Overview | HNet | Performance Aspects | Mathematics | Biology

Commutativity is another intrinsic property of holographic processing.  Stimulus-response pattern storage densities increase in direct proportion to the number of cortical memory elements across all neuron cells directly connected within an assembly.  This concept is illustrated by the following equality, considering [X]c as the cortical memory values stored within each cell (c) and [S]c the stimuli processed through each of those memory elements:

The resultant increase in memory storage capacity is exponential and permits one to construct assemblies that are effectively unrestricted with respect to associative memory storage.  Commutivity has important implications for neuromorphic structures that follow the neo-cortical architecture.

To illustrate, within a neo-cortical assembly stellate cells relay axonal processes to proximal pyramidal cells.  In human biology a typical stellate cell receives in the range of 20,000 input signals, a pyramidal cell receives in excess of 100,000 synaptic inputs.  Doing the math, commutativity facilitates storage densities in excess of 2 Billion associative patterns prior to saturation (degradation of learning rate and recall accuracy).  In real terms, this storage density equates to one memory trace for every second across an 80 year lifespan.