Accumulators in Context 1 Running head : ACCUMULATORS IN CONTEXT

An integrated theory of context effects in memory retrieval is introduced. The theory, called Retrieval by ACcumulating Evidence in an Architecture (RACE/A), integrates ideas from accumulator models in the cognitive architecture ACT-R. This new theory explains how a particular retrieval from declarative memory is influenced by concurrent cognitive processes. RACE/A accounts for memory interference and facilitation with asynchronously presentation of stimuli, masked priming, and repetition priming, as well as the effects of cognitive control on interference. The authors provide detailed simulations that demonstrate how RACE/A accounts for these effects, as well as model fits to existing and new experimental data. Accumulators in Context 3 Accumulators in Context: An Integrated Theory of Context Effects on Memory Retrieval Cognitive architectures (e.g., ACT-R, Anderson, 2007; EPIC, Meyer & Kieras, 1997a; Soar, Newell, 1990; CLARION, Sun, 2006), have had considerable success explaining cognition in an integrative way. This means that theories developed within a cognitive architecture are supported by theories of other aspects of cognition. For instance, for an explanation of visual search tasks, in which participants are asked to search an array of stimuli for a previously presented target stimulus, it is important to include a theory of decision processes to account for a stopping rule of the visual search, and of declarative memory to explain how participants retrieve the target from memory. During the task, participants have to decide whether they have found the target stimulus, based on a memory of the previous presentation of the stimulus. Therefore, it makes sense to study different cognitive phenomena within one framework, so that one theory (for instance about visual search) remains consistent with others (for instance about decision making or declarative memory). One of the successes of cognitive architectures (particularly from the architecture ACT-R) is its account of declarative learning. By incorporating a model that estimates the environmental demands on memory (Anderson & Milson, 1989; Anderson & Schooler, 1991), ACT-R models have been able to account for many effects related to learning and memory (e.g., Anderson, Bothell, Lebiere, & Matessa, 1998; Anderson, Fincham, & Douglass, 1999; Pavlik & Anderson, 2005). In addition, this declarative memory account has been used to study the role of memory in other cognitive processes, such as in prospective time estimation (e.g., Taatgen, Van Rijn, & Anderson, 2007; Van Rijn & Taatgen, 2008) and in cognitive control (e.g., Altmann & Gray, 2008). Also, the theory Accumulators in Context 4 of declarative memory in ACT-R has proven to be a successful account of interactive behavior (e.g., Lebiere & West, 1999; West, Lebiere, & Bothell, 2006). However, one of the drawbacks of the theory of declarative memory retrieval that has been adopted in the cognitive architecture ACT-R is that it does not provide a theory of the actual retrieval process. Rather, it provides a prediction of the retrieval time of declarative information, as well as the probability of successful retrieval, under normal conditions. However, circumstances exist where such a ballistic model (Brown & Heathcote, 2005; Van Maanen & Van Rijn, 2007b) of declarative memory retrieval does not provide accurate predictions. This is illustrated in Figure 1, which shows the retrieval process as captured by a ballistic theory of declarative memory retrieval. At the onset of the retrieval process, the time it takes to retrieve a declarative fact from memory (referred to as chunk A in Figure 1) as well as the identity of that fact are already known. However, cognition and perception do not stop while retrieving information from declarative memory, and it might very well be that new, relevant information becomes available during the interval between retrieval onset and the actual retrieval that may influence the retrieval process. Consider for example the following experiment. A participant is requested to name a picture that appears on a computer screen. The picture is accompanied by a word from the same semantic category (e.g., a picture of a cat with the word “dog”), which may appear at various time intervals just before or after the onset of the picture. When inspecting the latency data from this experiment (W. R. Glaser & Düngelhoff, 1984, see also Figure 8a below), it turns out that the presence of the word interferes with processing of the picture. Moreover, the time interval between the presentation of a word and the Accumulators in Context 5 presentation of a picture mediates the response latency for the picture. The closer the word precedes the picture, the slower the response. Surprisingly however, the maximum interference effect of the word on the picture is when the word trails the picture by 100ms. What this example shows is that when studying interference effects such as these, many task aspects may play an important role. In this case, the asynchronous presentation of stimuli mediates the interference effect, and also the different qualities of words and pictures influence the latency, reflected by the fact that the maximum interference is not at an stimulus onset asynchrony (SOA) of 0ms (when word and picture are presented simultaneously), but at an SOA of 100ms. Complex interference patterns such as this cannot be fully explained by traditional architectural models that focus on a broad range of tasks. In the “Asynchronously presented stimuli” section, we will further discuss how these two aspects (asynchronous presentation and stimulus quality) determine response latencies in this task. Many specialized models exist that specifically address the interference issues in declarative memory, however. For example, a large body of work is devoted to understanding the decision dynamics in two-choice reaction time tasks (Ratcliff & Smith, 2004). In these models, the decision process is thought of as a process in which evidence for two response options is sampled, until a decision for one or the other has been reached. The decision time is determined by the length of this “deliberation process” (Busemeyer & Townsend, 1993, p. 432), and will be influenced by the accrual rate of the evidence for the response options. Thus, if all evidence points in one direction, the deliberation will be fast, and the decision time will be short. Accumulators in Context 6 In this paper, we propose to integrate such a sampling process in a cognitive architecture, which we will refer to as Retrieval by Accumulating Evidence in an Architecture (RACE/A). This way, a number of new memory related phenomena can be explained by the architectural approach. Because in RACE/A it is possible to dynamically adapt the sampling process to new information, it becomes possible to model tasks in which asynchronies between stimulus presentations exist, something that is currently not possible in architectural models. For instance, in a dual-task in which the interval between the tasks governs the response latency (as for example in Psychological Refractory Period experiments), RACE/A explains how the decision process depends on the interval change (Van Maanen, Van Rijn, & Borst, submitted, as well as Experiments 1 and 2 of the current paper). For these situations, RACE/A can provide quantitative model fits. Related Theories of Memory Retrieval Dynamics Previous models of memory retrieval have focused on the functional process underlying simple decision making (e.g., Ratcliff & McKoon, 2008) or perceptual identification (e.g., Usher & McClelland, 2001). These models are often referred to as sequential sampling models (Ratcliff & Smith, 2004). In sequential sampling models, the discrimination between mental representations is thought of as a mechanism that accumulates the likelihood that a certain mental representation is the intended one. Typically, there is a boundary, either fixed or relative to another accumulator, above which the representation is discriminated and may be used in another cognitive process. Accumulation depends on the quality or the quantity of a stimulus, either absolute or relative to other stimuli. Because the latency in these kinds of paradigms depends for a Accumulators in Context 7 large extent on when the boundary for a specific accumulator is reached, and accuracy depends on which accumulator reaches the boundary first, sequential sampling models provide an elegant explanation for speed-accuracy trade-offs often observed in cognitive tasks (Ratcliff & Smith, 2004). Retrieval from declarative memory also involves discriminating between different mental representations. Thus, memory retrieval could also be described as a process in which the likelihood is accumulated that a certain mental representation is the intended one. Sequential sampling models therefore provide an explanation of many memory related phenomena (e.g., Ratcliff, 1978). The three most important parameters that determine behavior in sequential sampling models are (Wagenmakers, van der Maas, & Grasman, 2007): • A starting point of accumulation (z in Figure 2) • Match boundaries (a and b) • Mean drift rate (v) The match boundaries a and b in these kinds of models represent the two response options for a participant in the tasks that are modeled with the sequential sampling models. For instance, in lexical decision, the match boundary represents the amount of accumulated evidence to give a “word” response, and the non-match boundary represents the amount of evidence needed to give a “non-word” response. The position of the starting point (z) relative to the match boundaries determines the prior likelihood of a match and a non-match. For example, if the starting point is closer to match boundary a than to match boundary b, the accumulation needed to cross a is less than the accumulation necessary to cross b. In this case, in the absence of a any drift Accumulators in Context 8 towards a or b, the likelihood of reaching a is higher than reaching b. Manipulation of this parameter has been used to model participants’ prior expectations on the probability of stimuli, for instance the probability of non-words in a lexical decision task (Wagenmakers, Ratcliff, Gomez, & McKoon, 2008). In the model of Wagenmakers et al., a high non-word probability was modeled by setting z to a lower value. This meant that crossing the non-word boundary was faster than the word-boundary, because the accumulation process was shorter, which is visible in the data as well. The third important parameter, mean drift rate, indicates the average speed of accumulation. A high value indicates a faster accumulation (a high drift). This parameter has for instance been manipulated to account for stimulus discriminability effects (Usher & McClelland, 2001). Thus, highly discriminable stimuli may be modeled by a high drift in either direction, and stimuli that are more difficult to discriminate may be modeled with a lower drift rate. One of the drawbacks of the classical diffusion model is that it only accounts for two response options (a match and a non-match). Other memory retrieval models have been proposed that overcome this. For example, Usher and McClelland (2001) proposed a sequential sampling model for perceptual choice tasks in which each response option is represented by an accumulator, but in which the drift rates are dependent. Apart from accumulation caused by stimuli (the mean drift rate), the drift is also determined by lateral inhibition from other accumulators and decay. In this model, the time course of a perceptual choice is determined by the likelihood that a stimulus leads to one response, as well as the likelihoods of other responses. Accumulators in Context 9 Another well-known memory retrieval model is the REM model (Shiffrin & Steyvers, 1997). In this model, the retrieval process is thought of as a continuous Bayesian decision process, in which the odds that a particular decision will be made depend on the ratio of likelihoods between the response options. For instance, for lexical decision, the likelihoods for the “word” and “non-word” responses are considered to be a function of features of the stimulus. If the stimulus resembles a word, the likelihood of the “word” response is higher than if the stimulus consists of a completely randomized letter string. Certain instances of the REM model also include aspects of sequential sampling (e.g., Norris & Kinoshita, 2008; Wagenmakers, Steyvers, Raaijmakers, Shiffrin, van Rijn, & Zeelenberg, 2004a). In these models, the likelihoods of the response options continuously drift, and a decision is based on the current likelihood ratio in the system. In this way, the REM model accounts for pseudo-homophone effects in lexical decision under deadline or signal-to-respond conditions (Wagenmakers et al., 2004a). These accounts have provided much insight in how retrieval from declarative memory works. However, computational models that are derived from these theoretical accounts often only model a single retrieval event. These models fail to appreciate that retrieving declarative knowledge from memory does not stand alone, but is always part of the execution of a particular task. Cognitive architectures on the other hand provide a theory of task execution (Newell, 1990). However, the explanation provided by these models is not always at the level of detail of sequential sampling models. RACE/A reconciles both approaches. Accumulators in Context 10 Cognitive architectures From the many variants of a cognitive architecture that exist (e.g., ACT-R, Anderson, 2007; Anderson, Bothell, Byrne, Douglass, Lebiere, & Qin, 2004; Soar, Laird, Newell, & Rosenbloom, 1987; Newell, 1990; Rosenbloom, Laird, & Newell, 1993; EPIC, Meyer & Kieras, 1997a, b; CLARION, Sun, 2006, 2007), ACT-R is the theory with the most emphasis on declarative memory retrieval (e.g., Anderson et al., 1998; Anderson, Fincham, & Douglass, 1999; Anderson & Reder, 1999). However, we claim that ACT-R’s theory of declarative memory is too static to account for the competition and interference effects in declarative memory retrieval that we address. In what follows, we will first introduce the cognitive architecture ACT-R, and then clarify why in certain cases the current declarative memory theory in ACT-R is insufficient. Then we will introduce our new proposal for declarative memory retrieval, RACE/A. ACT-R ACT-R is a hybrid cognitive architecture in which behavior in a task can be described by a sequence of production rule executions. The rules specify which actions to execute given certain conditions. To execute a production rule, the conditions are matched against the current information state, which is represented by a set of buffers, each containing one piece of information. Which information is present at a certain point in time is determined by each of the specialized modules, that each process one kind of information. For instance, visual perception is handled by the visual module, and motor commands are executed by the motor module. The declarative module is used for storing and retrieving declarative memory information, the speech module handles the speech output, the aural module handles auditory perception, and the goal and imaginal are Accumulators in Context 11 modules for keeping track of (sub) goals and intentions (Figure 3). The modules can be regarded as theories on that particular aspect of cognition, and the production rule system connects these theories to account for overall behavior. Thus, the presence of information determines which production rule is selected and executed. Both the presence and absence of stimuli can modify the buffer content and determine the selection of production rules, and the actions that are executed as part of a previous production rule. For instance, a production rule’s actions may contain a request to retrieve certain information from memory, which will be stored in the retrieval buffer after it has been retrieved. Declarative information in the ACT-R cognitive architecture is represented by chunks. These are simple facts about the world, such as Amsterdam is the capital of the Netherlands, or The object I am looking at is a computer screen. Both these example chunks are declarative facts, but the first example can typically be found in the retrieval buffer, and thus represents a fact retrieved from declarative memory, whereas the second example represents a visually observable fact of the world, and might be present in the visual buffer. All chunks in declarative memory have an activation level that represents the likelihood that a chunk will be needed in the near future. The likelihood is partly determined by a component describing the history of usage of a chunk called the baselevel activation (Bi in Equation 1).