An algebraic model of an associative noise-like coding memory

A mathematical model of an associative memory is presented, sharing with the optical holography memory systems the properties which establish an analogy with biological memory. This memory system--developed from Gabor's model of memory--is based on a noise-like coding of the information by which it realizes a distributed, damage-tolerant, "equipotential" storage through simultaneous state changes of discrete substratum elements. Each two associated items being stored are coded by each other by means of two noise-like patterns obtained from them through a randomizing preprocessing. The algebraic transformations operating the information storage and retrieval are matrix-vector products involving Toeplitz type matrices. Several noise-like coded memory traces are superimposed on a common substratum without crosstalk interference; moreover, extraneous noise added to these memory traces does not injure the stored information. The main performances shown by this memory model are: i) the selective, complete recovering of stored information from incomplete keys, both mixed with extraneous information and translated from the position learnt; ii) a dynamic recollection where the information just recovered acts as a new key for a sequential retrieval process; iii) context-dependent responses. The hypothesis that the information is stored in the nervous system through a noise-like coding is suggested. The model has been simulated on a digital computer using bidimensional images.