Overview | HNeT2005 | Performance Aspects | Mathematics | Biology

HNeT is a non-linear model that applies complex combinatorics (generation of higher order relationships from input stimuli).  The specific cell type that performs this function is the granule cell.  The number of unique products increase as a factorial relationship to both the number of stimulus fields N and product order P, as indicated by the relationship:

Applying complex combinatorics; memory storage capacity remains directly proportional to the number of (now higher order) input fields and thus cortical memory elements.  Combinatorics facilitates rapid convergence for non-linear systems, providing a mechanism whereby extremely large numbers of stimulus-response memories may be accurately learned within an assembly that receives far lower numbers of input (stimulus) variables.

For instance, consider an assembly that reads 16 stimulus input variables, say axial positions and rates of movement in a robotic control device.  The assembly could employ downstream granules in the generation of up to 10th order product combinations.  In this case there are greater than 2 x 106 unique higher order combinations, allowing a proportional number of stimulus-response patterns (i.e. > 2 Million) to be rapidly and accurately learned.  The table on the left provides some indication of the combinatorial explosion that occurs when stimulus size and product order are increased.

Applying combinatorics, there is little restriction in terms of complexity (non-linearity) and storage density that may be learned within neuro-holographic assemblies.