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Information inflow into a computational system is by a sequence ofinformation items. Cognitive computing, i.e. performing transformations alongthat sequence, requires to represent item information as well as sequentialinformation. Among the most elementary operations is bundling, i.e. addingitems, leading to 'memory states', i.e. bundles, from which information can beretrieved. If the bundling operation used is associative, e.g. ordinaryvector-addition, sequential information can not be represented without imposingadditional algebraic structure. A simple stochastic binary bundling ruleinspired by the stochastic summation of neuronal activities allows theresulting memory state to represent both, item information as well assequential information as long as it is non-associative. The memory stateresulting from bundling together an arbitrary number of items isnon-homogeneous and has a degree of sparseness, which is controlled by theactivation threshold in summation. The bundling operation proposed allows tobuild a filter in the temporal as well as in the items' domain, which can beused to navigate the continuous inflow of information.

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