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...r that object features are drawn from a distribution of features and make uncertain inferences accordingly. In our desk example, this would imply that if you did not know exactly where a paper was, you might recall it as closer to the center of the pile to compensate for your uncertainty; although this strategy yields some bias in in your estimate of the location, it decreases variance and thus improves overall memory fidelity. The structure of multiple objects may also constrain the individual constituent objects more rigidly into multiobject ‘‘chunks’’ (Brady & Tenenbaum, 2013; Cowan, 2001; Miller, 1956). Chunking accounts tacitly assumes that an inferred chunk completely constrains its subparts (e.g., encoding ‘‘FBI’’ fully determines its constituent letters). Thus, chunking is classically considered to be a fixed memory structure (what we might call ‘‘hard chunking’’), such that people remember only the chunk and nothing about its constituent elements. However, if this encoding strategy is softened to allow some information to be preserved about the Citation: Lew, T. F., & Vul, E. (2015). Ensemble clustering in visual working memory biases location memories and reduces the Weber noise of re...

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...itions of objects: Rather than remember the absolute position of a paper, you may remember its position relative to your desk (e.g., the paper is one foot northwest of your desk; Hollingworth, 2007; Huttenlocher, Hedges, & Duncan, 1991). This relative encoding may be adapted to accommodate hierarchical structures via an assumption that people encode the relative discrepancy between features of individual objects and the average features of the ensemble. This relative encoding view is consistent with vector-summation models of multiobject motion parsing (Gershman, Tenenbaum & Jakel, in press; Johansson, 1973) and spatial positions (Mutluturk & Boduroglu, 2014). Intuitively, instead of remembering the locations of your papers relative to your desk, you may remember the locations of individual papers relative to the centroid of all the papers. Thus, the space of possible structures that people might use to encode objects can be considered along several dimensions: (a) Do people encode individual items with no information about their structure (independent encoding)? Or do they only encode the structure, losing all information about constituent elements (hard chunking)? Or something in between, such ...

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... ISSN 1534-7362 2015 ARVOReceived February 7, 2015; published September 11, 2015 Downloaded from jov.arvojournals.org on 07/01/2019 constituent elements of a chunk (‘‘soft chunking’’), such an account is consistent with encoding a hierarchical generative model that probabilistically constrains individual elements. Additionally, studies of spatial memory suggest that people encode the relative positions of objects: Rather than remember the absolute position of a paper, you may remember its position relative to your desk (e.g., the paper is one foot northwest of your desk; Hollingworth, 2007; Huttenlocher, Hedges, & Duncan, 1991). This relative encoding may be adapted to accommodate hierarchical structures via an assumption that people encode the relative discrepancy between features of individual objects and the average features of the ensemble. This relative encoding view is consistent with vector-summation models of multiobject motion parsing (Gershman, Tenenbaum & Jakel, in press; Johansson, 1973) and spatial positions (Mutluturk & Boduroglu, 2014). Intuitively, instead of remembering the locations of your papers relative to your desk, you may remember the locations of individual papers relative to the centroid ...

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...ructure of objects (Brady et al., 2009; Orhan, Sims, Jacobs, & Knill, 2014; Sims et al., 2012). By decreasing the relative distances between objects, clustering may have allowed a more efficient encoding of the objects, ostensibly increasing observers’ capacity. Limitations Although we defined chunking as subjects retaining memories of clusters but not individual objects, there are other ways subjects could have encoded objects’ structure while discarding information about the individual objects. Subjects may have encoded sets of locations as familiar shapes, such as squares, triangles, etc. (Yantis, 1992). They could have then used these remembered shapes, rather than the cluster centers, to constrain the locations of objects. Under this account, no information about individual objects would be preserved over and above the ‘‘chunk,’’ but our analysis would still yield reliable information about the relative (within cluster) positions of individual objects. Another ambiguity of our analysis arises from the assumption that subjects computed the centers of clusters and encoded individual objects relative to those centers (and reported objects with bias toward those center). An alternative possibi...

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..., Konkle, & Alvarez, 2009; Sims, Jacobs, & Knill, 2012). Knowing that your papers are scattered in a pile around your desk, for example, constrains their possible locations (e.g., it is unlikely they are in the bathroom) and can help you remember where individual papers are. Given that people appear to encode and utilize not only individual objects but also the higher-order structure of objects, what is the format of structured memories? In contrast to the traditional assumption that objects in visual working memory are encoded independently (Anderson, Vogel, & Awh, 2011; Bays & Husain, 2008; Zhang & Luck, 2008; for review, see Ma, Husain, & Bays, 2014), recent studies have demonstrated that memory exploits the statistical structure of scenes. Specifically, people infer the ensemble statistics of objects (such as the average location of objects; Alvarez & Oliva, 2009; Ariely, 2001) and combine these ensemble statistics with uncertain estimates of individual object properties (Brady & Alvarez, 2011; Brady & Tenenbaum, 2013; Orhan & Jacobs, 2013). This encoding strategy can be described as reliance on a hierarchical generative model: People infer that object features are drawn from a distribution of f...

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... 10 .1167 /15 .4 .10 ISSN 1534-7362 2015 ARVOReceived February 7, 2015; published September 11, 2015 Downloaded from jov.arvojournals.org on 07/01/2019 constituent elements of a chunk (‘‘soft chunking’’), such an account is consistent with encoding a hierarchical generative model that probabilistically constrains individual elements. Additionally, studies of spatial memory suggest that people encode the relative positions of objects: Rather than remember the absolute position of a paper, you may remember its position relative to your desk (e.g., the paper is one foot northwest of your desk; Hollingworth, 2007; Huttenlocher, Hedges, & Duncan, 1991). This relative encoding may be adapted to accommodate hierarchical structures via an assumption that people encode the relative discrepancy between features of individual objects and the average features of the ensemble. This relative encoding view is consistent with vector-summation models of multiobject motion parsing (Gershman, Tenenbaum & Jakel, in press; Johansson, 1973) and spatial positions (Mutluturk & Boduroglu, 2014). Intuitively, instead of remembering the locations of your papers relative to your desk, you may remember the locations of indiv...

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... (e.g., Brady, Konkle, Gill, Oliva, & Alvarez, 2013)4 and because they seem insufficient to attain the precision exhibited by visual spatial memory. Because verbally encoded spatial relations (such as ‘‘above’’ or ‘‘left’’) offer only imprecise location information, we suspect that the main benefit of such verbal encoding was to reduce misassociations between objects (Lew, Pashler, & Vul, in press) rather than encoding the locations themselves. Additionally, patterns of oculomotor movements and attentional shifts could have influenced performance by interfering with encoding in visual memory (Lawrence, Myerson, & Abrams, 2004). Although the uniform distribution of cluster centers in our study still mandates many changes of fixation, it is possible that clustering yields fewer eye movements and attentional shifts between objects in the same cluster, improving the fidelity of memories. Our presentation times were also longer than most visual working memory studies, which may have given subjects more time to encode objects. Given that performance appears to asymptote with display times shorter than those used in the current study (Bays, Gorgoraptis, Wee, Marshall, & Husain, 2011), our results may reflect how people e...

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...obs, & Knill, 2012). Knowing that your papers are scattered in a pile around your desk, for example, constrains their possible locations (e.g., it is unlikely they are in the bathroom) and can help you remember where individual papers are. Given that people appear to encode and utilize not only individual objects but also the higher-order structure of objects, what is the format of structured memories? In contrast to the traditional assumption that objects in visual working memory are encoded independently (Anderson, Vogel, & Awh, 2011; Bays & Husain, 2008; Zhang & Luck, 2008; for review, see Ma, Husain, & Bays, 2014), recent studies have demonstrated that memory exploits the statistical structure of scenes. Specifically, people infer the ensemble statistics of objects (such as the average location of objects; Alvarez & Oliva, 2009; Ariely, 2001) and combine these ensemble statistics with uncertain estimates of individual object properties (Brady & Alvarez, 2011; Brady & Tenenbaum, 2013; Orhan & Jacobs, 2013). This encoding strategy can be described as reliance on a hierarchical generative model: People infer that object features are drawn from a distribution of features and make uncertain inferences acco...

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...ers to recall the locations of objects. Importantly, the chunking model knows nothing about the locations of the individual objects. Instead, the model recalls the location of an object by randomly sampling from the object’s cluster based on the center and standard deviation of the cluster estimated by the Dirichlet process. The model has no free parameters. Hierarchical generative model The hierarchical generative model uses knowledge of clusters’ locations to compensate for uncertainty in the individual objects’ locations. This model is similar to the Dirichlet process mixture model used by Orhan and Jacobs (2013). The hierarchical generative model noisily encodes the absolute locations of all the objects as well as the properties of their clusters. Because the model pools memories of individual objects to determine the mean and dispersion of their respective clusters, each additional object in a cluster allows the model to estimate the position of that cluster more precisely. This model uses the same process to estimate the precision of the global center from the locations of the clusters. During recall, the model first recalls the locations of the clusters by averaging the positions of the clusters a...

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...all by biasing the recall of locations toward cluster centers to compensate for uncertainty and by reducing the magnitude of encoded relative distances. Introduction Our visual working memory is limited in its ability to remember objects. In addition to remembering the individual elements of scenes, people may also extract the higher-order structure of an image, such as the elements’ average size (e.g., Ariely, 2001) or average location (e.g., Alvarez & Oliva, 2009). People can then use that statistical structure to help remember objects (Brady & Alvarez, 2011; Brady, Konkle, & Alvarez, 2009; Sims, Jacobs, & Knill, 2012). Knowing that your papers are scattered in a pile around your desk, for example, constrains their possible locations (e.g., it is unlikely they are in the bathroom) and can help you remember where individual papers are. Given that people appear to encode and utilize not only individual objects but also the higher-order structure of objects, what is the format of structured memories? In contrast to the traditional assumption that objects in visual working memory are encoded independently (Anderson, Vogel, & Awh, 2011; Bays & Husain, 2008; Zhang & Luck, 2008; for review, see Ma, Husain, & Bays...

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...d; subjects may have consequently sought to connect the two. Because locations and identities were independent, the conflict between subjects’ priors and the lack of structure in the stimuli may have even impaired performance (Orhan et al., 2014). If the structure of locations and identities had been correlated—such as if all the objects in the same cluster were the same color or same type of animal— subjects may have used the structure of one to inform the other. Given that being able to perceptually group objects based on proximity appears to improve the ensemble encoding of other features (Im & Chong, 2014), it is possible that objects in the same spatial cluster would have even been recalled with more similar features/identities. Future studies may examine how the hierarchical encoding of objects affects binding. Other factors may have improved subjects’ apparent memory capacity in our study. Unlike many prior studies, we used distinct objects that never repeated, which may have reduced interference between objects (Endress & Potter, 2014). Furthermore, many subjects reported using verbal strategies (e.g., ‘‘the pants are above the shoes’’) to help remember displays. We suspect that such strate...

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...icated on a fixed number of slots in visual working memory (Anderson et al., 2011; Zhang & Luck, 2008). Additionally, neither such slot models nor flexible resource models (Bays & Husain, 2008; for review, see Ma et al., 2014) capture the effect of scene structure on memory fidelity. Instead, our results are consistent with recent work suggesting that visual working memory performance is constrained by both memory capacity Journal of Vision (2015) 15(4):10, 1–14 Lew & Vul 8 Downloaded from jov.arvojournals.org on 07/01/2019 and the encoded statistical structure of objects (Brady et al., 2009; Orhan, Sims, Jacobs, & Knill, 2014; Sims et al., 2012). By decreasing the relative distances between objects, clustering may have allowed a more efficient encoding of the objects, ostensibly increasing observers’ capacity. Limitations Although we defined chunking as subjects retaining memories of clusters but not individual objects, there are other ways subjects could have encoded objects’ structure while discarding information about the individual objects. Subjects may have encoded sets of locations as familiar shapes, such as squares, triangles, etc. (Yantis, 1992). They could have then used these remembered shapes, rather t...

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... of bias suggests that subjects encoded objects in a hierarchical generative model but did not rely primarily on this form of representation. Did subjects encode objects in a relative position tree? Subjects may have encoded objects in a relative position tree, wherein object positions are coded as relative offsets from the cluster centers, and cluster centers are coded as relative offsets from the global center. At first glance, this is no different from encoding the objects according to their absolute position. However, if relative positions are recalled with Weber noise (Sims et al., 2012; Tudusciuc & Nieder, 2010), then larger relative distances will be more difficult to recall. Because the relative distances between objects decrease with more clustering, this could explain why subjects remembered more densely clustered objects more accurately. Under such a relative encoding scheme, environments that happened to contain more dispersed clusters3 require larger relative distances to represent positions. Consequently, as the dispersion of clusters in the environment increases, subjects should recall clusters less precisely (that is, rc should increase). The dispersion of clusters in an environment was sig...

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...the absolute position of a paper, you may remember its position relative to your desk (e.g., the paper is one foot northwest of your desk; Hollingworth, 2007; Huttenlocher, Hedges, & Duncan, 1991). This relative encoding may be adapted to accommodate hierarchical structures via an assumption that people encode the relative discrepancy between features of individual objects and the average features of the ensemble. This relative encoding view is consistent with vector-summation models of multiobject motion parsing (Gershman, Tenenbaum & Jakel, in press; Johansson, 1973) and spatial positions (Mutluturk & Boduroglu, 2014). Intuitively, instead of remembering the locations of your papers relative to your desk, you may remember the locations of individual papers relative to the centroid of all the papers. Thus, the space of possible structures that people might use to encode objects can be considered along several dimensions: (a) Do people encode individual items with no information about their structure (independent encoding)? Or do they only encode the structure, losing all information about constituent elements (hard chunking)? Or something in between, such that the overarching structure informs individual ob...