Continuum model for quadratic memories

Quadratic Hadamard memories are investigated with the continuum model by means of theory and numerical computation. The memory serves as the second stage in a selective reflexive memory (SRM). The first stage of the SRM transforms the bipolar input into a linear combination of Hadamard vectors. The second stage selects from this linear combination the dominant Hadamard vector. Upon return of this vector to the front stage, a backstroke produces the stored vector which is labeled by the Hadamard vector selected. It is found that any SRM of dimension N that is a power of 2 performs perfect associative recall of up to N stored bipolar vectors for a certain choice of gain and the coupling between the two stages. This theoretical result is confirmed by numerical computations for N=8 and 16