Hierarchical neural networks perform both serial and parallel processing

Neural Networks : the Official Journal of the International Neural Network Society
Elena AgliariFlavia Tavani

Abstract

In this work we study a Hebbian neural network, where neurons are arranged according to a hierarchical architecture such that their couplings scale with their reciprocal distance. As a full statistical mechanics solution is not yet available, after a streamlined introduction to the state of the art via that route, the problem is consistently approached through signal-to-noise technique and extensive numerical simulations. Focusing on the low-storage regime, where the amount of stored patterns grows at most logarithmical with the system size, we prove that these non-mean-field Hopfield-like networks display a richer phase diagram than their classical counterparts. In particular, these networks are able to perform serial processing (i.e. retrieve one pattern at a time through a complete rearrangement of the whole ensemble of neurons) as well as parallel processing (i.e. retrieve several patterns simultaneously, delegating the management of different patterns to diverse communities that build network). The tune between the two regimes is given by the rate of the coupling decay and by the level of noise affecting the system. The price to pay for those remarkable capabilities lies in a network's capacity smaller than the mean field ...Continue Reading

References

Aug 1, 1985·Physical Review A: General Physics·D J AmitH Sompolinsky
Oct 29, 2005·The Journal of Comparative Neurology·Lique M Coolen
Dec 19, 2012·Neural Networks : the Official Journal of the International Neural Network Society·Elena AgliariAndrea Galluzzi
Feb 2, 2013·Physical Review Letters·Elena AgliariFrancesco Moauro
May 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Elena AgliariFrancesco Moauro
Dec 20, 2014·Physical Review Letters·Peter SollichAdriano Barra
Jan 31, 2015·Physical Review Letters·Elena AgliariFlavia Tavani

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Citations

Aug 19, 2016·Scientific Reports·Giampiero BardellaTiziano Squartini
Jan 10, 2017·Scientific Reports·Elena Agliari, Flavia Tavani
Feb 20, 2019·Physical Review. E·Diego Fasoli, Stefano Panzeri
Jul 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Elena AgliariFlavia Tavani
Mar 18, 2016·Physical Review. E·Flavia Tavani, Elena Agliari

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