Design of the fully connected binary neural network via linear programming

An attempt is made to develop an alternative to the Hebbian-hypothesis-based design, using a powerful linear-programming (LP)-based algorithm. The LP-based algorithm attempts to build around each pattern to be stored a ball with a prespecified radius (in the Hamming distance sense) which is the ball of convergence for the pattern: when the network starts as one of the states in the ball, it will eventually converge to the central pattern. The Hopfield model and the sum-of-outer-products (SOOP) design are presented. Calculations are made of the radius of the balls of convergence for any given design. The LP-based algorithm is developed, and examples are presented demonstrating the advantages accrued for the network´s retrieval capability through the LP algorithm