On the equivalence of two Hopfield-type networks

The inverted neural network (INN) and the Hopfield-clique network (HcN) are two models that may be viewed as modified versions of the Hopfield neural network. It is shown that the stable states of HcN and INN are equivalent for a particular choice of parameters. This equivalence extends to the storage of associative memories and its properties. It is also shown that steepest descent dynamics on HcN and INN are equivalent. Thus, HcN inherits the optical implementability of INN and INN inherits all the graph-theoretic analyses and applications of HcN. These equivalence results are obtained as corollaries of more general results for INN, the latter guided by previous partial graph-theoretic analyses of HcN in cases similar (but non-equivalent) to INN. An optimization algorithm on INN (t-annealing) is developed based on these results and in strong analogy with a similar previous algorithm on HcN (p-annealing). The efficacy of t-annealing is demonstrated