The IRMA Community
Newsletters
Research IRM
Click a keyword to search titles using our InfoSci-OnDemand powered search:
|
Neural Networks and Equilibria, Synchronization, and Time Lags
Abstract
All neural networks, both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”, in fact the sequential (discrete time) dynamics of the choice of synaptic weights. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. Regarding the second dynamics, the emergent computational capabilities of a recurrent neural network can be achieved provided it has many equilibria. The network task is achieved provided it approaches these equilibria. But the dynamical system has a dynamics induced a posteriori by the learning process that had established the synaptic weights. It is not compulsory that this a posteriori dynamics should have the required properties, hence they have to be checked separately. The standard stability properties (Lyapunov, asymptotic and exponential stability) are defined for a single equilibrium. Their counterpart for several equilibria are: mutability, global asymptotics, gradient behavior. For the definitions of these general concepts the reader is sent to Gelig et. al., (1978), Leonov et. al., (1992). In the last decades, the number of recurrent neural networks’ applications increased, they being designed for classification, identification and complex image, visual and spatio-temporal processing in fields as engineering, chemistry, biology and medicine (see, for instance: Fortuna et. al., 2001; Fink, 2004; Atencia et. al., 2004; Iwahori et. al., 2005; Maurer et. al., 2005; Guirguis & Ghoneimy, 2007). All these applications are mainly based on the existence of several equilibria for such networks, requiring them the “good behavior” properties above discussed. Another aspect of the qualitative analysis is the so-called synchronization problem, when an external stimulus, in most cases periodic or almost periodic has to be tracked (Gelig, 1982; Danciu, 2002). This problem is, from the mathematical point of view, nothing more but existence, uniqueness and global stability of forced oscillations.
Related Content
|
Kamel Mouloudj, Vu Lan Oanh LE, Achouak Bouarar, Ahmed Chemseddine Bouarar, Dachel Martínez Asanza, Mayuri Srivastava.
© 2024.
20 pages.
|
|
José Eduardo Aleixo, José Luís Reis, Sandrina Francisca Teixeira, Ana Pinto de Lima.
© 2024.
52 pages.
|
|
Jorge Figueiredo, Isabel Oliveira, Sérgio Silva, Margarida Pocinho, António Cardoso, Manuel Pereira.
© 2024.
24 pages.
|
|
Fatih Pinarbasi.
© 2024.
20 pages.
|
|
Stavros Kaperonis.
© 2024.
25 pages.
|
|
Thomas Rui Mendes, Ana Cristina Antunes.
© 2024.
24 pages.
|
|
Nuno Geada.
© 2024.
12 pages.
|
|
|