Complexity of Shallow Networks Representing Finite Mappings
Result description
Complexity of shallow (one-hidden-layer) networks representing finite multivariate mappings is investigated. Lower bounds are derived on growth of numbers of network units and sizes of output weights in terms of variational norms of mappings to be represented. Probability distributions of mappings whose computations require large networks are described. It is shown that due to geometrical properties of highdimensional Euclidean spaces, representation of almost any randomly chosen function on a sufficiently large domain by a shallow network with perceptrons requires untractably large network. Concrete examples of such functions are constructed using Hadamard matrices.
Keywords
Shallow feedforward networksSignum perceptronsFinite mappingsModel complexityHadamard matrices
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Complexity of Shallow Networks Representing Finite Mappings
Original language description
Complexity of shallow (one-hidden-layer) networks representing finite multivariate mappings is investigated. Lower bounds are derived on growth of numbers of network units and sizes of output weights in terms of variational norms of mappings to be represented. Probability distributions of mappings whose computations require large networks are described. It is shown that due to geometrical properties of highdimensional Euclidean spaces, representation of almost any randomly chosen function on a sufficiently large domain by a shallow network with perceptrons requires untractably large network. Concrete examples of such functions are constructed using Hadamard matrices.
Czech name
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Czech description
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Classification
Type
D - Article in proceedings
CEP classification
IN - Informatics
OECD FORD branch
—
Result continuities
Project
GA15-18108S: Model complexity of neural, radial, and kernel networks
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Article name in the collection
Artificial Intelligence and Soft Computing
ISBN
978-3-319-19323-6
ISSN
0302-9743
e-ISSN
—
Number of pages
10
Pages from-to
39-48
Publisher name
Springer
Place of publication
Cham
Event location
Zakopane
Event date
Jun 12, 2015
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
000364537800004
Basic information
Result type
D - Article in proceedings
CEP
IN - Informatics
Year of implementation
2015