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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 et al. (Fri,) studied this question.