Mathematical modeling of human memory

Abstract

The mathematical study of human memory is still an open challenge. Cognitive psychology and neuroscience have given a big contribution to understand how the human memory is structured and works. Cognitive psychologists developed experimental paradigms, conceived quantitative measures of performance in memory tasks for both healthy people and patients with memory disorders, but in terms of mathematical modeling human memory there is still a lot to do. There are many ways to mathematically model human memory, for example, by using mathematical analysis, linear algebra, statistics, and artificial neural networks. The aim of this study is to provide the reader with a description of some prominent models, involving mathematical analysis and linear algebra, designed to describe how memory works by predicting the results of psychological experiments. We have ordered the models from a chronological point of view and, for each model, we have emphasized what are, in our opinion, the strong and weak points. We are aware that this study covers just a part of human memory modeling as well as that we have made a personal selection, which is arguable. Nevertheless, our hope is to help scientists to modeling human memory and its diseases.

Keywords: amnesia; demantia; mathematics; memory; models; neuropsychology.

Figure 1

MNESIS, an overall representation of individual memory, and its interface with collective memory. MNESIS represents the five systems of individual memory. The three long-term representation systems (perceptual memory, semantic memory, and episodic memory) are organized hierarchically. Many episodic memories undergo a process of semantization over time. In addition, the phenomena of reviviscence, both conscious and unconscious, are essential for mnesic consolidation, thus underlining the importance of the dynamic and reconstructive nature of memory. This characteristic of memory has as its corollary the modification of the memory trace and the possible formation of false memories. At the center of the MNESIS model, there is the working memory, with the classic components (the central administrator, the phonological loop, and the visuo-spatial notebook) and the episodic buffer, a temporary interface structure that solicits different neurocognitive systems. Depending on the activity in progress, it can regulate the expression of self-awareness in the present or participate in the establishment of a new skill. Procedural memory is presented, with a hierarchy ranging from the support of motor and perceptual-motor skills to that of cognitive skills. The links with perceptual memory are favored for perceptual-motor procedural memory and with declarative systems for cognitive procedural memory. In any case, interactions with representation systems (including working memory) are particularly important during the procedural learning phase. The bonds loosen during the progressive automation of learning (adapted from Eustache et al., 2016).

Figure 2

The Atkinson-Shiffrin memory model: the flow chart characterizing inputs to the memory system (adapted from Atkinson et al., 1967).