Universal approximation theorem: Difference between revisions

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=== Reservoir computing and quantum reservoir computing===

In reservoir computing a sparse recurrent neural network with fixed weights equipped of fading memory and echo state property is followed by a trainable output layer. Its universality has been demonstrated separately for what concerns networks of rate neurons <ref>{{Cite journal |last1=Grigoryeva |first1=L. |last2=Ortega |first2=J.-P. |date=2018 |title=Echo state networks are universal |journal=Neural Networks |volume=108 |issue=1 |pages=495–508 |arxiv=1806.00797 |doi=10.1016/j.neunet.2018.08.025|pmid=30317134 }}</ref> and spiking neurons, respectively. <ref>{{Cite journal |lastlast1=Maass |firstfirst1=Wolfgang |last2=Markram |first2=Henry |date=2004 |title=On the computational power of circuits of spiking neurons |url=http://www.igi.tugraz.at/maass/psfiles/135.pdf |journal=Journal of computerComputer and systemSystem sciencesSciences |volume=69 |issue=4 |pages=593–616|doi=10.1016/j.jcss.2004.04.001 }}</ref> In 2024, the framework has been generalized and extended to quantum reservoirs where the reservoir is based on qubits defined over Hilbert spaces. <ref>{{cite arXiv |last1=Monzani |first1=Francesco |title=Universality conditions of unified classical and quantum reservoir computing |date=2024|eprint=2401.15067 |last2=Prati |first2=Enrico |class=quant-ph }}</ref>

=== Variants ===