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Design of Continuous Attractor Networks with Monotonic Tuning Using a Symmetry Principle.
- Source :
-
Neural Computation . Feb2008, Vol. 20 Issue 2, p452-485. 34p. 1 Chart, 6 Graphs. - Publication Year :
- 2008
-
Abstract
- Neurons that sustain elevated firing in the absence of stimuli have been found in many neural systems. In graded persistent activity, neurons can sustain firing at many levels, suggesting a widely found type of network dynamics in which networks can relax to any one of a continuum of stationary states. The reproduction of these findings in model networks of nonlinear neurons has turned out to be nontrivial. A particularly insightful model has been the "bump attractor," in which a continuous attractor emerges through an underlying symmetry in the network connectivity matrix. This model, however, cannot account for data in which the persistent firing of neurons is a monotonic-rather than a bell-shaped-function of a stored variable. Here, we show that the symmetry used in the bump attractor network can be employed to create a whole family of continuous attractor networks, including those with monotonic tuning. Our design is based on tuning the external inputs to networks that have a connectivity matrix with Toeplitz symmetry. In particular, we provide a complete analytical solution of a line attractor network with monotonic tuning and show that for many other networks, the numerical tuning of synaptic weights reduces to the computation of a single parameter. [ABSTRACT FROM AUTHOR]
- Subjects :
- *NERVOUS system
*NEURONS
*REPRODUCTION
*CELLS
*PHYSIOLOGY
*EMBRYOLOGY
Subjects
Details
- Language :
- English
- ISSN :
- 08997667
- Volume :
- 20
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Neural Computation
- Publication Type :
- Academic Journal
- Accession number :
- 28320675
- Full Text :
- https://doi.org/10.1162/neco.2007.07-06-297