The main result in this paper is that for a neural circuit of the Hopfield type with a symmetric connection matrix T, the negative semidefiniteness of T is a necessary and sufficient condition for Absolute Stability. The most significant theoretical implication is that the class of neural circuits with a negative semidefinite T is the largest class of circuits that can be employed for embedding and solving optimization problems without the risk of spurious responses.
Forti, M., Manetti, S., Marini, M. (1994). Necessary and sufficient condition for absolute stability of neural networks. IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I. FUNDAMENTAL THEORY AND APPLICATIONS, 41(7), 491-494 [10.1109/81.298364].
Necessary and sufficient condition for absolute stability of neural networks
Forti M.;
1994-01-01
Abstract
The main result in this paper is that for a neural circuit of the Hopfield type with a symmetric connection matrix T, the negative semidefiniteness of T is a necessary and sufficient condition for Absolute Stability. The most significant theoretical implication is that the class of neural circuits with a negative semidefinite T is the largest class of circuits that can be employed for embedding and solving optimization problems without the risk of spurious responses.
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https://hdl.handle.net/11365/9088
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