publication . Article . 2017

Consecutive and non-consecutive heteroclinic cycles in Hopfield networks

Chossat, Pascal; Krupa, Martin;
Restricted
  • Published: 07 Feb 2017 Journal: Dynamical Systems, volume 32, pages 46-60 (issn: 1468-9367, eissn: 1468-9375, Copyright policy)
  • Publisher: Informa UK Limited
  • Country: France
Abstract
International audience; We review and extend the previous work where a model was introduced for Hopfield-type neural networks, which allows for the existence of heteroclinic dynamics between steady patterns. This dynamics is a mathematical model of periodic or aperiodic switching between stored information items in the brain, in particular, in the context of sequential memory or cognitive tasks as observed in experiments. The basic question addressed in this work is whether, given a sequence of steady patterns, it is possible by applying classical learning rules to build a matrix of connections between neurons in the network, such that a heteroclinic dynamics li...
Subjects
free text keywords: Topology, Hopfield network, Learning rule, Aperiodic graph, Matrix (mathematics), Periodic graph (geometry), Artificial neural network, Mathematics, Sequential access memory, Network architecture, [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS], [SCCO.NEUR]Cognitive science/Neuroscience
Funded by
EC| NERVI
Project
NERVI
From single neurons to visual perception
  • Funder: European Commission (EC)
  • Project Code: 227747
  • Funding stream: FP7 | SP2 | ERC
,
EC| BRAINSCALES
Project
BRAINSCALES
Brain-inspired multiscale computation in neuromorphic hybrid systems
  • Funder: European Commission (EC)
  • Project Code: 269921
  • Funding stream: FP7 | SP1 | ICT
,
EC| MATHEMACS
Project
MATHEMACS
MATHEmatics of Multi-level Anticipatory Complex Systems
  • Funder: European Commission (EC)
  • Project Code: 318723
  • Funding stream: FP7 | SP1 | ICT
Communities
FET FP7FET Proactive: FET proactive 8: Brain Inspired ICT
FET FP7FET Proactive: Brain-inspired multiscale computation in neuromorphic hybrid systems
FET FP7FET Proactive: Dynamics of Multi-Level Complex Systems (DyM-CS)
FET FP7FET Proactive: MATHEmatics of Multi-level Anticipatory Complex Systems
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publication . Article . 2017

Consecutive and non-consecutive heteroclinic cycles in Hopfield networks

Chossat, Pascal; Krupa, Martin;