Performing complex associations using a feature-extracting bidirectional associative memory

Learning in Bidirectional Associative Memory (BAM) is typically based on Hebbian-type learning. Since Kosko's paper on BAM in late 80s many improvements have been proposed. However, none of the proposed modifications allowed BAM to perform complex associative tasks that combine many-to-one with one-to-many associations. Even though BAMs are often deemed more plausible biologically, if they are not able to solve such mappings they will have difficulties establishing themselves as good models of cognition. This paper presents a BAM that can perform complex associations using only covariance matrices. It will be demonstrated that this network can be trained to learn both the 2- and 3-bit parity problem. The conditions that provide optimal learning performance within this latter network framework are then explored along with some of its dynamical properties. Results show that contrary to other associative memory models, the proposed neural network is able to perform parity tasks while maintaining a basic property of BAMs, namely, its pattern reconstruction abilities