schema:value 10.1007/bf02551274
86 rdf:type schema:PropertyValue
87 anzsrc-for:01 schema:inDefinedTermSet anzsrc-for:
88 schema:name Mathematical Sciences
89 rdf:type schema:DefinedTerm
90 anzsrc-for:0102 schema:inDefinedTermSet anzsrc-for:
91 schema:name Applied Mathematics
92 rdf:type schema:DefinedTerm
93 anzsrc-for:09 schema:inDefinedTermSet anzsrc-for:
94 schema:name Engineering
95 rdf:type schema:DefinedTerm
96 anzsrc-for:0906 schema:inDefinedTermSet anzsrc-for:
97 schema:name Electrical and Electronic Engineering
98 rdf:type schema:DefinedTerm
99 anzsrc-for:0913 schema:inDefinedTermSet anzsrc-for:
100 schema:name Mechanical Engineering
101 rdf:type schema:DefinedTerm
102 sg:journal.1135855 schema:issn 0932-4194
103 1435-568X
104 schema:name Mathematics of Control, Signals, and Systems
105 schema:publisher Springer Nature
106 rdf:type schema:Periodical
107 sg:person.011441523233.54 schema:affiliation grid-institutes:grid.35403.31
108 schema:familyName Cybenko
109 schema:givenName G.
110 schema:sameAs https://app.dimensions.ai/discover/publication?and_facet_researcher=ur.011441523233.54
111 rdf:type schema:Person
112 sg:pub.10.1007/bf00336857 schema:sameAs https://app.dimensions.ai/details/publication/pub.1040529426
113 https://doi.org/10.1007/bf00336857
114 rdf:type schema:CreativeWork
115 grid-institutes:grid.35403.31 schema:alternateName Center for Supercomputing Research and Development and Department of Electrical and Computer Engineering, University of Illinois, 61801, Urbana, Illinois, USA
116 schema:name Center for Supercomputing Research and Development and Department of Electrical and Computer Engineering, University of Illinois, 61801, Urbana, Illinois, USA
117 rdf:type schema:Organization
 




Preview window. Press ESC to close (or click here)


...