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Author (up) Goles, E.; Ruz, G.A. pdf  doi
  Title Dynamics of neural networks over undirected graphs Type
  Year 2015 Publication Neural Networks Abbreviated Journal Neural Netw.  
  Volume 63 Issue Pages 156-169  
  Keywords Neural networks; Undirected graphs; Discrete updating schemes; Attractors; Fixed points; Cycles  
  Abstract In this paper we study the dynamical behavior of neural networks such that their interconnections are the incidence matrix of an undirected finite graph G = (V, E) (i.e., the weights belong to {0, 1}). The network may be updated synchronously (every node is updated at the same time), sequentially (nodes are updated one by one in a prescribed order) or in a block-sequential way (a mixture of the previous schemes). We characterize completely the attractors (fixed points or cycles). More precisely, we establish the convergence to fixed points related to a parameter alpha(G), taking into account the number of loops, edges, vertices as well as the minimum number of edges to remove from E in order to obtain a maximum bipartite graph. Roughly, alpha(G') < 0 for any G' subgraph of G implies the convergence to fixed points. Otherwise, cycles appear. Actually, for very simple networks (majority functions updated in a block-sequential scheme such that each block is of minimum cardinality two) we exhibit cycles with nonpolynomial periods. (C) 2014 Elsevier Ltd. All rights reserved.  
  Address [Goles, Eric; Ruz, Gonzalo A.] Univ Adolfo Ibanez, Fac Ingn & Ciencias, Santiago, Chile, Email:;  
  Corporate Author Thesis  
  Publisher Pergamon-Elsevier Science Ltd Place of Publication Editor  
  Language English Summary Language Original Title  
  Series Editor Series Title Abbreviated Series Title  
  Series Volume Series Issue Edition  
  ISSN 0893-6080 ISBN Medium  
  Area Expedition Conference  
  Notes WOS:000349730800015 Approved  
  Call Number UAI @ eduardo.moreno @ Serial 460  
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