A novel HD Computing Algebra: Non-associative superposition of states creating sparse bundles representing order information

Information inflow into a computational system is by a sequence of information items. Cognitive computing, i.e. performing transformations along that sequence, requires to represent item information as well as sequential information. Among the most elementary operations is bundling, i.e. adding items, leading to 'memory states', i.e. bundles, from which information can be retrieved. If the bundling operation used is associative, e.g. ordinary vector-addition, sequential information can not be represented without imposing additional algebraic structure. A simple stochastic binary bundling rule inspired by the stochastic summation of neuronal activities allows the resulting memory state to represent both, item information as well as sequential information as long as it is non-associative. The memory state resulting from bundling together an arbitrary number of items is non-homogeneous and has a degree of sparseness, which is controlled by the activation threshold in summation. The bundling operation proposed allows to build a filter in the temporal as well as in the items' domain, which can be used to navigate the continuous inflow of information.