LearningCyclesbringsChaos inContinuous HopfieldNetworks
Colin Molter · 2005
Thispaperaimsatstudying theimpact ofan hebbian learning algorithm ontherecurrent neural network's un- derlying dynamics. Twodifferent kinds oflearning arecompared inordertoencode information intheattractors oftheHopfield neural net: thestoring ofstatic patterns andthestoring ofcyclic patterns. Weshowthat ifthestoring ofstatic patterns leads toa reduction ofthepotential dynamics following thelearning phase, thelearning ofcyclic patterns tends toincrease thedimension ofthepotential attractors instead. Infact, suchlearning may beusedasa extraroute tochaos: themorecycles tobe learned, themorethenetwork showsasspontaneous dynamics a formofchaotic itinerancy amongbrief oscillatory periods. These results areinline withtheobservations madebyFreeman inthe olfactory bulboftherabbit: cycles areusedtostore information andthechaotic dynaniics appears asthebackground regime composed ofthose cyclic memory bags. Itconfirms precedent papers inwhichitwasobserved thathugeencoding capacity in termofcyclic attractors implies strong presence ofchaos.