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Limitations of Shallow Networks Representing Finite Mappings

SYSNO ASEP	0485613
Document Type	J - Journal Article
R&D Document Type	Journal Article
Subsidiary J	Článek ve WOS
Title	Limitations of Shallow Networks Representing Finite Mappings
Author(s)	Kůrková, Věra (UIVT-O)_{RID, SAI, ORCID}
Source Title	Neural Computing & Applications. - : Springer - ISSN 0941-0643 Roč. 31, č. 6 (2019), s. 1783-1792
Number of pages	10 s.
Language	eng - English
Country	US - United States
Keywords	shallow and deep networks ; sparsity ; variational norms ; functions on large finite domains ; finite dictionaries of computational units ; pseudo-noise sequences ; perceptron networks
Subject RIV	IN - Informatics, Computer Science
OECD category	Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
R&D Projects	GA15-18108S GA ČR - Czech Science Foundation (CSF)
	GA18-23827S GA ČR - Czech Science Foundation (CSF)
Method of publishing	Open access
Institutional support	UIVT-O - RVO:67985807
UT WOS	000470746700008
EID SCOPUS	85052492938
DOI	10.1007/s00521-018-3680-1
Annotation	Limitations of capabilities of shallow networks to efficiently compute real-valued functions on finite domains are investigated. Efficiency is studied in terms of network sparsity and its approximate measures. It is shown that when a dictionary of computational units is not sufficiently large, computation of almost any uniformly randomly chosen function either represents a well-conditioned task performed by a large network or an ill-conditioned task performed by a network of a moderate size. The probabilistic results are complemented by a concrete example of a class of functions which cannot be efficiently computed by shallow perceptron networks. The class is constructed using pseudo-noise sequences which have many features of random sequences but can be generated using special polynomials. Connections to the No Free Lunch Theorem and the central paradox of coding theory are discussed.
Workplace	Institute of Computer Science
Contact	Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800
Year of Publishing	2020
Electronic address	http://dx.doi.org/10.1007/s00521-018-3680-1

Number of the records: 1