Machens, C. K., Brody, C. D. (February 2008) Design of continuous attractor networks with monotonic tuning using a symmetry principle. Neural Comput, 20 (2). pp. 452-85.
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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.
| Item Type: | Paper |
|---|---|
| Subjects: | organs, tissues, organelles, cell types and functions > tissues types and functions > neural networks organs, tissues, organelles, cell types and functions organs, tissues, organelles, cell types and functions > tissues types and functions |
| CSHL Authors: | |
| Communities: | CSHL labs > Brody lab |
| Depositing User: | Matt Covey |
| Date: | February 2008 |
| Date Deposited: | 26 Feb 2013 21:33 |
| Last Modified: | 26 Feb 2013 21:33 |
| Related URLs: | |
| URI: | https://repository.cshl.edu/id/eprint/27513 |
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