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Limitations of Shallow Networks Representing Finite Mappings
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SYSNO ASEP 0485613 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Limitations of Shallow Networks Representing Finite Mappings Tvůrce(i) Kůrková, Věra (UIVT-O) RID, SAI, ORCID Zdroj.dok. Neural Computing & Applications. - : Springer - ISSN 0941-0643
Roč. 31, č. 6 (2019), s. 1783-1792Poč.str. 10 s. Jazyk dok. eng - angličtina Země vyd. US - Spojené státy americké Klíč. slova shallow and deep networks ; sparsity ; variational norms ; functions on large finite domains ; finite dictionaries of computational units ; pseudo-noise sequences ; perceptron networks Vědní obor RIV IN - Informatika Obor OECD Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) CEP GA15-18108S GA ČR - Grantová agentura ČR GA18-23827S GA ČR - Grantová agentura ČR Způsob publikování Open access Institucionální podpora UIVT-O - RVO:67985807 UT WOS 000470746700008 EID SCOPUS 85052492938 DOI 10.1007/s00521-018-3680-1 Anotace 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. Pracoviště Ústav informatiky Kontakt Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Rok sběru 2020 Elektronická adresa http://dx.doi.org/10.1007/s00521-018-3680-1
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