Quadratic Hadamard memories

An associative memory, called selective reflexive memory (SRM), appears to have perfect associative recall of up to N stored bipolar vectors, where N is the memory dimension. The memory consists of a bidirectional linear transformer (BLT), followed by a dominant label selector (DLS). The BLT transforms the bipolar input vector into a linear combination of Hadamard vectors; the DLS selects, from this linear combination, the dominant Hadamard vector. The latter is returned to the BLT, which in its backstroke produces the stored vector closest to the input. DLS is an associative memory with quadratic activation, in which the stored vectors are Hadamard vectors. The number of physical connections is the same as for a fully connected Hopfield memory, and all the connections have the same weight. In the discrete asynchronous model, the DLS is stable, and its only stable states are the Hadamard vectors; there are no spurious stable states