TY - JOUR
T1 - Positive and negative circuits in discrete neural networks
AU - Aracena, Julio
AU - Demongeot, Jacques
AU - Goles, Eric
N1 - Funding Information:
Manuscript received May 30, 2001; revised July 30, 2002 and April 28, 2003. The work of J. Aracena and E. Goles was supported in part by the FONDAP program on Discrete Mathematics and French Cooperation.
PY - 2004/1
Y1 - 2004/1
N2 - We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points depending on the architecture of the network.
AB - We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points depending on the architecture of the network.
KW - Discrete neural networks (DNNs)
KW - Fixed points
KW - Graph
KW - Positive and negative circuits
KW - Positive feedback vertex sets
UR - http://www.scopus.com/inward/record.url?scp=1242331292&partnerID=8YFLogxK
U2 - 10.1109/TNN.2003.821555
DO - 10.1109/TNN.2003.821555
M3 - Article
C2 - 15387249
AN - SCOPUS:1242331292
VL - 15
SP - 77
EP - 83
JO - IEEE Transactions on Neural Networks
JF - IEEE Transactions on Neural Networks
SN - 1045-9227
IS - 1
ER -