Fundamental Law of Memory Recall

Abstract

Human memory appears to be fragile and unpredictable. Free recall of random lists of words is a standard paradigm used to probe episodic memory. We proposed an associative search process that can be reduced to a deterministic walk on random graphs defined by the structure of memory representations. The corresponding graph model can be solved analytically, resulting in a novel parameter-free prediction for the average number of memory items recalled (R) out of M items in memory: R ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi 3πM=2 p. This prediction was verified with a specially designed experimental protocol combining large-scale crowd-sourced free recall and recognition experiments with randomly assembled lists of words or common facts. Our results show that human memory can be described by universal laws derived from first principles.

Latching dynamics as a basis for short-term recall

“…We show that this formulation fits with the general hypothesis that interference between memories is critical [11] as well as with the gist of the recently proposed statistical theory of free recall, as implemented by stochastic trajectories among ensembles of items [12], in fact unifying them: depending on the task, the limiting factor turns out to be either interference from items in long-term memory or the randomness in retrieval trajectories.…”

“…Given such simple transition rules, the power-law dependence R / ffi ffi ffi L p can be derived (a similar derivation can be found in S1 Appendix). In a more recent study, this power law dependence has been observed for lists of up to 512 words [12].…”

“…However we can still compute a measure somewhat similar to R, labeled as M it , as the number of retrieved patterns until the network repeats one transition-which would be the first element in a loop, given deterministic dynamics. Compared to lnR / 0.5 lnL (see [12]), M it has a steeper scaling with L, but still sublinear (Fig 3A). Alternatively, we can look at the number M i1 of retrieved items until the network simply revisits one of those already visited.…”

“…To explain this finding and more generally to investigate the putative mechanisms that could hinder recall, a theoretical model for memory recall has been proposed. We refer to this model as the SAM++ model, as it was developed by Sandro Romani, Misha Tsodyks and colleagues [12,27], with some roots in the SAM theory of Raaijmakers and Shiffrin [28], which however does not envisage the deterministic loops that terminate the search dynamics in SAM++ model. In this model, L STM items are drawn from a virtually unlimited reservoir of (LTM) memory items.…”

The Similarity Structure of Real-World Memories

“…More generally, processes of priming, association, interference, and forgetting all depend on the similarity relationships between items in memory [Gonnerman et al, 2007, Ritvo et al, 2019. Once we have mapped the similarity structure of information in memory [Shepard, 1980, Tversky, 1977, we can build quantitative models of how we search and sample from that space [Anderson and Bower, 1972, Gillund and Shiffrin, 1984, Howard and Kahana, 2002, Naim et al, 2020, Polyn et al, 2009. However, we currently know little about the similarity structure of the memories that matter most to us -the events of our own lives, which shape our identities and our life decisions [Bluck, 2003, Bluck et al, 2005, Conway and Pleydell-Pearce, 2000.…”