Equilibrium and attractivity analysis for a class of hetero-associative neural memories

Based on the natural structure of Kosko's Bidirectional Associative Memories (BAM), a high-performance, high-capacity associative neural model is proposed which is capable of simultaneous hetero-associative recall. The proposed model, Modified Bidirectional Decoding Strategy (MBDS), improves the recall rate by adding some association fascicles to Kosko's BAM. The association fascicles are sparse coding neuron structures that provide activating strengths between two neuron fields (say, field X and field Y). The sufficient conditions for a state to become an equilibrium state of the MBDS network is derived. Based on these results, we discuss the basins of attraction of the training pairs in one iteration. The upper bound of the number of error bits which can be tolerated by MBDS is also derived. Because the attractivity of a stored training pair can be increased markedly with the aid of its corresponding association fascicles, we recommend a high capacity realization of MBDS, Bidirectional Holographic Memory (BHM), so that each training pair is stored uniquely and directly in the connection weights rather than encoded in a correlation matrix. Finally, computer simulations demonstrate the attractiveness of three different realizations of MBDS to verify our results.