Continuous attractors of a class of recurrent neural networks |
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Authors: | Haixian Zhang Zhang Yi Lei Zhang |
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Affiliation: | aComputational Intelligence Laboratory, School of Computer Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, PR China |
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Abstract: | Recurrent neural networks (RNNs) may possess continuous attractors, a property that many brain theories have implicated in learning and memory. There is good evidence for continuous stimuli, such as orientation, moving direction, and the spatial location of objects could be encoded as continuous attractors in neural networks. The dynamical behaviors of continuous attractors are interesting properties of RNNs. This paper proposes studying the continuous attractors for a class of RNNs. In this network, the inhibition among neurons is realized through a kind of subtractive mechanism. It shows that if the synaptic connections are in Gaussian shape and other parameters are appropriately selected, the network can exactly realize continuous attractor dynamics. Conditions are derived to guarantee the validity of the selected parameters. Simulations are employed for illustration. |
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Keywords: | Continuous attractors Recurrent neural networks Gaussian functions Convergence Stable equilibrium point |
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