A condition for global convergence of a class of symmetric neural circuits

A sufficient condition is proved guaranteeing that a class of neural circuits that includes the Hopfield model as a special case is globally convergent towards a unique stable equilibrium. The condition only requires symmetry and negative semi-definiteness of the neuron connection matrix T and is extremely simple to check and apply in practice. The consequences of the above result are discussed in the context of neural circuits for optimization of quadratic cost functions