Dynamics of neural networks over undirected graphs
Goles
E
author
Ruz
G
A
author
2015
English
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.
Neural networks
Undirected graphs
Discrete updating schemes
Attractors
Fixed points
Cycles
WOS:000349730800015
exported from refbase (show.php?record=460), last updated on Sat, 11 Apr 2015 08:00:29 -0300
text
files/421_Goles+Ruz2014.pdf
10.1016/j.neunet.2014.10.013
Goles+Ruz2015
Neural Networks
Neural Netw.
2015
Pergamon-Elsevier Science Ltd
continuing
periodical
academic journal
63
156
169
0893-6080