Complexity of Shallow Networks Representing Finite Mappings

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00443724" target="_blank" >RIV/67985807:_____/15:00443724 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1007/978-3-319-19324-3_4" target="_blank" >http://dx.doi.org/10.1007/978-3-319-19324-3_4</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-319-19324-3_4" target="_blank" >10.1007/978-3-319-19324-3_4</a>

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
—
Czech description
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Project
<a href="/en/project/GA15-18108S" target="_blank" >GA15-18108S: Model complexity of neural, radial, and kernel networks</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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