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They are in fact [[recursive neural network]]s with a particular structure: that of a linear chain. Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step.
From a time-series perspective, RNNs can appear as nonlinear versions of [[finite impulse response]] and [[infinite impulse response]] filters and also as a [[nonlinear autoregressive exogenous model]] (NARX).<ref>{{cite journal |url={{google books |plainurl=y |id=830-HAAACAAJ |page=208}} |title=Computational Capabilities of Recurrent NARX Neural Networks |last1=Siegelmann |first1=Hava T. |last2=Horne |first2=Bill G. |last3=Giles |first3=C. Lee |journal= IEEE Transactions on Systems, Man, and Cybernetics - Part B: Cybernetics|volume=27 |issue=2 |pages=208–15 |year=1995 |pmid=18255858 |doi=10.1109/3477.558801 |citeseerx=10.1.1.48.7468 }}</ref> RNN has infinite impulse response whereas [[convolutional neural network]]
The effect of memory-based learning for the recognition of sequences can also be implemented by a more biological-based model which uses the silencing mechanism exhibited in neurons with a relatively high frequency spiking activity.<ref>{{Cite journal |last1=Hodassman |first1=Shiri |last2=Meir |first2=Yuval |last3=Kisos |first3=Karin |last4=Ben-Noam |first4=Itamar |last5=Tugendhaft |first5=Yael |last6=Goldental |first6=Amir |last7=Vardi |first7=Roni |last8=Kanter |first8=Ido |date=2022-09-29 |title=Brain inspired neuronal silencing mechanism to enable reliable sequence identification |journal=Scientific Reports |volume=12 |issue=1 |pages=16003 |doi=10.1038/s41598-022-20337-x |pmid=36175466 |pmc=9523036 |arxiv=2203.13028 |bibcode=2022NatSR..1216003H |issn=2045-2322|doi-access=free }}</ref>
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