Overview | HNeT2005 | Performance Aspects | Mathematics | Biology

Holographic neural operation is based upon phase interactions, following phase coherence / decoherence principles observed within electromagnetic wave theory and quantum mechanics (QM).  Operations performed at the synaptic level of the cortical cell (Purkinje or stellate) are of identical form to the QM wave equation, if one follows the simplified linear framework of HNeT.  However, in practice we apply far more sophisticated non-linear processes.

The inner product shown below describes the learning process that takes place within each cortical memory element Xn of the cortical cell.  Each cortical cell may possess many thousands of such cortical memory elements.

The learning operation stores phase information pertaining to each separate stimulus-response memory trace (indexed by t ) onto the identically same set of complex scalars, again each represented by Xn.  For clarity, the S vector indicates the stimulus input, and R the associated response.

The response recall process within holographic neural processing follows a similar form, however, the inner product is performed across cortical memory elements (indexed by n) rather than time.  During the above recall operation, a new stimuli S* is processed through each prior learned stimulus-response memory superimposed within the cell’s cortical memory to produce a response recall R' as shown on the next page.