Graph degree sequence solely determines the expected hopfield network pattern stability

Daniel Berend, Shlomi Dolev, Ariel Hanemann

Research output: Contribution to journalLetterpeer-review

2 Scopus citations

Abstract

We analyze the effect of network topology on the pattern stability of the Hopfield neural network in the case of general graphs. The patterns are randomly selected from a uniform distribution. We start the Hopfield procedure from some pattern v. An error in an entry e of v is the situation where, if the procedure is started at e, the value of e flips. Such an entry is an instability point. Note that we disregard the value at e by the end of the procedure, as well as what happens if we start the procedure from another pattern v v' or another entry e' of v. We measure the instability of the system by the expected total number of instability points of all the patterns. Ourmain result is that the instability of the system does not depend on the exact topology of the underlying graph, but rather only on its degree sequence. Moreover, for a large number of nodes, the instability can be approximated by, where ϕ is the standard normal distribution function and δ1, . . . , δn are the degrees of the nodes.

Original languageEnglish
Pages (from-to)202-210
Number of pages9
JournalNeural Computation
Volume27
Issue number1
DOIs
StatePublished - 26 Jan 2015

ASJC Scopus subject areas

  • Arts and Humanities (miscellaneous)
  • Cognitive Neuroscience

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