Nonpositive Hopfield networks for unidirectional error correcting coding

We consider a class of symmetric Hopfield networks, with nonpositive synapses and zero thresholds. We call such networks Nonpositive Hopfield networks and address a variety of design and analysis issues connected with their application to a specific form of Error Correcting Coding. In particular we show that this class is naturally suited to work in a unidirectional error environment and hence can find application in unidirectional error correcting coding. We give a necessary and sufficient condition for a set of codewords to be storable in a Nonpositive network. We propose a simple word storage algorithm, which is amenable to on line implementation, and guarantees storage of all storage compatible words. We show that the storage algorithm creates a network that is fundamentally maximally tolerant to physical faults and is free from spurious stationary points, whenever that freedom is available. We also give a word forgetting algorithm; a tight, deterministic bound on the storage capacity, and conditions under which the network created by our storage scheme tolerates a given number of arbitrary physical faults