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Cognitive Science

The Generalized Quantum Episodic Memory Model

Jennifer S. Trueblood, Pernille Hemmer

Published Dec 21, 2016• 16 citations
Publisher

Abstract

Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory.

DOI
10.1111/cogs.12460

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Recent evidence suggests that experienced events are often mapped to too many episodic states, including those that are logically or experimentally incompatible with one another. For example, episodic over-distribution patterns show that the probability of accepting an item under different mutually exclusive conditions violates the disjunction rule. A related example, called subadditivity, occurs when the probability of accepting an item under mutually exclusive and exhaustive instruction conditions sums to a number >1. Both the over-distribution effect and subadditivity have been widely observed in item and source-memory paradigms. These phenomena are difficult to explain using standard memory frameworks, such as signal-detection theory. A dual-trace model called the over-distribution (OD) model (Brainerd & Reyna, 2008) can explain the episodic over-distribution effect, but not subadditivity. Our goal is to develop a model that can explain both effects. In this paper, we propose the Generalized Quantum Episodic Memory (GQEM) model, which extends the Quantum Episodic Memory (QEM) model developed by Brainerd, Wang, and Reyna (2013). We test GQEM by comparing it to the OD model using data from a novel item-memory experiment and a previously published source-memory experiment (Kellen, Singmann, & Klauer, 2014) examining the over-distribution effect. Using the best-fit parameters from the over-distribution experiments, we conclude by showing that the GQEM model can also account for subadditivity. Overall these results add to a growing body of evidence suggesting that quantum probability theory is a valuable tool in modeling recognition memory.
While people famously forget genuine memories over time, they also tend to mistakenly over-recall equivalent memories concerning a given event. The memory phenomenon is known by the name of \emph{episodic overdistribution} and occurs both in memories of disjunctions and partitions of mutually exclusive events and has been tested, modeled and documented in the literature. The total classical probability of recalling exclusive sub-events most often exceeds the probability of recalling the composed event, i.e. a \emph{subadditive} total. We present a Hamiltonian driven propagation for the Quantum Episodic Memory model developed by Brainerd (et al., 2015) for the episodic memory overdistribution in the experimental immediate \emph{item false memory} paradigm (Brainerd and Reyna, 2008, 2010, 2015). Following the Hamiltonian method of Busemeyer and Bruza (2012) our model adds time-evolution of the perceived memory state through the stages of the experimental process based on psychologically interpretable parameters -- γc\gamma_cγc​ for \emph{recollection capability} of cues, κp\kappa_pκp​ for bias or description-dependence by probes and β\betaβ for the average gist component in the memory state at start. With seven parameters the Hamiltonian model shows good accuracy of predictions both in the EOD-disjunction and in the EOD-subadditivity paradigm. We noticed either an outspoken preponderance of the gist over verbatim trace, or the opposite, in the initial memory state when β\betaβ is real. Only for complex β\betaβ a mix of both traces is present in the initial state for the EOD-subadditivity paradigm.
Memory exhibits episodic superposition, an analog of the quantum superposition of physical states: Before a cue for a presented or unpresented item is administered on a memory test, the item has the simultaneous potential to occupy all members of a mutually exclusive set of episodic states, though it occupies only one of those states after the cue is administered. This phenomenon can be modeled with a nonadditive probability model called overdistribution (OD), which implements fuzzy-trace theory's distinction between verbatim and gist representations. We show that it can also be modeled based on quantum probability theory. A quantum episodic memory (QEM) model is developed, which is derived from quantum probability theory but also implements the process conceptions of global matching memory models. OD and QEM have different strengths, and the current challenge is to identify contrasting empirical predictions that can be used to pit them against each other.
One of the goals of quantum Cognition and decision is to explain findings that seem paradoxical from a classic probability point of view. This is important to justify the introduction of this new theory. So far we have used the theory to explain paradoxical findings from research on human probability judgments and conceptual combinations. These are both considered higher level cognitive functions that involve more complex reasoning. What about more primitive cognitive functions such as memory recognition? Do paradoxical findings with respect to classic probability theory occur in this basic area of cognition? If so, how can a quantum model help to explain these findings over and above current explanations? This chapter presents a new application of quantum theory to a puzzling phenomenon observed in human memory recognition called the episodic overdistribution (EOD) effect (Brainerd & Reyna, 2008). First we describe the phenomena and explain why it is a puzzle, and then we present a quantum solution to the puzzle and compare it with previous memory recognition models. Episodic overdistribution effect In the conjoint–recognition paradigm, participants are rehearsed on a single set T of memory targets (e.g., each member is a short description of an event). After a delay, a recognition test phase occurs, during which they are presented with a series of test probes that consist of trained targets from T , related non-targets from a different set R of distracting events (e.g., each member is a new event that has some meaningful relation to a target event), and an unrelated set U of non-target items (e.g., each member is completely unrelated to the targets).
In a conjoint memory recognition task, a person is presented a list of target items to remember. Afterwards, a test probe is presented which is sampled from one of three mutually exclusive and exhaustive categories: one is a target from the set of previously presented targets; a second is a non target but meaningfully related to a target; and a third is a non target and unrelated to any target. The episodic overestimate effect refers to the fact that the probability of accepting a probe when asked if it is a target plus the probability of accepting a probe when asked if it is a related non target is greater than the probability of accepting a probe when asked if it is either a target or a non related target. Logically these two probabilities should be identical. Previously these results were explained by a dual process theory. This article presents an alternative quantum memory recognition model for this effect that addresses some problematic issues that arise with the dual process explanation.
How can we use quantum theory to model other phenomena of interest to researchers in cognition and decision making? Quantum theory is not easy for researchers in cognition and decision making to accept. In fact, quantum mechanics was not easy for physicists to accept either, but it was forced on them by several paradoxical findings that could not be explained using classical physics. We have a similar problem in cognition and decision making – there are numerous paradoxical findings that just seem irrational according to classic probability theory. For example, under some conditions, people judge the probability of event A and B to be greater than the probability of event B , which is called the conjunction fallacy (Tversky & Kahneman, 1983). Also, under the same conditions, they judge the probability of A or B to be less than the probability of event A (Carlson & Yates, 1989), which is called the disjunction fallacy. In this chapter we examine how quantum probability theory explains these and other puzzling results from human probability judgment research. This chapter has two main parts. In the first part, we use a quantum model to derive qualitative predictions for conjunction errors, disjunction errors, and other closely related findings. The first section provides a general set of predictions that do not depend on specific assumptions about the features used to represent events, and the predictions are parameter free. In the second part, we examine the quantitative predictions of the quantum model for a Bayesian inference task, which we use to explain order effects on inference.
A quantum probability model is introduced and used to explain human probability judgment errors including the conjunction, disjunction, inverse, and conditional fallacies, as well as unpacking effects and partitioning effects. Quantum probability theory is a general and coherent theory based on a set of (von Neumann) axioms which relax some of the constraints underlying classic (Kolmogorov) probability theory. The quantum model is compared and contrasted with other competing explanations for these judgment errors including the representativeness heuristic, the averaging model, and a memory retrieval model for probability judgments. The quantum model also provides ways to extend Bayesian, fuzzy set, and fuzzy trace theories. We conclude that quantum information processing principles provide a viable and promising new way to understand human judgment and reasoning.