Mathematical models of human memory

Abstract

Human memory is an incredibly complex system of vast capacity but often unreliable. Measuring memory for realistic material, such as narratives, is quantitatively challenging as people rarely remember narratives verbatim. Cognitive psychologists developed experimental paradigms involving randomly collected lists of items that make possible quantitative measures of performance in memory tasks, such as recall and recognition. Here, we describe a set of mathematical models designed to predict the results of these experiments. The models are based on simple underlying assumptions and surprisingly agree with experimental results quite well, in addition to that they exhibit quite interesting mathematical behavior that can partially be understood analytically.

Face familiarity detection with complex synapses

“…A recent study showed that the two-alternative forced-choice task performance for images (sketches) is around 85% when there are 100 interposed items between the first presentation and the test (with a speed of 1s for each stimulus and 0.5s for the inter-item interval). 49 We thus take as an educated guess, which could be even smaller for a shorter stimulus duration (i.e., less than 1s). For , the relevant range in which it should vary would be between zero and one to estimate the complexity of synapses (e.g.…”

“…Taking and , the interval lengths would be for . Roughly speaking, within a 1-h experiment containing 2400 interleaved images (about 1s for each stimulus plus 0.5s for response and inter-item interval, the same speed as in 49 ), we will have test images refreshed at least six times. Then how the signal gain (and the corresponding probability of successful familiarity detection) develops as a function of the interval/presentation number will determine the temporal decay kernel of the memory signal and therefore it will allow us to infer the complexity of the memory consolidation process.…”

Forgetting dynamics for items of different categories

“…An equivalent closed-form solution to the retention function can also be found to be where is the binomial coefficient ( Katkov et al 2022 ). The model yields a family of distinct curves by varying the free integer parameter n , with higher n leading to a better retention; that is, higher values of retention function (see Fig.…”

Forgetting Dynamics For Items of Different Categories

“…An equivalent closed-form solution to the retention function can also be found to be where is binomial coefficient (Katkov et al [2022]). The model yields a family of distinct curves by varying the free integer parameter n , with higher n leading to better retention, i.e.…”