On the number of solutions of a class of nonlinear equations related to neural networks with tapered connections

Tetsuo Nishi, Norikazu Takahashi

Research output: Contribution to journalArticle

2 Citations (Scopus)


The number of solutions of a nonlinear equation x = sgn(Wx) is discussed. The equation is derived for the determination of equilibrium points of a kind of Hopfield neural networks. We impose some conditions on W. The conditions correspond to the case where a Hopfield neural network has n neurons arranged on a ring, each neuron has connections only from k preceding neurons and the magnitude of k connections decrease as the distance between two neurons increases. We show that the maximum number of solutions for the above case is extremely few and is independent of the number of neurons, n, if k is less than or equal to 4. We also show that the number of solutions generally increases exponentially with n by considering the case where k = n - 1.

Original languageEnglish
Pages (from-to)1299-1305
Number of pages7
JournalIEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
Issue number10
Publication statusPublished - Oct 1995
Externally publishedYes


ASJC Scopus subject areas

  • Hardware and Architecture
  • Information Systems
  • Electrical and Electronic Engineering

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