Journal of Statistical Physics

, Volume 164, Issue 1, pp 105–129 | Cite as

A Comparative Study of Sparse Associative Memories

  • Vincent Gripon
  • Judith Heusel
  • Matthias Löwe
  • Franck Vermet


We study various models of associative memories with sparse information, i.e. a pattern to be stored is a random string of 0s and 1s with about \(\log N\) 1s, only. We compare different synaptic weights, architectures and retrieval mechanisms to shed light on the influence of the various parameters on the storage capacity.


Neural networks Associative memory Sparse patterns Storage capacity Exponential inequalities 

Mathematics Subject Classification

Primary: 82C32 60K35 Secondary: 68T05 92B20 



We are very grateful to two anonymous referees for a very careful reading of a first version of the manuscript and valuable remarks that helped to improve its readability significantly.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Vincent Gripon
    • 1
  • Judith Heusel
    • 2
  • Matthias Löwe
    • 2
  • Franck Vermet
    • 3
  1. 1.Telecom Bretagne UMR CNRS Lab-STICCTechnopole Brest IroiseBrestFrance
  2. 2.Fachbereich Mathematik und InformatikUniversity of MünsterMünsterGermany
  3. 3.Laboratoire de Mathématiques, UMR CNRS 6205Université de Bretagne OccidentaleBrest Cedex 3France

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