Topics in Cognitive Science 7 (2015) 494–512 Copyright © 2015 Cognitive Science Society, Inc. All rights reserved. ISSN:1756-8757 print / 1756-8765 online DOI: 10.1111/tops.12146
Semantic Search in the Remote Associates Test Eddy J. Davelaar Birkbeck, University of London Received 7 June 2012; received in revised form 31 January 2014; accepted 12 February 2014
Abstract Searching through semantic memory may involve the use of several retrieval cues. In a verbal fluency task, the set of available cues is limited and every candidate word is a target. Individuals exhibit clustering behavior as predicted by optimal foraging theory. In another semantic search task, the remote associates task (RAT), three cues are presented and a single target word has to be found. Whereas the task has been widely studied as a task of creativity or insight problem solving, in this article, the RAT is treated as a semantic retrieval task and assessed from the perspective of information foraging theory. Experiments are presented that address the superadditive combination of cues and the anti-clustering behavior in the recall sequence. A new type of search behavior in the RAT is put forward that involves maximizing the difference in activation between target and distractors. This type of search is advantageous when the target is weak and cue patches are contaminated with strong competitors. Keywords: Information foraging; Optimal foraging; Memory search; Remote associates test; Word association space; Cued recall; Consistent information accumulation
1. Introduction The human cognitive system can be caricaturized as a system that relentlessly gathers information. Such a caricature implies that, similar to an animal that forages for food, the cognitive system forages for information. From this perspective, one could hypothesize that the rules that describe the stereotyped foraging behavior in animals (Stephens & Krebs, 1986) may also describe information foraging behavior in cognitive systems (e.g., Pirolli, 2007; Pirolli & Card, 1999). Research into this hypothesis has largely led to the conclusion that information foraging behavior is indeed well described by rules that govern animal foraging behavior, whether it be searching on the Internet (Fu & Pirolli, 2007; Pirolli & Card, 1999), problem solving (Payne, Duggan, & Neth, 2007), or stopping Correspondence should be sent to Eddy J. Davelaar, Department of Psychological Sciences, Birkbeck, University of London, Malet Street, WC1E 7HX, London, UK. E-mail: [email protected]
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
495
behavior (Payne & Duggan, 2011; Wilke, Hutchinson, Todd & Czienkowski, 2009). Although the reason for the success in applying these rules might reflect a deeper common origin such as evolutionary pressures (Hills, 2006), the information is still coming from the external environment. The proposition is that the foraging rules that apply to external search might also apply to internal cognitive search. In other words, when an individual is searching for information in memory, the search behavior exhibits regularities that resemble those observed with external search. Evidence is accumulating that internal search processes produce behavior that can be captured by the same foraging rules, albeit with various degrees of adjustments (Dougherty & Harbison, 2007; Harbison, Dougherty, Davelaar, & Fayyad, 2009; Hills, Jones, & Todd, 2012). This article focuses on the Remote Associates Test (RAT; Mednick, 1962), which has been used as a task to investigate creativity, insight, and problem-solving abilities. This task is of interest as the search is for a single target, as in typical visual search tasks, in the presence of multiple cues. The task is complementary to the verbal fluency task of which performance has recently been shown to be welldescribed by the patch model of foraging (Hills et al., 2012), and requires searching for multiple targets given a single cue.
2. Foraging animals versus memory paradigms Foraging theory (Stephens & Krebs, 1986) supposes that an animal’s search for food is optimal when considering the environmental conditions, such as food density within a food patch and the distribution of food patches over an extended region. There are a number of optimal animal foraging models depending on the goal of the forager, the costs of search, and the benefits of finding food. The model that has received the most attention in the cognitive search literature is the patch model, which is based on Charnov (1976) marginal value theorem. The premises of this model are that (a) food is distributed in patches over a larger region of patches, (b) this food depletes during the process of foraging, and (c) the animal’s goal is to maximize the gain per unit of foraging time. The optimal patch model involves a tradeoff between exploiting a current patch of food and leaving the patch in search for richer food patches. The theorem states that the animal should leave a particular food patch when the rate of return within the patch becomes smaller than the long-term average rate of return. This leads to successive samples from the same patch to be more closely spaced in time than the last sample of one patch and the first sample of a new patch. When addressing whether human memory search can be meaningfully compared to animal foraging behavior, an assessment needs to be made about how well the analogy fits several of the common human memory paradigms (see, e.g., Davelaar & Raaijmakers, 2012). As the term search implies a sequence of events, the recall paradigm seems most applicable to studying information foraging in memory.1 Recall paradigms come in two main flavors: cued recall, where a cue word is given to a participant to use in the memory search; and “no-cue” recall, such as free and serial
496
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
recall. In these tasks, participants are typically shown a sequence of items (e.g., pictures, words) and after the final item are requested to report all the items in any order (free recall) or in serial order (serial recall). Although practically no explicit cue is provided to participants, memory theorists agree that an internally generated cue is used in these paradigms. In cued recall paradigms, the participants are given a cue word and have to recall the information that was associated with that cue word. The association might have been formed during an explicit learning phase in which case we can speak of an episodic cued recall task. When no learning phase was present, we can speak of a semantic, phonemic, or visual cued recall task, depending on the information that is provided by the cue. An example of such a task is naming as many animals as possible (e.g., Hills et al., 2012). This task, called verbal fluency, or semantic fluency, has the category label animal as the cue word. Cued recall tasks can be grouped by the number of target words and the number of cue words. In the verbal fluency task, one cue is given and there exist many target items (i.e., multi-target single cue). A simple free association task consists of providing a single cue word (e.g., cat) to the participant, who then reports the first word that comes to mind (e.g., dog) (i.e., single-target single cue). Conveniently, there is a large database (Nelson, McEvoy, & Schreiber, 1998) for free-association norms, which will be used in the analyses below. In the RAT, participants are presented with three cue words that are unrelated to each other and are instructed to produce a fourth word that is related to each cue word (i.e., single-target multi-cue). For example, when presented with the words cry, front, ship, the target word is battle. In this particular example, the target word forms compound words with each cue word and we refer to such a RAT version as a compound RAT or cRAT. To satisfy the analogy between animal foraging and memory search (and applying the patch model), one has to assume that items in memory are organized into patches and that the search process is sensitive to this distribution. In memory, a patch could be defined as a category or subcategory of items. In the verbal fluency test in which as many animals need to be reported, participants have a strong tendency to report animals in clusters, such as pets, zoo animals, farm animals, aquatic animals, and so on. The time between successive recalls of within-category items is faster than those of between-category items (Bousfield & Sedgewick, 1944). Hills et al. (2012) found that the pattern of recalls are well predicted by optimal foraging theory. Although these findings are congruent with the view that semantic memory is organized in clusters, an alternative view is that items are only associatively connected and that the clustering is the result of processes during the retrieval phase. For example, when given the cue animal, the current patch would include all animal names. However, after the word cat is selected, three scenarios are possible. In the first scenario, the word cat is not used as a cue itself and the next word is retrieved based on the animal cue. This scenario allows for successive retrieval of items that do not have strong associative links and is referred to as global search by Hills et al. (2012). In the second scenario, the word cat is selected to function as a cue. Together with the animal cue this leads to the next item to be an animal name that is associated with cat. Hills et al. (2012) referred to this as
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
497
local search. The patch or search set has now shrunk from including all animal names to a collection of cat-associated animal names.2 With each subsequent retrieved item, the current patch is dynamically redefined. In the third scenario, the word cat triggers the retrieval of a salient category name, such as pets, which is used as an additional cue. Hills et al. (2012) did not consider this type of search process, which is referred to here as latent search. It is not impossible that all three scenarios operate simultaneously with varying probabilities, as successive animal names can have weak associative links and belong to different subcategories. This forms a problem when defining a patch in memory based on sequences of retrieved items. For this reason, the following pragmatic approach is used to define a patch:3 a patch in memory is defined as the collection of items that are retrieved first given the available cues. For example, when given the cue animal, the word bumblebee is not likely to be among the first items generated, yet it is an animal. The assumption is that the word bumblebee is retrieved after the word fly or the subcategory cue insect was retrieved. This is not to say that bumblebee is not part of the entire animal set, but instead that like berries on a bush varying in ripeness, words differ in their associative link to the animal cue, with bumblebee being weakly associated. This definition implies that activation in the semantic memory system is dynamic and changes with each new item retrieved. It also embodies a strong assumption that the items from a (dynamic) patch are those that are highly activated given the cues and that weakly activated items will not be retrievable without further help (i.e., supporting cues through local or latent search). In memory theory, the presentation of a cue leads to a partitioning of the memory space within which search for the requested information ensues, called the memory search set. Providing additional cues that partially overlap with the current cue will decrease the size of the search set, making it easier to locate the target, as the target will receive converging input. This beneficial effect of additional cues is implemented explicitly in models of memory search (e.g., Raaijmakers & Shiffrin, 1981) in which the cues are combined multiplicatively, leaving only items that are associated with all cues to be candidates for retrieval. In the case of the RAT, only one item, the target, remains in the search set. Yet, as will be discussed, in the RAT, retrieval success can be very low. As there are three cue words in the RAT, the question becomes how search unfolds in a situation where several patches exist with irrelevant information and only a single target item. The search problem is one in which the searcher needs to maximize the activation of the target relative to the activation of the distractors. The following scenarios are considered: 1. Parallel search around each cue. In this scenario, three independent searches unfold, one in each location around each of three cues. 2. Serial search in which the search path moves from one cue patch to the next. Each cue patch is first depleted before moving to the next cue patch. 3. Serial search in which the search path moves from one cue patch to the next without depleting the patch.
510
4.
5.
6.
7.
8.
9.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
algorithm would need to define a similarity threshold below which a patch switch is assumed. Critically, the similarity-drop model requires not only that memory is structured in patches but also that the search follows the patch model of foraging. Here, the focus is on identifying the type of search observed when solving the cRAT, allowing for the possibility that the patch model of search may not apply. The term “optimal” might seem contentious. Hills et al. (2012) referred to “optimal” semantic search in verbal fluency based on the finding that the patch model is an optimal solution for problems of a certain description (resources distributed in patches, patches deplete when consumed, cost function to foraging behavior). However, the observation that the patch model captures some of the findings in verbal fluency tasks does not mean that all search in semantic memory can be captured using the patch model. Thus, an optimal search process for the RAT might be fundamentally different than processes that are closely linked to the patch model. Cues can also have detrimental effects on retrieval when the additional cue is strongly associated with many nontarget items. To truly be beneficial, the additional cues should be diagnostic or discriminative of the target (Goh & Lu, 2012; Nairne, 2002; Poirier et al., 2012). An alternative approach is to use a regression equation derived from the word association database that links the maximum likely conditional probability to the cosine similarity between vectors of response i and cue j. This procedure led to a constant for the maximal likely conditional probability due the extreme exponential distribution of the probabilities. The qualitative pattern remains the same when individual cue patches are introduced. The only difference is that transitions between cue patches are more prominent than transitions within cue patches. The ARC is calculated as the ratio between the observed within-patch transitions minus the expected within-patch transitions and the maximum number of withinpatch transitions minus the expected within-patch transitions. In addition, the interresponse times increased over successive transitions as shown in the free recall literature (Murdock & Okada, 1970). Interestingly, for solved trials that ended with the solution word, the last interresponse time was independent of the number of items retrieved (p > .38). For unsolved trials, the last interresponse times were slower (t(1372) = 3.34, p = .001) and decreased with the number of items retrieved (t(984) = 2.76, p < .01). A regression analysis confirmed the interaction (t(1372) = 1.99, p < .05). Although the study was not designed to obtain precise temporal data, these results do indicate that enough precision was present.
References Ash, I. K., & Wiley, J. (2006). The nature of restructuring in insight: An individual-differences approach. Psychonomic Bulletin & Review, 13, 66–73.
E. J. Davelaar / Topics in Cognitive Science 7 (2015) (A)
(B)
499
(C)
Fig. 1. Three possible scenarios in which three cues demarcate the cRAT patch in semantic space. The cRAT patch is defined as the collection of first-reported items following the presentation of the three cues. Each cue on its own would activate the area given by one circle. The target, indicated by the black dot, is per definition located in the intersection of the cues’ semantic neighborhoods and may be more similar to one of the cues. (A) The multiplicative model: only items that are in the intersection form the cRAT patch. (B) The additive model: all items in all neighborhoods belong to the cRAT patch. (C) The superadditive model: items in the intersection and items with strong cue-target similarities form the cRAT patch. These items are assumed to be the first to be reported.
To evaluate these models with respect to actual solution rates, a statistical approach is used based on the word association database by Nelson et al. (1998). This database contains word association norms of 5,018 words. From these norms, Steyvers, Shiffrin, and Nelson (2004) created a Word Association Space by compressing the 5,018 by 5,018 associations into 5,018 vectors of 400 features each. The cosine similarities between these vectors provide an index of semantic similarity. The main reason for using the WAS matrix instead of other matrices is that the WAS is based on data that were gathered using free association, which is close to the procedure used in the RAT and justifies the use of WAS as a foundation from which to build a semantic memory for RAT problems. Another approach is to use latent semantic spaces constructed from text corpora. Although these capture latent semantic information by virtue of contextual fits, they also include syntactic information that end up creating a different solution space. As the work here is not related to syntactic processing, the minimal semantic space was chosen. Of the 144 cRAT problems published by Bowden and Jung-Beeman (2003), the cue and target words of 117 problems were present in the word association database and could therefore be analyzed. For each of the 117 cRAT problems, the cosine similarity between the 400-features vectors of the target and each of the cue words was computed and between the remaining 5,014 words and each of the cue words. A variety of distance and similarity measures were derived to ascertain whether any of these measures predicted the problem solution rates. 3.1. Results and discussion The first analysis is to check whether the target word is located near the composite vector, vc, of the semantic space activated by the cue words. As the 400-feature vector,
500
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
vc, does not correspond to a unique item in the WAS, the item with the highest similarity to vc was chosen as the actual response. For all 117 cRATs, the chosen response was not the target, 108 responses were one of the cues. When the cue words were excluded, all responses were still nontargets. This means that the item closest to vc is unlikely to be a target word. However, the target word was always within the top 15 of all items. To compare, the similarity between the target item and the nearest cue word (mean = .32, median = .27) was larger than the similarity between the target item and the word nearest to vc (mean = .10, median = .03) (13 vs. 104, p < .001). Yet vc might not be an appropriate vector to use for comparison, as the similarity does not correlate with the solution rate. For example, the easiest cRAT problem (96% solution rate; cheese: cottage, swiss, cake) had three other items closer to vc, whereas the problem with only one item closer to vc (straight: forward, flush, razor) had a solution rate of 3%. Instead, the Euclidean distance between the target and cue words was used. With respect to the three-dimensional Euclidean distance, the target word was on average in the 91st percentile (median = 97.9%) of the items that were closest to the cue words. More important, the top 20 easiest cRAT problems had a maximum of nine other items that had a smaller Euclidean distance than the target word. The reported solution rates for the 15 s presentation duration (Bowden & JungBeeman, 2003) were correlated with the Euclidean distance, the sum of cue-target similarities, the minimum and maximum cue-target similarity per triplet, and the difference between the minimum and maximum cue-target similarity. All five variables correlated with the solution rate (distance: .49; summed_sim: .52; min_sim: .33; max_sim: .51; diff_sim: .48). As max_sim and diff_sim were indistinguishable (r = .99, p < .001) and summed_sim correlated highly (r > .90) with all but min_sim, both max_sim and summed_sim were excluded from further analyses. A regression analysis using distance, min_sum, and diff_sim as predictors revealed that only the similarity between the target and the weakest cue (t(113) = 2.73, p = .007) and the difference in cue-target similarity between the strongest and weakest cue (t(133) = 2.20, p = .03) remained significant. Taken together, these results suggest that performance in the cRAT is sensitive to the differential similarity between the target and the individual cue words. This finding is interpreted to indicate that search in cRAT problems involves at least local search, where each cue has an independent (and competing) contribution. It also implies that a search model that combines the cues multiplicatively and therefore focuses only on the intersection (Fig. 1A) does not capture the observed solution rates. There is ample evidence in the literature showing that the probability of recalling an item given one cue is a poor predictor of recall probability when a combination of cues is given (Rubin & Wallace, 1989). In particular, superadditive effects have been observed with dual cues, suggesting that the cues are combined in a nonlinear weighted fashion (Wiles, Humphreys, Bain, & Dennis, 1991). The exact functional form of this nonlinearity remains unknown, but it is likely to be the result of dynamic processes during the activation of items by the cue words (cf. Chappell & Humphreys, 1994). The result is that adding cues can have strong beneficial effects on semantic retrieval by honing in on the intersection of the three cue words.5
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
501
Therefore, a third, and here favored, possibility is that the three cues are combined in such a manner that the activated semantic space is smaller than expected by additive combination. Fig. 1C illustrates how superadditive cue combination could hone in on the intersection, but still be sensitive to the individual cues.
4. Experiment 1: Semantic activation Previous research has shown that individuals are able to judge whether a triplet of cue words has a solution with as little as 1.5 s exposure to the cue words (Bolte & Goschke, 2005). In human memory, the first available source for such a judgment is the pattern of memory activation in response to presentation of the triplet. This process is likely to precede any nonlinear dynamics that enhances the relative activation of the intersection compared to the items in the semantic fields of one or two cues. When given more time, participants are indeed more able to judge the solvability of a triplet (Bolte & Goschke, 2005), irrespective of actually solving the cRAT problem. Experiment 1 directly tested the hypothesis that global semantic activation provides information about solvability and thus can direct global search by providing what could be considered a “semantic saliency map” or “semantic hotspots.” 4.1. Methods 4.1.1. Participants A total of 40 participants (20 female; Mage = 45 years) volunteered for this experiment. 4.1.2. Materials and procedure Thirty triplets were constructed, of which 15 had a valid solution (e.g., watch: strap, pocket, time) and 15 triplets had no solution (e.g., hair, snack, cloud). The cue words were presented vertically on a computer screen for 3 s, followed by a screen asking the participant to indicate whether the triplet might have a solution or not. This was then followed by a blank screen in which the participant could try to solve the cRAT problem by typing in the answer. A maximum of 10 s was provided for solving the cRAT problem. 4.2. Results and discussion Results replicated previous studies (Bolte & Goschke, 2005) in that participants were above chance in correctly judging a triplet as solvable (hit rate = .66, SD = .17, t(39) = 6.17, p < .001). For the unsolvable triplets, participants were at chance (false alarm rate = .49, SD = .16, p > .69). The nonparametric detection measure of discriminability, A’, which varies between 0 and 1 (chance level is 0.5), revealed that participants were above chance in detecting a solvable triplet (A0 = .64, SD = .14, t(39) = 6.29, p < .001). When a trial was judged as solvable, only 21% of the time a correct solution
502
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
was given, 7% of the time an incorrect word was typed, and in the remaining 72% no response was provided. For every triplet, the similarity between each cue word and all 5,015 items was calculated and summed. These summed similarities form a proxy for the increased activation in semantic memory in response to the three cues. Critically, the summed similarity is maximal for items in the intersection of the cues’ semantic neighborhoods. The following measures were derived from the 5,015 summed similarities: the total, the maximum, the minimum, and the difference between the maximum and minimum. The probability of judging solvability correlated only with the maximum summed similarity (r = .53, p < .001) and the difference score (r = .55, p < .001). The two measures were indistinguishable (r = .99, p < .001). The analysis of Experiment 1 suggests that a global activation as measured with the summed similarity is available to the cognitive system and that therefore there is access to the semantic intersection at the beginning of the search. This supports the view that cues are combined, but together with solution rates being sensitive to differential targetcue similarities, the evidence favors a superadditive model (Fig. 1C). We are now in a position to address how the actual search process unfolds over time by analyzing the search protocol.
5. Experiment 2: Search protocol analysis Given that a global activation provides information about solvability, how does the search itself unfold over time? The following experiment addressed whether search in the cRAT follows a pattern consistent with optimal foraging in semantic memory. Hills et al. (2012) investigated this question in the verbal fluency task and observed that when items were grouped by subcategory, corresponding to patches, within-patch transitions had higher interitem similarity and shorter interresponse times than between-patch transitions. The study by Hills et al. (2012) contained a single external cue, that is, animal, and many targets. Essentially, verbal fluency is similar to picking berries from a field of berry bushes. The cRAT contains three external cues and only has a single target. In the introduction, three search scenarios were presented: (1) parallel search around each cue, (2) serial search around each cue until cue patch is depleted, and (3) serial search around each cue without depleting the cue patch. The analysis of the cRAT norms provided evidence in favor of cue-patch-sensitive search, whereas Experiment 1 provided further support for the view that the intersection of the cues’ semantic neighborhoods is accessible early on in search. In the current experiment, participants are required to type in any word that comes to mind while searching for the target. This procedure is necessary to produce multiple responses even though there is only a single target. Note that the goal is not to report as many items as possible, as is the case in the verbal fluency task. Therefore one cannot assume a priori that semantic search in the cRAT resembles semantic search in the fluency task, which in turn is well-described by the patch model of animal foraging.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
503
To evaluate the patch model for search behavior in the cRAT, two sets of patches are defined. First, a cRAT patch is defined as the collection of first-reported items given the three cues. All other items reported during search that were not reported in the first instance by any participant are outside the cRAT patch. This is not to say that these items are not cued by any of the cues. Considering Fig. 1C, the areas outside the cRAT patch include items that are within the cues’ semantic neighborhoods. Second, semantic neighborhoods of each cue form cue patches. Allocation of an item to a neighborhood is based on the highest similarity value between the item and the cues. With these definitions of patches, the following two questions can be addressed: Is there direct evidence for superadditive cue combination? Can patch transitions during cRAT search be described by the patch model of animal foraging? The parallel search model is predicted to produce a sequence of responses that has faster between- than within-patch transitions. The serial search model under (2) would predict larger associative strengths and smaller interresponse times for within- than between-patch transitions. In contrast, the serial search model under (3) would have more between- than within-patch transitions and interresponse times would not differ. 5.1. Methods 5.1.1. Participants A total of 300 participants volunteered in an online study using Amazon Turk. After applying strict inclusion criteria, data from 230 participants (122 female, Mage = 34 years) were used in the analyses. 5.1.2. Materials A total of 30 triplets were selected from the Bowden and Jung-Beeman (2003) norms that had .13), which could imply that a random search process is operational. Given the evidence of cue-sensitivity (from the analysis of cRAT norms), the ARC scores were recalculated when the responses were labeled in terms of cue patches (based on largest cue-response similarity) and inside/outside the RAT patch. Thus, six different patches were defined. A response was in the RAT patch if it was a word that at least one participant had mentioned at the beginning of a sequence of attempts; otherwise it was defined as being in the out of RAT patch. This inside/outside the RAT patch distinction is crossed with the cue patch, producing six patches. The ARC scores for unsolved and solved trials were at chance (ARC = .0005; p > .99) and negative (ARC = .30; t(131) = 2.88 p < .01), respectively. The negative ARC score is a crucial finding, as it suggests that multiple responses from a patch are temporally spread out more than expected by chance. In other words, the same patch is left before it was depleted and revisited during the search process. Given that this pattern differentiates solved and unsolved cRAT trials, it is assumed that this anti-clustering pattern is an indicator of a beneficial search process. According to the patch model as applied to semantic search, items obtained during within-patch transitions are more similar and have shorter interresponse times than items obtained during between-patch transitions. An ANOVA with the factors accuracy (solved/ unsolved), cue patch transition (within/between), and cRAT patch transition (inside/outside) revealed that the interitem similarities of transitions within cue patches were larger than between cue patches (F(1, 213) = 64.47, MSE = 0.004, p < .001, g2 = .23). Only for transitions in and out of the cRAT patch in solved trials were the interitem similarities unrelated to the type of cue patch transition (three-way interaction: F(1, 213) = 4.022, MSE = 0.004, p < .05, g2 = .02; two-way interaction between accuracy and cue patch transition: F(1, 213) = 10.46, MSE = 0.004, p = .001, g2 = .05). The same ANOVA conducted on interresponse times revealed only a main effect of accuracy (F(1, 215) = 9.44, MSE < 0.001, p < .01, g2 = .04), with transitions in unsolved trials being slower than in solved trials. No other main effect or interaction reached significance. Finally, for all trials that were at least three responses long, the similarity between the response words and the target was calculated (with target responses omitted for solved trials). The response-target similarity was constant across output positions and numerically higher for solved than for unsolved trials (mean solved = .046, mean unsolved = .032; p > .30). In other words, participants were not exhibiting search behavior that follows some similarity gradient. To sum up, there is evidence for the following: (a) items in the intersection are preferentially activated in semantic memory and available for selection, (b) prolonged residence in the cRAT patch is associated with solving the cRAT, (c) interresponse times do not signal cue patch boundaries as defined by cue-response similarity, and (d) solved trials exhibit a pattern of anti-clustering—less within-patch transitions than expected by chance. The absence of clustering and the benefit of anti-clustering indicates a different type of
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
507
search process that is particularly beneficial in a single-target, multi-cued recall task, such as the cRAT.
6. General discussion The aim of this work was to evaluate the patch model of foraging in semantic memory on a semantic search task that differs in the number of target items and cues. The cRAT can be considered a closed-ended task that requires convergence to a single target in semantic memory. This contrasts with the more divergent or open-ended approach needed to name as many animal names, as is the case with semantic fluency tasks. Two main questions were addressed in this article. First, how are the multiple cues used in solving the cRAT? Second, does the search behavior in the cRAT follow the optimal behavior seen in semantic fluency tasks? The statistical analysis of the cRAT norms published by Bowden and Jung-Beeman (2003) revealed that solution rates are sensitive to the cue-target similarities, as computed using semantic vectors obtained from the word association space (Steyvers et al., 2004). Experiment 1 revealed that the global semantic activation triggered by the three cues is sufficient to judge whether a triplet of cues is solvable. Finally, in Experiment 2 the probability of reporting an item given the three cues was 4.5 times higher than expected by the cues independently. These findings are consistent with a view in which the three cues activate cue-specific regions in semantic memory that interact in such a manner that the intersection among the three semantic neighborhoods get activated more strongly, but where not all cue-specific items get excluded. This pattern is depicted in Fig. 1C and is used to define a triplet-specific cRAT patch. In Experiment 2, it was found that search within the cRAT patch is more likely to lead to finding the target than search that exits the cRAT patch. Furthermore, when considering the patches around the cues, as defined by similarity between the WAS vectors of the response and cues, solved cRAT trials exhibit less within-patch transitions than expected by chance. In addition, within-patch transitions show stronger interresponse associative strengths than between-patch transitions, but no difference in interresponse times. Three search processes were considered in the introduction that produce distinct predictions with regard to clustering behavior during search. The patch model addressed by Hills et al. (2012) is a serial search model that clusters items by virtue of patch-leaving dynamics that are based on Charnov (1976) marginal value theorem. Such patch models predict clustering scores—as measured with ARC—that are larger than zero. For example, in a social fluency task, which requires the participant to name as many people that they know, Hills and Pachur (2012) obtained an ARC score of .58 with patches defined by social category (partner, family, friend, acquaintance). A parallel search model assumes that the responses are independent of each other and thus would predict chancelevel clustering behavior, that is, ARC score of zero. This was only found for cRAT trials that were unsolved. When considering the local cue patches and the global cRAT patch, for solved cRAT trials in Experiment 2, the ARC score was negative. This is consistent
508
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
with a serial search model that leaves the patch well before it is depleted and revisits the same patch later during the search process. To explain this search behavior, one needs to realize that the cRAT is a task that embodies a different optimization problem than tasks such as semantic or social fluency. Searching for the target in the cRAT leads to retrieving words that are strongly related to one of the cues. If search would follow an associative path, the process would gravitate to a local search around one of the cues. Charnov’s (1976) marginal value theorem optimizes the overall rate of gain in targets per unit time and thus can be applied to search tasks that have multiple targets distributed around several (semantic, social) patches in memory. In the cRAT, the optimal search strategy maximizes the difference in memory activation between the target and distractors. As only the target is associated to all three cues, both a local or global search will activate the target. However, a local search within a cue patch will only activate those items that are in that patch. As the three cues are unrelated words, their patches are quite separable. To maximize the difference in memory activation between the target and distractors, every retrieval attempt should increase the target activation and allow previously activated distractors to decay. This is only the case when successive samples are from different cue patches. Thus an advantageous search strategy when faced with multiple cues, each of which activates competing distractors, is to activate the cues in a sequence, transitioning to cues for which the items in cue patch has decayed most. The anti-clustering behavior is a pattern that emerges from such a search process. More generally, search for a single target given multiple cues will benefit from having the global search patch centered on the intersection of the cues’ semantic neighborhood. Thus, the observation of superadditive cue combination might reflect an adaptive process to such problems, especially when considering that the global activation is sufficient to judge whether the triplet has a solution. Future research could investigate whether other tasks involving multiple external cues lead to search patterns similar to that seen in the cRAT. A common finding in the cognitive foraging literature is that leaving a patch is associated with increased interresponse time and decreased interitem similarity. However, in this study, the interresponse times did not signal patch boundaries. One possibility is that the typed responses were too slow to meaningfully discern patch boundaries. However, there was a significant effect of solution status on interresponse times, suggesting sufficient resolution.9 A more likely explanation is that the drive to maximize the difference between target and distractor activation leads to faster between-patches transitions than expected or that the differences in interresponse times are only observed when a sizeable cluster from one patch has been retrieved. The results presented in this article contribute to the current literature on cognitive search in two ways. First, they highlight that not all search tasks in a particular domain (in this case memory) can be captured by a single search strategy. Even though data from semantic fluency are consistent with Charnov’s marginal value theorem, the theorem fails for semantic search that is constrained by multiple cues. Thus, search processes found for one task may not be useful for another task. Second, the results underscore the need to
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
509
address the question of how the search processes are discovered by the participant (if at all) and utilized. In other words, there is a need to investigate the control and selection of search processes. Future research could use tasks with multiple cues and multiple targets to test the participants’ ability to control the deployment of specific search processes. A ubiquitous aspect of searching through a pile of papers or through memory is the decision to give up the search. Search termination decisions in memory search are under intense investigation (Davelaar, Yu, Harbison, Hussey, & Dougherty, 2013; Harbison et al., 2009; Unsworth, Brewer, & Spiller, 2011). With the cRAT, giving up the search might induce new stages of the search process, such as allowing the activation of competitor items to fully decay. This process might underlie the forgetting of distracting information as with incubation effects (Vul & Pashler, 2007) and might be the mechanism behind restructuring in insight problems (Ash & Wiley, 2006). Targets that come to mind might be accompanied with a feeling of insight. The current experiments were not designed to look at stopping decisions in the cRAT or to investigate processes of insight. Further research could take a closer look at the relation between giving up decisions and the occurrence of insight in the cRAT. 6.1. Conclusion Solving cRAT problems involves searching for a single target in semantic memory using three cues. The search process differs from search in verbal fluency tasks, which also involve search through semantic memory, in that competing candidates are retrieved in response to the cues. Optimal search in cRAT involves continuous switching between cue patches, which produces a characteristic signature of anti-clustering behavior.
Acknowledgments The author thanks Michael Dougherty, Thomas Hills, Padraic Monaghan, Peter Todd, and Erica Yu for discussions and detailed comments on a previous version of this article. Experiment 2 was made possible with support by the National Science Foundation under grant BCS-1030831.
Notes 1. Some models of recognition memory involve two steps, of which the second step is a recall process (Diller, Nobel, & Shiffrin, 2001). However, the first step, a binary (old/new) decision process, is not regarded a search process. 2. This holds only if the cues are combined multiplicatively as was done by Hills et al. (2012). Other options of cue combination will be discussed below. 3. Hills et al. (2012) used a similarity-drop model to find patch boundaries. However, only 65% of the drops coincided with switches in hand-coded patches. A formal
510
4.
5.
6.
7.
8.
9.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
algorithm would need to define a similarity threshold below which a patch switch is assumed. Critically, the similarity-drop model requires not only that memory is structured in patches but also that the search follows the patch model of foraging. Here, the focus is on identifying the type of search observed when solving the cRAT, allowing for the possibility that the patch model of search may not apply. The term “optimal” might seem contentious. Hills et al. (2012) referred to “optimal” semantic search in verbal fluency based on the finding that the patch model is an optimal solution for problems of a certain description (resources distributed in patches, patches deplete when consumed, cost function to foraging behavior). However, the observation that the patch model captures some of the findings in verbal fluency tasks does not mean that all search in semantic memory can be captured using the patch model. Thus, an optimal search process for the RAT might be fundamentally different than processes that are closely linked to the patch model. Cues can also have detrimental effects on retrieval when the additional cue is strongly associated with many nontarget items. To truly be beneficial, the additional cues should be diagnostic or discriminative of the target (Goh & Lu, 2012; Nairne, 2002; Poirier et al., 2012). An alternative approach is to use a regression equation derived from the word association database that links the maximum likely conditional probability to the cosine similarity between vectors of response i and cue j. This procedure led to a constant for the maximal likely conditional probability due the extreme exponential distribution of the probabilities. The qualitative pattern remains the same when individual cue patches are introduced. The only difference is that transitions between cue patches are more prominent than transitions within cue patches. The ARC is calculated as the ratio between the observed within-patch transitions minus the expected within-patch transitions and the maximum number of withinpatch transitions minus the expected within-patch transitions. In addition, the interresponse times increased over successive transitions as shown in the free recall literature (Murdock & Okada, 1970). Interestingly, for solved trials that ended with the solution word, the last interresponse time was independent of the number of items retrieved (p > .38). For unsolved trials, the last interresponse times were slower (t(1372) = 3.34, p = .001) and decreased with the number of items retrieved (t(984) = 2.76, p < .01). A regression analysis confirmed the interaction (t(1372) = 1.99, p < .05). Although the study was not designed to obtain precise temporal data, these results do indicate that enough precision was present.
References Ash, I. K., & Wiley, J. (2006). The nature of restructuring in insight: An individual-differences approach. Psychonomic Bulletin & Review, 13, 66–73.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
511
Bolte, A., & Goschke, T. (2005). On the speed of intuition: Intuitive judgments of semantic coherence under different response deadlines. Memory & Cognition, 33, 1248–1255. Bousfield, W. A., & Sedgewick, C. H. W. (1944). An analysis of sequences of restricted associative responses. Journal of General Psychology, 30, 149–165. Bowden, E. M., & Jung-Beeman, M. (2003). One hundred forty-four compound remote associate problems: Short insight-like problems with one-word solutions. Behavioral Research, Methods, Instruments, and Computers, 35, 634–639. Chappell, M., & Humphreys, M. S. (1994). An auto-associative neural network for sparse representations: Analysis and application to models of recognition and cued recall. Psychological Review, 101, 103–128. Charnov, E. L. (1976). Optimal foraging: The marginal value theorem. Theoretical Population Biology, 9, 129–136. Davelaar, E. J., & Raaijmakers, J. G. W. (2012). Human memory search. In P. M. Todd, T. Hills & T. Robbins (Eds.), Cognitive search: Evolution, algorithms, and the brain. Str€ ungmann forum reports (pp. 177–193). Cambridge, MA: MIT Press. Davelaar, E. J., Yu, E. C., Harbison, J. I., Hussey, E. K., & Dougherty, M. R. (2013). A rational approach to memory search termination. Cognitive Systems Research, 24, 96–103. Diller, D. E., Nobel, P. A., & Shiffrin, R. M. (2001). An ARC-REM model for accuracy and response time in recognition and recall. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 414–435. Dougherty, M. R., & Harbison, J. I. (2007). Motivated to retrieve: How often are you willing to go back to the well when the well is dry? Journal of Experimental Psychology: Learning, Memory, and Cognition, 33, 1108–1117. Fu, W.-T., & Pirolli, P. (2007). SNIF-ACT: A cognitive model of user navigation on the world wide web. Human-Computer Interaction, 22, 255–412. Goh, W. D., & Lu, S. H. (2012). Testing the myth of the encoding-retrieval match. Memory & Cognition, 40, 28–39. Harbison, J. I., Dougherty, M. R., Davelaar, E. J., & Fayyad, B. (2009). On the lawfulness of the decision to terminate memory search. Cognition, 111, 397–402. Hills, T. T. (2006). Animal foraging and the evolution of goal-directed cognition. Cognitive Science, 30, 3– 41. Hills, T. T., Jones, M. N., & Todd, P. M. (2012). Optimal foraging in semantic memory. Psychological Review, 119, 431–440. Hills, T. T., & Pachur, T. (2012). Dynamic search and working memory in social recall. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38, 218–228. Mednick, S. A. (1962). The associative basis of the creative process. Psychological Review, 69, 220–232. Murdock, B. B., & Okada, R. (1970). Interresponse times in single-trial free recall. Journal of Experimental Psychology, 86, 263–267. Nairne, J. S. (2002). The myth of the encoding-retrieval match. Memory, 10, 389–395. Najemnik, J., & Geisler, W. S. (2005). Optimal eye movement strategies in visual search. Nature, 434, 387– 391. Nelson, D. L., McEvoy, C. L., & Schreiber, T. A. (1998). The University of South Florida word association, rhyme and word fragment norms, 1999. Available at http://w3.usf.edu/FreeAssociation/. Accessed June 7, 2012. Payne, J. S., & Duggan, G. B. (2011). Giving up problem solving. Memory & Cognition, 39, 902–913. Payne, S. J., Duggan, G. B., & Neth, H. (2007). Discretionary task interleaving: Heuristics for time allocation in cognitive foraging. Journal of Experimental Psychology: General, 136, 370–388. Pirolli, P. (2007). Information foraging theory: Adaptive interaction with information. New York, NY: Oxford University Press. Pirolli, P., & Card, S. (1999). Information foraging. Psychological Review, 106, 643–675.
512
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
Poirier, M., Nairne, J. S., Morin, C., Zimmermann, F. G. S., Koutmeridou, K., & Fowler, J. (2012). Memory as discrimination: A challenge to the encoding–retrieval match principle. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38, 16–29. Raaijmakers, J. G. W., & Shiffrin, R. M. (1981). Search of associative memory. Psychological Review, 88, 93–134. Roenker, D. L., Thompson, C. P., & Brown, S. C. (1971). Comparison of measures for the estimation of clustering in free recall. Psychological Bulletin, 76, 45–48. Rubin, D. C., & Wallace, W. T. (1989). Rhyme and reason: Analysis of dual retrieval cues. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 698–709. Stephens, D. W., & Krebs, J. R. (1986). Foraging theory. Princeton, NJ: Princeton University Press. Steyvers, M., Shiffrin, R. M., & Nelson, D. L. (2004). Word association spaces for predicting semantic similarity effects in episodic memory. In A. F. Healy (Ed.), Experimental cognitive psychology and its application (pp. 237–249). Washington, DC: American Psychological Association. Unsworth, N., Brewer, G. A., & Spiller, G. J. (2011). Factors that influence search termination decision in free recall: An examination of response type and confidence. Acta Psychologica, 138, 19–29. Vul, E., & Pashler, H. (2007). Incubation effects only after people have been misdirected. Memory & Cognition, 35, 701–710. Wiles, J., Humphreys, M. S., Bain, J. D., & Dennis, S. (1991). Direct memory access using two cues: Finding the intersection of sets in a connectionist model. In R. P. Lippman, J. E. Moody, & D. S. Touretzky (Eds.), Advances in neural information processing systems 3 (pp. 635–641). San Mateo, CA: Morgan Kaufman. Wilke, A., Hutchinson, J. M. C., Todd, P. M., & Czienskowski, U. (2009). Fishing for the right words: Decision rules for human foraging behavior in internal search tasks. Cognitive Science, 33, 497–529.
Semantic Search in the Remote Associates Test Eddy J. Davelaar Birkbeck, University of London Received 7 June 2012; received in revised form 31 January 2014; accepted 12 February 2014
Abstract Searching through semantic memory may involve the use of several retrieval cues. In a verbal fluency task, the set of available cues is limited and every candidate word is a target. Individuals exhibit clustering behavior as predicted by optimal foraging theory. In another semantic search task, the remote associates task (RAT), three cues are presented and a single target word has to be found. Whereas the task has been widely studied as a task of creativity or insight problem solving, in this article, the RAT is treated as a semantic retrieval task and assessed from the perspective of information foraging theory. Experiments are presented that address the superadditive combination of cues and the anti-clustering behavior in the recall sequence. A new type of search behavior in the RAT is put forward that involves maximizing the difference in activation between target and distractors. This type of search is advantageous when the target is weak and cue patches are contaminated with strong competitors. Keywords: Information foraging; Optimal foraging; Memory search; Remote associates test; Word association space; Cued recall; Consistent information accumulation
1. Introduction The human cognitive system can be caricaturized as a system that relentlessly gathers information. Such a caricature implies that, similar to an animal that forages for food, the cognitive system forages for information. From this perspective, one could hypothesize that the rules that describe the stereotyped foraging behavior in animals (Stephens & Krebs, 1986) may also describe information foraging behavior in cognitive systems (e.g., Pirolli, 2007; Pirolli & Card, 1999). Research into this hypothesis has largely led to the conclusion that information foraging behavior is indeed well described by rules that govern animal foraging behavior, whether it be searching on the Internet (Fu & Pirolli, 2007; Pirolli & Card, 1999), problem solving (Payne, Duggan, & Neth, 2007), or stopping Correspondence should be sent to Eddy J. Davelaar, Department of Psychological Sciences, Birkbeck, University of London, Malet Street, WC1E 7HX, London, UK. E-mail: [email protected]
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
495
behavior (Payne & Duggan, 2011; Wilke, Hutchinson, Todd & Czienkowski, 2009). Although the reason for the success in applying these rules might reflect a deeper common origin such as evolutionary pressures (Hills, 2006), the information is still coming from the external environment. The proposition is that the foraging rules that apply to external search might also apply to internal cognitive search. In other words, when an individual is searching for information in memory, the search behavior exhibits regularities that resemble those observed with external search. Evidence is accumulating that internal search processes produce behavior that can be captured by the same foraging rules, albeit with various degrees of adjustments (Dougherty & Harbison, 2007; Harbison, Dougherty, Davelaar, & Fayyad, 2009; Hills, Jones, & Todd, 2012). This article focuses on the Remote Associates Test (RAT; Mednick, 1962), which has been used as a task to investigate creativity, insight, and problem-solving abilities. This task is of interest as the search is for a single target, as in typical visual search tasks, in the presence of multiple cues. The task is complementary to the verbal fluency task of which performance has recently been shown to be welldescribed by the patch model of foraging (Hills et al., 2012), and requires searching for multiple targets given a single cue.
2. Foraging animals versus memory paradigms Foraging theory (Stephens & Krebs, 1986) supposes that an animal’s search for food is optimal when considering the environmental conditions, such as food density within a food patch and the distribution of food patches over an extended region. There are a number of optimal animal foraging models depending on the goal of the forager, the costs of search, and the benefits of finding food. The model that has received the most attention in the cognitive search literature is the patch model, which is based on Charnov (1976) marginal value theorem. The premises of this model are that (a) food is distributed in patches over a larger region of patches, (b) this food depletes during the process of foraging, and (c) the animal’s goal is to maximize the gain per unit of foraging time. The optimal patch model involves a tradeoff between exploiting a current patch of food and leaving the patch in search for richer food patches. The theorem states that the animal should leave a particular food patch when the rate of return within the patch becomes smaller than the long-term average rate of return. This leads to successive samples from the same patch to be more closely spaced in time than the last sample of one patch and the first sample of a new patch. When addressing whether human memory search can be meaningfully compared to animal foraging behavior, an assessment needs to be made about how well the analogy fits several of the common human memory paradigms (see, e.g., Davelaar & Raaijmakers, 2012). As the term search implies a sequence of events, the recall paradigm seems most applicable to studying information foraging in memory.1 Recall paradigms come in two main flavors: cued recall, where a cue word is given to a participant to use in the memory search; and “no-cue” recall, such as free and serial
496
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
recall. In these tasks, participants are typically shown a sequence of items (e.g., pictures, words) and after the final item are requested to report all the items in any order (free recall) or in serial order (serial recall). Although practically no explicit cue is provided to participants, memory theorists agree that an internally generated cue is used in these paradigms. In cued recall paradigms, the participants are given a cue word and have to recall the information that was associated with that cue word. The association might have been formed during an explicit learning phase in which case we can speak of an episodic cued recall task. When no learning phase was present, we can speak of a semantic, phonemic, or visual cued recall task, depending on the information that is provided by the cue. An example of such a task is naming as many animals as possible (e.g., Hills et al., 2012). This task, called verbal fluency, or semantic fluency, has the category label animal as the cue word. Cued recall tasks can be grouped by the number of target words and the number of cue words. In the verbal fluency task, one cue is given and there exist many target items (i.e., multi-target single cue). A simple free association task consists of providing a single cue word (e.g., cat) to the participant, who then reports the first word that comes to mind (e.g., dog) (i.e., single-target single cue). Conveniently, there is a large database (Nelson, McEvoy, & Schreiber, 1998) for free-association norms, which will be used in the analyses below. In the RAT, participants are presented with three cue words that are unrelated to each other and are instructed to produce a fourth word that is related to each cue word (i.e., single-target multi-cue). For example, when presented with the words cry, front, ship, the target word is battle. In this particular example, the target word forms compound words with each cue word and we refer to such a RAT version as a compound RAT or cRAT. To satisfy the analogy between animal foraging and memory search (and applying the patch model), one has to assume that items in memory are organized into patches and that the search process is sensitive to this distribution. In memory, a patch could be defined as a category or subcategory of items. In the verbal fluency test in which as many animals need to be reported, participants have a strong tendency to report animals in clusters, such as pets, zoo animals, farm animals, aquatic animals, and so on. The time between successive recalls of within-category items is faster than those of between-category items (Bousfield & Sedgewick, 1944). Hills et al. (2012) found that the pattern of recalls are well predicted by optimal foraging theory. Although these findings are congruent with the view that semantic memory is organized in clusters, an alternative view is that items are only associatively connected and that the clustering is the result of processes during the retrieval phase. For example, when given the cue animal, the current patch would include all animal names. However, after the word cat is selected, three scenarios are possible. In the first scenario, the word cat is not used as a cue itself and the next word is retrieved based on the animal cue. This scenario allows for successive retrieval of items that do not have strong associative links and is referred to as global search by Hills et al. (2012). In the second scenario, the word cat is selected to function as a cue. Together with the animal cue this leads to the next item to be an animal name that is associated with cat. Hills et al. (2012) referred to this as
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
497
local search. The patch or search set has now shrunk from including all animal names to a collection of cat-associated animal names.2 With each subsequent retrieved item, the current patch is dynamically redefined. In the third scenario, the word cat triggers the retrieval of a salient category name, such as pets, which is used as an additional cue. Hills et al. (2012) did not consider this type of search process, which is referred to here as latent search. It is not impossible that all three scenarios operate simultaneously with varying probabilities, as successive animal names can have weak associative links and belong to different subcategories. This forms a problem when defining a patch in memory based on sequences of retrieved items. For this reason, the following pragmatic approach is used to define a patch:3 a patch in memory is defined as the collection of items that are retrieved first given the available cues. For example, when given the cue animal, the word bumblebee is not likely to be among the first items generated, yet it is an animal. The assumption is that the word bumblebee is retrieved after the word fly or the subcategory cue insect was retrieved. This is not to say that bumblebee is not part of the entire animal set, but instead that like berries on a bush varying in ripeness, words differ in their associative link to the animal cue, with bumblebee being weakly associated. This definition implies that activation in the semantic memory system is dynamic and changes with each new item retrieved. It also embodies a strong assumption that the items from a (dynamic) patch are those that are highly activated given the cues and that weakly activated items will not be retrievable without further help (i.e., supporting cues through local or latent search). In memory theory, the presentation of a cue leads to a partitioning of the memory space within which search for the requested information ensues, called the memory search set. Providing additional cues that partially overlap with the current cue will decrease the size of the search set, making it easier to locate the target, as the target will receive converging input. This beneficial effect of additional cues is implemented explicitly in models of memory search (e.g., Raaijmakers & Shiffrin, 1981) in which the cues are combined multiplicatively, leaving only items that are associated with all cues to be candidates for retrieval. In the case of the RAT, only one item, the target, remains in the search set. Yet, as will be discussed, in the RAT, retrieval success can be very low. As there are three cue words in the RAT, the question becomes how search unfolds in a situation where several patches exist with irrelevant information and only a single target item. The search problem is one in which the searcher needs to maximize the activation of the target relative to the activation of the distractors. The following scenarios are considered: 1. Parallel search around each cue. In this scenario, three independent searches unfold, one in each location around each of three cues. 2. Serial search in which the search path moves from one cue patch to the next. Each cue patch is first depleted before moving to the next cue patch. 3. Serial search in which the search path moves from one cue patch to the next without depleting the patch.
510
4.
5.
6.
7.
8.
9.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
algorithm would need to define a similarity threshold below which a patch switch is assumed. Critically, the similarity-drop model requires not only that memory is structured in patches but also that the search follows the patch model of foraging. Here, the focus is on identifying the type of search observed when solving the cRAT, allowing for the possibility that the patch model of search may not apply. The term “optimal” might seem contentious. Hills et al. (2012) referred to “optimal” semantic search in verbal fluency based on the finding that the patch model is an optimal solution for problems of a certain description (resources distributed in patches, patches deplete when consumed, cost function to foraging behavior). However, the observation that the patch model captures some of the findings in verbal fluency tasks does not mean that all search in semantic memory can be captured using the patch model. Thus, an optimal search process for the RAT might be fundamentally different than processes that are closely linked to the patch model. Cues can also have detrimental effects on retrieval when the additional cue is strongly associated with many nontarget items. To truly be beneficial, the additional cues should be diagnostic or discriminative of the target (Goh & Lu, 2012; Nairne, 2002; Poirier et al., 2012). An alternative approach is to use a regression equation derived from the word association database that links the maximum likely conditional probability to the cosine similarity between vectors of response i and cue j. This procedure led to a constant for the maximal likely conditional probability due the extreme exponential distribution of the probabilities. The qualitative pattern remains the same when individual cue patches are introduced. The only difference is that transitions between cue patches are more prominent than transitions within cue patches. The ARC is calculated as the ratio between the observed within-patch transitions minus the expected within-patch transitions and the maximum number of withinpatch transitions minus the expected within-patch transitions. In addition, the interresponse times increased over successive transitions as shown in the free recall literature (Murdock & Okada, 1970). Interestingly, for solved trials that ended with the solution word, the last interresponse time was independent of the number of items retrieved (p > .38). For unsolved trials, the last interresponse times were slower (t(1372) = 3.34, p = .001) and decreased with the number of items retrieved (t(984) = 2.76, p < .01). A regression analysis confirmed the interaction (t(1372) = 1.99, p < .05). Although the study was not designed to obtain precise temporal data, these results do indicate that enough precision was present.
References Ash, I. K., & Wiley, J. (2006). The nature of restructuring in insight: An individual-differences approach. Psychonomic Bulletin & Review, 13, 66–73.
E. J. Davelaar / Topics in Cognitive Science 7 (2015) (A)
(B)
499
(C)
Fig. 1. Three possible scenarios in which three cues demarcate the cRAT patch in semantic space. The cRAT patch is defined as the collection of first-reported items following the presentation of the three cues. Each cue on its own would activate the area given by one circle. The target, indicated by the black dot, is per definition located in the intersection of the cues’ semantic neighborhoods and may be more similar to one of the cues. (A) The multiplicative model: only items that are in the intersection form the cRAT patch. (B) The additive model: all items in all neighborhoods belong to the cRAT patch. (C) The superadditive model: items in the intersection and items with strong cue-target similarities form the cRAT patch. These items are assumed to be the first to be reported.
To evaluate these models with respect to actual solution rates, a statistical approach is used based on the word association database by Nelson et al. (1998). This database contains word association norms of 5,018 words. From these norms, Steyvers, Shiffrin, and Nelson (2004) created a Word Association Space by compressing the 5,018 by 5,018 associations into 5,018 vectors of 400 features each. The cosine similarities between these vectors provide an index of semantic similarity. The main reason for using the WAS matrix instead of other matrices is that the WAS is based on data that were gathered using free association, which is close to the procedure used in the RAT and justifies the use of WAS as a foundation from which to build a semantic memory for RAT problems. Another approach is to use latent semantic spaces constructed from text corpora. Although these capture latent semantic information by virtue of contextual fits, they also include syntactic information that end up creating a different solution space. As the work here is not related to syntactic processing, the minimal semantic space was chosen. Of the 144 cRAT problems published by Bowden and Jung-Beeman (2003), the cue and target words of 117 problems were present in the word association database and could therefore be analyzed. For each of the 117 cRAT problems, the cosine similarity between the 400-features vectors of the target and each of the cue words was computed and between the remaining 5,014 words and each of the cue words. A variety of distance and similarity measures were derived to ascertain whether any of these measures predicted the problem solution rates. 3.1. Results and discussion The first analysis is to check whether the target word is located near the composite vector, vc, of the semantic space activated by the cue words. As the 400-feature vector,
500
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
vc, does not correspond to a unique item in the WAS, the item with the highest similarity to vc was chosen as the actual response. For all 117 cRATs, the chosen response was not the target, 108 responses were one of the cues. When the cue words were excluded, all responses were still nontargets. This means that the item closest to vc is unlikely to be a target word. However, the target word was always within the top 15 of all items. To compare, the similarity between the target item and the nearest cue word (mean = .32, median = .27) was larger than the similarity between the target item and the word nearest to vc (mean = .10, median = .03) (13 vs. 104, p < .001). Yet vc might not be an appropriate vector to use for comparison, as the similarity does not correlate with the solution rate. For example, the easiest cRAT problem (96% solution rate; cheese: cottage, swiss, cake) had three other items closer to vc, whereas the problem with only one item closer to vc (straight: forward, flush, razor) had a solution rate of 3%. Instead, the Euclidean distance between the target and cue words was used. With respect to the three-dimensional Euclidean distance, the target word was on average in the 91st percentile (median = 97.9%) of the items that were closest to the cue words. More important, the top 20 easiest cRAT problems had a maximum of nine other items that had a smaller Euclidean distance than the target word. The reported solution rates for the 15 s presentation duration (Bowden & JungBeeman, 2003) were correlated with the Euclidean distance, the sum of cue-target similarities, the minimum and maximum cue-target similarity per triplet, and the difference between the minimum and maximum cue-target similarity. All five variables correlated with the solution rate (distance: .49; summed_sim: .52; min_sim: .33; max_sim: .51; diff_sim: .48). As max_sim and diff_sim were indistinguishable (r = .99, p < .001) and summed_sim correlated highly (r > .90) with all but min_sim, both max_sim and summed_sim were excluded from further analyses. A regression analysis using distance, min_sum, and diff_sim as predictors revealed that only the similarity between the target and the weakest cue (t(113) = 2.73, p = .007) and the difference in cue-target similarity between the strongest and weakest cue (t(133) = 2.20, p = .03) remained significant. Taken together, these results suggest that performance in the cRAT is sensitive to the differential similarity between the target and the individual cue words. This finding is interpreted to indicate that search in cRAT problems involves at least local search, where each cue has an independent (and competing) contribution. It also implies that a search model that combines the cues multiplicatively and therefore focuses only on the intersection (Fig. 1A) does not capture the observed solution rates. There is ample evidence in the literature showing that the probability of recalling an item given one cue is a poor predictor of recall probability when a combination of cues is given (Rubin & Wallace, 1989). In particular, superadditive effects have been observed with dual cues, suggesting that the cues are combined in a nonlinear weighted fashion (Wiles, Humphreys, Bain, & Dennis, 1991). The exact functional form of this nonlinearity remains unknown, but it is likely to be the result of dynamic processes during the activation of items by the cue words (cf. Chappell & Humphreys, 1994). The result is that adding cues can have strong beneficial effects on semantic retrieval by honing in on the intersection of the three cue words.5
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
501
Therefore, a third, and here favored, possibility is that the three cues are combined in such a manner that the activated semantic space is smaller than expected by additive combination. Fig. 1C illustrates how superadditive cue combination could hone in on the intersection, but still be sensitive to the individual cues.
4. Experiment 1: Semantic activation Previous research has shown that individuals are able to judge whether a triplet of cue words has a solution with as little as 1.5 s exposure to the cue words (Bolte & Goschke, 2005). In human memory, the first available source for such a judgment is the pattern of memory activation in response to presentation of the triplet. This process is likely to precede any nonlinear dynamics that enhances the relative activation of the intersection compared to the items in the semantic fields of one or two cues. When given more time, participants are indeed more able to judge the solvability of a triplet (Bolte & Goschke, 2005), irrespective of actually solving the cRAT problem. Experiment 1 directly tested the hypothesis that global semantic activation provides information about solvability and thus can direct global search by providing what could be considered a “semantic saliency map” or “semantic hotspots.” 4.1. Methods 4.1.1. Participants A total of 40 participants (20 female; Mage = 45 years) volunteered for this experiment. 4.1.2. Materials and procedure Thirty triplets were constructed, of which 15 had a valid solution (e.g., watch: strap, pocket, time) and 15 triplets had no solution (e.g., hair, snack, cloud). The cue words were presented vertically on a computer screen for 3 s, followed by a screen asking the participant to indicate whether the triplet might have a solution or not. This was then followed by a blank screen in which the participant could try to solve the cRAT problem by typing in the answer. A maximum of 10 s was provided for solving the cRAT problem. 4.2. Results and discussion Results replicated previous studies (Bolte & Goschke, 2005) in that participants were above chance in correctly judging a triplet as solvable (hit rate = .66, SD = .17, t(39) = 6.17, p < .001). For the unsolvable triplets, participants were at chance (false alarm rate = .49, SD = .16, p > .69). The nonparametric detection measure of discriminability, A’, which varies between 0 and 1 (chance level is 0.5), revealed that participants were above chance in detecting a solvable triplet (A0 = .64, SD = .14, t(39) = 6.29, p < .001). When a trial was judged as solvable, only 21% of the time a correct solution
502
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
was given, 7% of the time an incorrect word was typed, and in the remaining 72% no response was provided. For every triplet, the similarity between each cue word and all 5,015 items was calculated and summed. These summed similarities form a proxy for the increased activation in semantic memory in response to the three cues. Critically, the summed similarity is maximal for items in the intersection of the cues’ semantic neighborhoods. The following measures were derived from the 5,015 summed similarities: the total, the maximum, the minimum, and the difference between the maximum and minimum. The probability of judging solvability correlated only with the maximum summed similarity (r = .53, p < .001) and the difference score (r = .55, p < .001). The two measures were indistinguishable (r = .99, p < .001). The analysis of Experiment 1 suggests that a global activation as measured with the summed similarity is available to the cognitive system and that therefore there is access to the semantic intersection at the beginning of the search. This supports the view that cues are combined, but together with solution rates being sensitive to differential targetcue similarities, the evidence favors a superadditive model (Fig. 1C). We are now in a position to address how the actual search process unfolds over time by analyzing the search protocol.
5. Experiment 2: Search protocol analysis Given that a global activation provides information about solvability, how does the search itself unfold over time? The following experiment addressed whether search in the cRAT follows a pattern consistent with optimal foraging in semantic memory. Hills et al. (2012) investigated this question in the verbal fluency task and observed that when items were grouped by subcategory, corresponding to patches, within-patch transitions had higher interitem similarity and shorter interresponse times than between-patch transitions. The study by Hills et al. (2012) contained a single external cue, that is, animal, and many targets. Essentially, verbal fluency is similar to picking berries from a field of berry bushes. The cRAT contains three external cues and only has a single target. In the introduction, three search scenarios were presented: (1) parallel search around each cue, (2) serial search around each cue until cue patch is depleted, and (3) serial search around each cue without depleting the cue patch. The analysis of the cRAT norms provided evidence in favor of cue-patch-sensitive search, whereas Experiment 1 provided further support for the view that the intersection of the cues’ semantic neighborhoods is accessible early on in search. In the current experiment, participants are required to type in any word that comes to mind while searching for the target. This procedure is necessary to produce multiple responses even though there is only a single target. Note that the goal is not to report as many items as possible, as is the case in the verbal fluency task. Therefore one cannot assume a priori that semantic search in the cRAT resembles semantic search in the fluency task, which in turn is well-described by the patch model of animal foraging.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
503
To evaluate the patch model for search behavior in the cRAT, two sets of patches are defined. First, a cRAT patch is defined as the collection of first-reported items given the three cues. All other items reported during search that were not reported in the first instance by any participant are outside the cRAT patch. This is not to say that these items are not cued by any of the cues. Considering Fig. 1C, the areas outside the cRAT patch include items that are within the cues’ semantic neighborhoods. Second, semantic neighborhoods of each cue form cue patches. Allocation of an item to a neighborhood is based on the highest similarity value between the item and the cues. With these definitions of patches, the following two questions can be addressed: Is there direct evidence for superadditive cue combination? Can patch transitions during cRAT search be described by the patch model of animal foraging? The parallel search model is predicted to produce a sequence of responses that has faster between- than within-patch transitions. The serial search model under (2) would predict larger associative strengths and smaller interresponse times for within- than between-patch transitions. In contrast, the serial search model under (3) would have more between- than within-patch transitions and interresponse times would not differ. 5.1. Methods 5.1.1. Participants A total of 300 participants volunteered in an online study using Amazon Turk. After applying strict inclusion criteria, data from 230 participants (122 female, Mage = 34 years) were used in the analyses. 5.1.2. Materials A total of 30 triplets were selected from the Bowden and Jung-Beeman (2003) norms that had .13), which could imply that a random search process is operational. Given the evidence of cue-sensitivity (from the analysis of cRAT norms), the ARC scores were recalculated when the responses were labeled in terms of cue patches (based on largest cue-response similarity) and inside/outside the RAT patch. Thus, six different patches were defined. A response was in the RAT patch if it was a word that at least one participant had mentioned at the beginning of a sequence of attempts; otherwise it was defined as being in the out of RAT patch. This inside/outside the RAT patch distinction is crossed with the cue patch, producing six patches. The ARC scores for unsolved and solved trials were at chance (ARC = .0005; p > .99) and negative (ARC = .30; t(131) = 2.88 p < .01), respectively. The negative ARC score is a crucial finding, as it suggests that multiple responses from a patch are temporally spread out more than expected by chance. In other words, the same patch is left before it was depleted and revisited during the search process. Given that this pattern differentiates solved and unsolved cRAT trials, it is assumed that this anti-clustering pattern is an indicator of a beneficial search process. According to the patch model as applied to semantic search, items obtained during within-patch transitions are more similar and have shorter interresponse times than items obtained during between-patch transitions. An ANOVA with the factors accuracy (solved/ unsolved), cue patch transition (within/between), and cRAT patch transition (inside/outside) revealed that the interitem similarities of transitions within cue patches were larger than between cue patches (F(1, 213) = 64.47, MSE = 0.004, p < .001, g2 = .23). Only for transitions in and out of the cRAT patch in solved trials were the interitem similarities unrelated to the type of cue patch transition (three-way interaction: F(1, 213) = 4.022, MSE = 0.004, p < .05, g2 = .02; two-way interaction between accuracy and cue patch transition: F(1, 213) = 10.46, MSE = 0.004, p = .001, g2 = .05). The same ANOVA conducted on interresponse times revealed only a main effect of accuracy (F(1, 215) = 9.44, MSE < 0.001, p < .01, g2 = .04), with transitions in unsolved trials being slower than in solved trials. No other main effect or interaction reached significance. Finally, for all trials that were at least three responses long, the similarity between the response words and the target was calculated (with target responses omitted for solved trials). The response-target similarity was constant across output positions and numerically higher for solved than for unsolved trials (mean solved = .046, mean unsolved = .032; p > .30). In other words, participants were not exhibiting search behavior that follows some similarity gradient. To sum up, there is evidence for the following: (a) items in the intersection are preferentially activated in semantic memory and available for selection, (b) prolonged residence in the cRAT patch is associated with solving the cRAT, (c) interresponse times do not signal cue patch boundaries as defined by cue-response similarity, and (d) solved trials exhibit a pattern of anti-clustering—less within-patch transitions than expected by chance. The absence of clustering and the benefit of anti-clustering indicates a different type of
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
507
search process that is particularly beneficial in a single-target, multi-cued recall task, such as the cRAT.
6. General discussion The aim of this work was to evaluate the patch model of foraging in semantic memory on a semantic search task that differs in the number of target items and cues. The cRAT can be considered a closed-ended task that requires convergence to a single target in semantic memory. This contrasts with the more divergent or open-ended approach needed to name as many animal names, as is the case with semantic fluency tasks. Two main questions were addressed in this article. First, how are the multiple cues used in solving the cRAT? Second, does the search behavior in the cRAT follow the optimal behavior seen in semantic fluency tasks? The statistical analysis of the cRAT norms published by Bowden and Jung-Beeman (2003) revealed that solution rates are sensitive to the cue-target similarities, as computed using semantic vectors obtained from the word association space (Steyvers et al., 2004). Experiment 1 revealed that the global semantic activation triggered by the three cues is sufficient to judge whether a triplet of cues is solvable. Finally, in Experiment 2 the probability of reporting an item given the three cues was 4.5 times higher than expected by the cues independently. These findings are consistent with a view in which the three cues activate cue-specific regions in semantic memory that interact in such a manner that the intersection among the three semantic neighborhoods get activated more strongly, but where not all cue-specific items get excluded. This pattern is depicted in Fig. 1C and is used to define a triplet-specific cRAT patch. In Experiment 2, it was found that search within the cRAT patch is more likely to lead to finding the target than search that exits the cRAT patch. Furthermore, when considering the patches around the cues, as defined by similarity between the WAS vectors of the response and cues, solved cRAT trials exhibit less within-patch transitions than expected by chance. In addition, within-patch transitions show stronger interresponse associative strengths than between-patch transitions, but no difference in interresponse times. Three search processes were considered in the introduction that produce distinct predictions with regard to clustering behavior during search. The patch model addressed by Hills et al. (2012) is a serial search model that clusters items by virtue of patch-leaving dynamics that are based on Charnov (1976) marginal value theorem. Such patch models predict clustering scores—as measured with ARC—that are larger than zero. For example, in a social fluency task, which requires the participant to name as many people that they know, Hills and Pachur (2012) obtained an ARC score of .58 with patches defined by social category (partner, family, friend, acquaintance). A parallel search model assumes that the responses are independent of each other and thus would predict chancelevel clustering behavior, that is, ARC score of zero. This was only found for cRAT trials that were unsolved. When considering the local cue patches and the global cRAT patch, for solved cRAT trials in Experiment 2, the ARC score was negative. This is consistent
508
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
with a serial search model that leaves the patch well before it is depleted and revisits the same patch later during the search process. To explain this search behavior, one needs to realize that the cRAT is a task that embodies a different optimization problem than tasks such as semantic or social fluency. Searching for the target in the cRAT leads to retrieving words that are strongly related to one of the cues. If search would follow an associative path, the process would gravitate to a local search around one of the cues. Charnov’s (1976) marginal value theorem optimizes the overall rate of gain in targets per unit time and thus can be applied to search tasks that have multiple targets distributed around several (semantic, social) patches in memory. In the cRAT, the optimal search strategy maximizes the difference in memory activation between the target and distractors. As only the target is associated to all three cues, both a local or global search will activate the target. However, a local search within a cue patch will only activate those items that are in that patch. As the three cues are unrelated words, their patches are quite separable. To maximize the difference in memory activation between the target and distractors, every retrieval attempt should increase the target activation and allow previously activated distractors to decay. This is only the case when successive samples are from different cue patches. Thus an advantageous search strategy when faced with multiple cues, each of which activates competing distractors, is to activate the cues in a sequence, transitioning to cues for which the items in cue patch has decayed most. The anti-clustering behavior is a pattern that emerges from such a search process. More generally, search for a single target given multiple cues will benefit from having the global search patch centered on the intersection of the cues’ semantic neighborhood. Thus, the observation of superadditive cue combination might reflect an adaptive process to such problems, especially when considering that the global activation is sufficient to judge whether the triplet has a solution. Future research could investigate whether other tasks involving multiple external cues lead to search patterns similar to that seen in the cRAT. A common finding in the cognitive foraging literature is that leaving a patch is associated with increased interresponse time and decreased interitem similarity. However, in this study, the interresponse times did not signal patch boundaries. One possibility is that the typed responses were too slow to meaningfully discern patch boundaries. However, there was a significant effect of solution status on interresponse times, suggesting sufficient resolution.9 A more likely explanation is that the drive to maximize the difference between target and distractor activation leads to faster between-patches transitions than expected or that the differences in interresponse times are only observed when a sizeable cluster from one patch has been retrieved. The results presented in this article contribute to the current literature on cognitive search in two ways. First, they highlight that not all search tasks in a particular domain (in this case memory) can be captured by a single search strategy. Even though data from semantic fluency are consistent with Charnov’s marginal value theorem, the theorem fails for semantic search that is constrained by multiple cues. Thus, search processes found for one task may not be useful for another task. Second, the results underscore the need to
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
509
address the question of how the search processes are discovered by the participant (if at all) and utilized. In other words, there is a need to investigate the control and selection of search processes. Future research could use tasks with multiple cues and multiple targets to test the participants’ ability to control the deployment of specific search processes. A ubiquitous aspect of searching through a pile of papers or through memory is the decision to give up the search. Search termination decisions in memory search are under intense investigation (Davelaar, Yu, Harbison, Hussey, & Dougherty, 2013; Harbison et al., 2009; Unsworth, Brewer, & Spiller, 2011). With the cRAT, giving up the search might induce new stages of the search process, such as allowing the activation of competitor items to fully decay. This process might underlie the forgetting of distracting information as with incubation effects (Vul & Pashler, 2007) and might be the mechanism behind restructuring in insight problems (Ash & Wiley, 2006). Targets that come to mind might be accompanied with a feeling of insight. The current experiments were not designed to look at stopping decisions in the cRAT or to investigate processes of insight. Further research could take a closer look at the relation between giving up decisions and the occurrence of insight in the cRAT. 6.1. Conclusion Solving cRAT problems involves searching for a single target in semantic memory using three cues. The search process differs from search in verbal fluency tasks, which also involve search through semantic memory, in that competing candidates are retrieved in response to the cues. Optimal search in cRAT involves continuous switching between cue patches, which produces a characteristic signature of anti-clustering behavior.
Acknowledgments The author thanks Michael Dougherty, Thomas Hills, Padraic Monaghan, Peter Todd, and Erica Yu for discussions and detailed comments on a previous version of this article. Experiment 2 was made possible with support by the National Science Foundation under grant BCS-1030831.
Notes 1. Some models of recognition memory involve two steps, of which the second step is a recall process (Diller, Nobel, & Shiffrin, 2001). However, the first step, a binary (old/new) decision process, is not regarded a search process. 2. This holds only if the cues are combined multiplicatively as was done by Hills et al. (2012). Other options of cue combination will be discussed below. 3. Hills et al. (2012) used a similarity-drop model to find patch boundaries. However, only 65% of the drops coincided with switches in hand-coded patches. A formal
510
4.
5.
6.
7.
8.
9.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
algorithm would need to define a similarity threshold below which a patch switch is assumed. Critically, the similarity-drop model requires not only that memory is structured in patches but also that the search follows the patch model of foraging. Here, the focus is on identifying the type of search observed when solving the cRAT, allowing for the possibility that the patch model of search may not apply. The term “optimal” might seem contentious. Hills et al. (2012) referred to “optimal” semantic search in verbal fluency based on the finding that the patch model is an optimal solution for problems of a certain description (resources distributed in patches, patches deplete when consumed, cost function to foraging behavior). However, the observation that the patch model captures some of the findings in verbal fluency tasks does not mean that all search in semantic memory can be captured using the patch model. Thus, an optimal search process for the RAT might be fundamentally different than processes that are closely linked to the patch model. Cues can also have detrimental effects on retrieval when the additional cue is strongly associated with many nontarget items. To truly be beneficial, the additional cues should be diagnostic or discriminative of the target (Goh & Lu, 2012; Nairne, 2002; Poirier et al., 2012). An alternative approach is to use a regression equation derived from the word association database that links the maximum likely conditional probability to the cosine similarity between vectors of response i and cue j. This procedure led to a constant for the maximal likely conditional probability due the extreme exponential distribution of the probabilities. The qualitative pattern remains the same when individual cue patches are introduced. The only difference is that transitions between cue patches are more prominent than transitions within cue patches. The ARC is calculated as the ratio between the observed within-patch transitions minus the expected within-patch transitions and the maximum number of withinpatch transitions minus the expected within-patch transitions. In addition, the interresponse times increased over successive transitions as shown in the free recall literature (Murdock & Okada, 1970). Interestingly, for solved trials that ended with the solution word, the last interresponse time was independent of the number of items retrieved (p > .38). For unsolved trials, the last interresponse times were slower (t(1372) = 3.34, p = .001) and decreased with the number of items retrieved (t(984) = 2.76, p < .01). A regression analysis confirmed the interaction (t(1372) = 1.99, p < .05). Although the study was not designed to obtain precise temporal data, these results do indicate that enough precision was present.
References Ash, I. K., & Wiley, J. (2006). The nature of restructuring in insight: An individual-differences approach. Psychonomic Bulletin & Review, 13, 66–73.
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
511
Bolte, A., & Goschke, T. (2005). On the speed of intuition: Intuitive judgments of semantic coherence under different response deadlines. Memory & Cognition, 33, 1248–1255. Bousfield, W. A., & Sedgewick, C. H. W. (1944). An analysis of sequences of restricted associative responses. Journal of General Psychology, 30, 149–165. Bowden, E. M., & Jung-Beeman, M. (2003). One hundred forty-four compound remote associate problems: Short insight-like problems with one-word solutions. Behavioral Research, Methods, Instruments, and Computers, 35, 634–639. Chappell, M., & Humphreys, M. S. (1994). An auto-associative neural network for sparse representations: Analysis and application to models of recognition and cued recall. Psychological Review, 101, 103–128. Charnov, E. L. (1976). Optimal foraging: The marginal value theorem. Theoretical Population Biology, 9, 129–136. Davelaar, E. J., & Raaijmakers, J. G. W. (2012). Human memory search. In P. M. Todd, T. Hills & T. Robbins (Eds.), Cognitive search: Evolution, algorithms, and the brain. Str€ ungmann forum reports (pp. 177–193). Cambridge, MA: MIT Press. Davelaar, E. J., Yu, E. C., Harbison, J. I., Hussey, E. K., & Dougherty, M. R. (2013). A rational approach to memory search termination. Cognitive Systems Research, 24, 96–103. Diller, D. E., Nobel, P. A., & Shiffrin, R. M. (2001). An ARC-REM model for accuracy and response time in recognition and recall. Journal of Experimental Psychology: Learning, Memory, and Cognition, 27, 414–435. Dougherty, M. R., & Harbison, J. I. (2007). Motivated to retrieve: How often are you willing to go back to the well when the well is dry? Journal of Experimental Psychology: Learning, Memory, and Cognition, 33, 1108–1117. Fu, W.-T., & Pirolli, P. (2007). SNIF-ACT: A cognitive model of user navigation on the world wide web. Human-Computer Interaction, 22, 255–412. Goh, W. D., & Lu, S. H. (2012). Testing the myth of the encoding-retrieval match. Memory & Cognition, 40, 28–39. Harbison, J. I., Dougherty, M. R., Davelaar, E. J., & Fayyad, B. (2009). On the lawfulness of the decision to terminate memory search. Cognition, 111, 397–402. Hills, T. T. (2006). Animal foraging and the evolution of goal-directed cognition. Cognitive Science, 30, 3– 41. Hills, T. T., Jones, M. N., & Todd, P. M. (2012). Optimal foraging in semantic memory. Psychological Review, 119, 431–440. Hills, T. T., & Pachur, T. (2012). Dynamic search and working memory in social recall. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38, 218–228. Mednick, S. A. (1962). The associative basis of the creative process. Psychological Review, 69, 220–232. Murdock, B. B., & Okada, R. (1970). Interresponse times in single-trial free recall. Journal of Experimental Psychology, 86, 263–267. Nairne, J. S. (2002). The myth of the encoding-retrieval match. Memory, 10, 389–395. Najemnik, J., & Geisler, W. S. (2005). Optimal eye movement strategies in visual search. Nature, 434, 387– 391. Nelson, D. L., McEvoy, C. L., & Schreiber, T. A. (1998). The University of South Florida word association, rhyme and word fragment norms, 1999. Available at http://w3.usf.edu/FreeAssociation/. Accessed June 7, 2012. Payne, J. S., & Duggan, G. B. (2011). Giving up problem solving. Memory & Cognition, 39, 902–913. Payne, S. J., Duggan, G. B., & Neth, H. (2007). Discretionary task interleaving: Heuristics for time allocation in cognitive foraging. Journal of Experimental Psychology: General, 136, 370–388. Pirolli, P. (2007). Information foraging theory: Adaptive interaction with information. New York, NY: Oxford University Press. Pirolli, P., & Card, S. (1999). Information foraging. Psychological Review, 106, 643–675.
512
E. J. Davelaar / Topics in Cognitive Science 7 (2015)
Poirier, M., Nairne, J. S., Morin, C., Zimmermann, F. G. S., Koutmeridou, K., & Fowler, J. (2012). Memory as discrimination: A challenge to the encoding–retrieval match principle. Journal of Experimental Psychology: Learning, Memory, and Cognition, 38, 16–29. Raaijmakers, J. G. W., & Shiffrin, R. M. (1981). Search of associative memory. Psychological Review, 88, 93–134. Roenker, D. L., Thompson, C. P., & Brown, S. C. (1971). Comparison of measures for the estimation of clustering in free recall. Psychological Bulletin, 76, 45–48. Rubin, D. C., & Wallace, W. T. (1989). Rhyme and reason: Analysis of dual retrieval cues. Journal of Experimental Psychology: Learning, Memory, and Cognition, 15, 698–709. Stephens, D. W., & Krebs, J. R. (1986). Foraging theory. Princeton, NJ: Princeton University Press. Steyvers, M., Shiffrin, R. M., & Nelson, D. L. (2004). Word association spaces for predicting semantic similarity effects in episodic memory. In A. F. Healy (Ed.), Experimental cognitive psychology and its application (pp. 237–249). Washington, DC: American Psychological Association. Unsworth, N., Brewer, G. A., & Spiller, G. J. (2011). Factors that influence search termination decision in free recall: An examination of response type and confidence. Acta Psychologica, 138, 19–29. Vul, E., & Pashler, H. (2007). Incubation effects only after people have been misdirected. Memory & Cognition, 35, 701–710. Wiles, J., Humphreys, M. S., Bain, J. D., & Dennis, S. (1991). Direct memory access using two cues: Finding the intersection of sets in a connectionist model. In R. P. Lippman, J. E. Moody, & D. S. Touretzky (Eds.), Advances in neural information processing systems 3 (pp. 635–641). San Mateo, CA: Morgan Kaufman. Wilke, A., Hutchinson, J. M. C., Todd, P. M., & Czienskowski, U. (2009). Fishing for the right words: Decision rules for human foraging behavior in internal search tasks. Cognitive Science, 33, 497–529.
