A mathematical model of capacious and efficient memory that survives trauma

Abstract

The brain's memory system can store without any apparent constraint, it recalls stored information efficiently and it is robust against lesion. Existing models of memory do not fully account for all these features. The model due to Hopfield (Proc. Natl. Acad. Sci. USA 79 (1982) 2554) based on Hebbian learning (The Organization of Behaviour, Wiley, New York, 1949) shows an early saturation of memory with the retrieval from memory becoming slow and unreliable before collapsing at this limit. Our hypothesis (Physica A 276 (2000) 352) that the brain might store orthogonalized information improved the situation in many ways but was still constrained in that the information to be stored had to be linearly independent, i.e., signals that could be expressed as linear combinations of others had to be excluded. Here we present a model that attempts to address the problem quite comprehensively in the background of the above attributes of the brain. We demonstrate that if the brain devolves incoming signals in analogy with Fourier analysis, the noise created by interference of stored signals diminishes systematically (which yields prompt retrieval) and most importantly it can withstand partial damages to the brain. © 2003 Elsevier B.V. All rights reserved.