Construction of energy landscape for discrete Hopfield associative memory with guaranteed error correction capability

An energy function-based auto-associative memory design method to store a given set of unipolar binary memory vectors as attractive fixed points of an asynchronous discrete Hopfield network is presented. The discrete quadratic energy function whose local minima correspond to the attractive fixed points of the network is constructed via solving a system of linear inequalities derived from the strict local minimality conditions. In spite of its computational complexity, the method performs better than the conventional design methods, also ensuring the attractiveness for almost all memory sets whose cardinality is less than or equal to the dimension of its elements, as verified by computer simulations.