Categorization training increases the perceptual separability of novel dimensions

Highlights

• Little is known about how dimensions and features become perceptually separable.

• We explore whether categorization training increases dimensional separability.

• We use general recognition theory to test perceptual and decisional separability.

• Categorization increases perceptual separability of the relevant dimension.

• This challenges the common assumption that separability is fixed and hardwired.

Abstract

Perceptual separability is a foundational concept in cognitive psychology. A variety of research questions in perception – particularly those dealing with notions such as “independence,” “invariance,” “holism,” and “configurality” – can be characterized as special cases of the problem of perceptual separability. Furthermore, many cognitive mechanisms are applied differently to perceptually separable dimensions than to non-separable dimensions. Despite the importance of dimensional separability, surprisingly little is known about its origins. Previous research suggests that categorization training can lead to learning of novel dimensions, but it is not known whether the separability of such dimensions also increases with training. Here, we report evidence that training in a categorization task increases perceptual separability of the category-relevant dimension according to a variety of tests from general recognition theory (GRT). In Experiment 1, participants who received pre-training in a categorization task showed reduced Garner interference effects and reduced violations of marginal invariance, compared to participants who did not receive such pre-training. Both of these tests are theoretically related to violations of perceptual separability. In Experiment 2, participants who received pre-training in a categorization task showed reduced violations of perceptual separability according to a model-based analysis of data using GRT. These results are at odds with the common assumption that separability and independence are fixed, hardwired characteristics of features and dimensions.

Introduction

An important task of perceptual systems is to produce a re-description of the incoming sensory input, through a representation that is useful for the tasks that are usually encountered in the natural environment. One way to characterize internal stimulus representations is to determine whether a set of “privileged” stimulus properties exists, which can be used to describe a variety of stimuli, and that are processed and represented independently from one another. In perceptual science, an important amount of effort has been dedicated to understanding what aspects of stimuli are represented in such an independent fashion (e.g., Bruce and Young, 1986, Haxby et al., 2000, Kanwisher, 2000, Op de Beeck et al., 2008, Stankiewicz, 2002, Ungerleider and Haxby, 1994, Vogels et al., 2001).

There are many different conceptual and operational definitions of what it means for two stimulus dimensions to be independent (Ashby & Townsend, 1986), but perhaps the most widely studied and influential type of independence is dimensional separability. Separable stimulus dimensions are those that can be selectively attended and that directly determine the similarity among stimuli (Garner, 1974, Shepard, 1991). This is in contrast to integral dimensions, which cannot be selectively attended and do not directly determine the similarity among stimuli. When stimuli vary along integral dimensions, their similarity is directly perceived and the notion of dimensions loses meaning.

There are two main reasons to believe that a complete understanding of complex forms of visual cognition, such as object recognition and categorization, will benefit from a good understanding of perceptual separability. The first reason is that many important questions in perceptual science can be understood as questions about perceptual separability of object dimensions.

For example, in the area of visual object recognition, the question of whether object representations are invariant across changes in identity-preserving variables (such as rotation and translation; for reviews, see Biederman, 2001, Kravitz et al., 2008, Peissig and Tarr, 2007) is essentially the same as the question of whether object representations are perceptually separable from such variables. Shape dimensions that may be important for invariant object recognition have been shown to be separable from other shape dimensions and from viewpoint information, according to traditional tests of separability (Stankiewicz, 2002).

A second example comes from the area of face perception. It has been proposed that a hallmark of human face perception is that faces are processed in a configural or holistic manner (for reviews, see Farah et al., 1998, Maurer et al., 2002, Richler et al., 2012). Configural or holistic face perception can be seen as non-separable processing of different face features (e.g., Mestry et al., 2012, Richler et al., 2008, Thomas, 2001). Similarly, influential theories of face processing have proposed that different aspects of faces, such as identity and emotional expression, are processed independently (e.g., Bruce and Young, 1986, Haxby et al., 2000) and these hypotheses are usually investigated using tests of perceptual separability (e.g., Fitousi and Wenger, 2013, Ganel and Goshen-Gottstein, 2004, Schweinberger and Soukup, 1998, Soto et al., 2015).

Casting such research questions in terms of perceptual separability is not only possible, but desirable. As we will see below, perceptual separability has a precise formal definition within multidimensional signal detection theory (Ashby & Townsend, 1986; for a review, see Ashby & Soto, 2015), which offers the advantage of providing strict definitions to rather ambiguous concepts such as independence, holistic processing, configural processing, etcetera (e.g., Fitousi and Wenger, 2013, Mestry et al., 2012, Richler et al., 2008). Furthermore, it allows us to determine whether behavioral evidence of a dimensional interaction is due to true perceptual interactions versus interactions at the level of decisional processes.

The fact that a variety of research questions in visual cognition can be characterized as special cases of the problem of perceptual separability suggests that a better understanding of this general problem, including explanations of why some dimensions are separable and how they acquired such status, would necessarily lead to a better understanding of each of the special cases.

A second reason why an understanding of perceptual separability is important to understand visual cognition is that considerable evidence suggests that higher-level cognitive mechanisms are applied differently when stimuli differ along separable dimensions rather than along integral dimensions. Given the definition of perceptual separability, the most obvious of such mechanisms is selective attention, which is more easily deployed to separable than to non-separable dimensions (e.g., Garner, 1970, Garner, 1974, Goldstone, 1994b). Other examples of processes that might be applied differently to separable-dimension and integral-dimension stimuli are the rules by which different sources of predictive and causal knowledge are combined (Soto, Gershman, & Niv, 2014), as well as the performance cost of storing an additional object in visual working memory (Bae & Flombaum, 2013).

There is much evidence suggesting that the mechanisms used by people to categorize stimuli vary depending on whether or not categories differ along separable dimensions. Some of this evidence comes from studies using unsupervised categorization tasks, in which people are asked to group stimuli in two or more categories without feedback about their performance. When stimuli in unsupervised categorization tasks vary along separable dimensions, people rely almost exclusively on one-dimensional strategies (Handel and Imai, 1972, Handel et al., 1980, Medin et al., 1987), even in tasks in which categories are not defined by a simple one-dimensional rule and after being explicitly told that the optimal strategy is to integrate information from two dimensions (Ashby, Queller, & Berretty, 1999). Furthermore, unsupervised learning is possible only when the categories clearly differ along a single dimension (Ashby et al., 1999). On the other hand, when stimuli vary along integral dimensions, people show limited ability to learn unsupervised categories and they do not show a strong preference for one-dimensional rules. Instead, they show a variety of strategies, including integration of information from both dimensions (Ell, Ashby, & Hutchinson, 2012).

A similar pattern of results is found in supervised categorization tasks, in which categorization choices are followed by feedback. When stimuli vary along separable dimensions, learning a category structure in which good performance requires attending to a single dimension is much easier for people than learning an equivalent category structure in which good performance requires integration of information from two dimensions (e.g., Smith, Beran, Crossley, Boomer, & Ashby, 2010). There is a large body of evidence suggesting that the one-dimensional categorization task is learned through a rule-based categorization system, whereas the information-integration task is learned through a separate procedural categorization system (for reviews, see Ashby and Maddox, 2005, Ashby and Valentin, 2005). On the other hand, when stimuli vary along integral dimensions, a one-dimensional task is not consistently easier to learn than an information-integration task (Ell et al., 2012).

Despite the importance of dimensional separability for our understanding of both perception and high-level cognition, surprisingly little is known about its origins. Specifically, an important open question is whether separable dimensions can be learned and what are the conditions that might foster such learning. Our previous review of the literature suggests that this is a foundational question in the field of object categorization and recognition. If perceptual separability of a dimension can be learned and we could understand the mechanisms by which such learning happens, then we would not only be in a better position to explain why some object dimensions are “special,” in the sense of being processed independently, but also how they became special (i.e., what conditions fostered this learning) and why they should be processed in such a privileged fashion (i.e., why it is adaptive for high-level cognitive mechanisms to operate differently on these representations).

In the following section, we introduce general recognition theory (GRT), a formal framework within which perceptual separability can be defined and studied. This is followed by a review of previous literature related to the idea of separability learning.

GRT is an extension of signal detection theory to cases in which stimuli vary along two or more dimensions (Ashby & Townsend, 1986; for a tutorial review, see Ashby & Soto, 2015). It offers a framework in which different types of dimensional interactions can be defined formally and studied, while inheriting from signal detection theory the ability to dissociate perceptual from decisional sources for such interactions. For this reason, GRT is arguably the best framework for the analysis and interpretation of studies aimed at testing different forms of dimensional independence.

GRT assumes that repeated presentations of a single stimulus produce different perceptual effects, which follow some probability distribution. The most common applications of GRT are to tasks in which stimuli vary in two dimensions, A and B, each with two stimulus components, resulting in four stimuli: A₁B₁, A₂B₁, A₂B₁ and A₂B₂. Fig. 1 is an example of a GRT model for such a 2 × 2 design. In this model, each stimulus generates perceptual effects according to a different bivariate normal distribution. Each distribution is represented in the figure by a different ellipse, which represents the set of all percepts that are elicited with equal likelihood by the stimulus. For any ellipse (and therefore any stimulus), percepts inside the ellipse are more likely than percepts outside the ellipse. After many presentations of a particular stimulus, the scatterplot of perceptual effects will take the shape of the ellipse corresponding to that stimulus. However, in some cases, presenting a stimulus will produce a percept that lies outside that stimulus’ ellipse, perhaps closer to the ellipse corresponding to a different stimulus. In all cases, a decision must be made about what stimulus was actually presented. This decision process is modeled by assuming that a participant sets decision bounds that divide the perceptual space into different regions, each corresponding to the identification of a particular stimulus. The simplest decision bounds are lines, like those shown in Fig. 1, which are used to make decisions about both the level of dimension A and the level of dimension B.

In this framework, dimension A is perceptually separable from dimension B if the perceptual effects associated with dimension A do not depend on the level of dimension B. Mathematically this occurs if (and only if) the marginal distribution of perceptual effects along dimension A is the same across levels of B. Marginal distributions for dimensions A and B are depicted at the bottom and left of Fig. 1, respectively. The marginal distributions for dimension B are identical, regardless of the level of A, meaning that dimension B is perceptually separable from dimension A. Conversely, the marginal distributions for dimension A are farther apart for level 1 of dimension B than for level 2 of dimension B, meaning that dimension A is not perceptually separable from dimension B.

There are other forms of dimensional interaction that can be defined within GRT besides perceptual separability (Ashby & Townsend, 1986). One of these is decisional separability. Dimension A is decisionally separable from dimension B if the strategy used to decide the level of dimension A does not depend on the perceived value of dimension B. Mathematically, decisional separability holds if (and only if) the decision bounds are linear and orthogonal to each stimulus dimension. In Fig. 1, this means that dimension A is decisionally separable from dimension B, but dimension B is not decisionally separable from dimension A.

Finally, perceptual independence refers to dimensional interactions within a single stimulus. Perceptual independence holds for stimulus A_iB_j if the perceived value of the A component is statistically independent from the perceived value of the B component, which is true in the multivariate normal case when the correlation between dimensions is zero. In Fig. 1, the diagonally-oriented ellipse for stimulus A₁B₂, representing a positive correlation between dimensions, is a sign of violations of perceptual independence for that stimulus.

In applications of GRT, inferences are made about these types of dimensional interactions from behavioral data. There is a number of theorems in the literature that link each type of dimensional interaction with statistics that can be computed from identification and categorization data (Ashby and Maddox, 1994, Ashby and Townsend, 1986, Kadlec and Townsend, 1992a, Kadlec and Townsend, 1992b). Another approach is to fit one or more GRT models directly to the data; the parameter values of the best-fitting model can then be used to characterize the pattern of dimensional interactions (Ashby and Lee, 1991, Soto et al., 2015, Thomas, 2001). Here, we will use both the summary statistics and model-based approaches to study perceptual separability.

There are clear advantages to using GRT for the study of perceptual separability, instead of simply relying on traditional tests and operational definitions. The theory provides a formal definition of perceptual separability that coherently links together a number of operational definitions. This permits the consistent study of the same underlying concept through different tests and experimental designs. Furthermore, GRT allows the focus to be on perceptual separability by dissociating its influence on behavior from other forms of interactions. In particular, here we will be interested in whether training in categorization tasks produces changes in perceptual separability, independently of any changes in decision strategies. The analysis of dimensional interactions via GRT is critical to achieving this goal, as it is known that traditional tests of separability are influenced by variables such as experimental instructions (Foard and Kemler-Nelson, 1984, Melara et al., 1992), which are likely to affect decision strategies instead of perceptual interactions (Ashby, Waldron, Lee, & Berkman, 2001).

The hypothesis that learning might have an influence on the separability of psychological dimensions is as old as the concept of separability itself (see Garner, 1970). In support of this hypothesis, developmental data have shown that the ability to selectively attend to separable stimulus dimensions develops with age. Stimulus dimensions that are perceived as integrated wholes by pre-school children are instead perceived as analytic components by older children and adults (for a recent review, see Hanania & Smith, 2010). However, it is not clear that such developmental trends are a product of learning, or even of increments in the separability of specific dimensions, as they could be the product of developmental changes in selective attention abilities. Evidence suggesting that color experts can selectively attend to at least some integral color dimensions more easily than non-experts more clearly points towards a role of learning in determining dimensional separability (Burns & Shepp, 1988).

Although little is known about what conditions might foster learning of separable dimensions, one possibility is that these conditions are met in categorization tasks. A controversial hypothesis in the field of object categorization and recognition is that these processes are often accompanied by the creation of new features (Schyns, Goldstone, & Thibaut, 1998).

There is a large body of work suggesting that categorization training does produce changes in perceptual representations of the stimuli involved (for recent reviews, see Goldstone et al., 2009, Goldstone and Hendrickson, 2010). Stimulus dimensions that are relevant for category discrimination become more distinctive, in what has been termed “acquired distinctiveness.” Operationally, acquired distinctiveness is observed as an increase in discriminability along the category-relevant dimension after categorization training. A special case occurs when the greatest enhancement in discriminability is seen at the boundary between categories, which can be interpreted as a case of acquired categorical perception. On the other hand, stimulus components that are irrelevant for category discrimination become less distinctive, in what has been termed “acquired equivalence.” Operationally, acquired equivalence is observed as a decrease in discriminability along the category-irrelevant dimension after categorization training.

Some evidence suggests that categorization training involving already-existing separable dimensions produces both acquired distinctiveness along the relevant dimension and acquired equivalence along the irrelevant dimension. On the other hand, categorization training involving integral dimensions produces acquired distinctiveness in both relevant and irrelevant dimensions (Goldstone, 1994b). These results are consistent with the possibility that categorization training alters selective attention to the category-relevant dimension. With separable dimensions, the category-relevant dimension can be selectively attended, whereas with integral dimensions, attention must be paid to both dimensions. Still, the increase in discriminability of integral dimensions was larger for the category-relevant dimension than the category-irrelevant dimension. Goldstone interpreted these results as suggesting that categorization training produces differentiation of integral dimensions.

However, using the same integral dimensions as Goldstone (saturation and brightness), Foard and Kemler-Nelson (1984) found evidence that learning effects in a sorting task transferred across different sets of stimuli only when the task-relevant dimension corresponded to the dimensions identified by the experimenter (that is, either saturation or brightness). If the task-relevant dimension was rotated 45 degrees from the original dimensions, learning did not transfer. This suggests that the integral dimensions of saturation and brightness might be primary axes in stimulus space (Smith & Kemler, 1978) despite the fact that they usually interact during perceptual tasks (see also Melara, Marks, & Potts, 1993). Thus, the results reported by Goldstone (1994b) can be interpreted as an increase in selective attention or as further differentiation of already-existing psychological dimensions.

There is also evidence suggesting that categorization training produces novel psychologically-differentiated stimulus dimensions. Goldstone and Steyvers (2001) were the first to report evidence for such an effect. In their study, complex novel stimulus dimensions were created by taking two faces and gradually morphing one into the other in a continuous sequence. A two-dimensional face space was then created by taking two such face dimensions and factorially morphing each of their levels (see Fig. 2). In their first experiment, Goldstone and Steyvers found that training in a categorization task in which one novel dimension was relevant and another was irrelevant transferred to a new task in which either the relevant or the irrelevant dimension was replaced by a completely new dimension. Further experiments showed that these effects are not simply due to similarity-based transfer, but are better explained as the outcome of dimension differentiation. People were trained with two categorization rules using the same pair of stimulus dimensions. After learning the first categorization rule, better transfer was observed if the second rule was a 90-degree rotation from the first (i.e., the irrelevant dimension became relevant and vice versa) than if it involved a 45-degrees rotation, despite the fact that a smaller number of stimuli switched labels in the latter case. The same effects were not found if the stimuli could be described by relatively separable dimensions from the start, such as the shape of eyes and mouth. This suggests that the existence of previously available separable dimensions impairs learning of new dimensions during categorization tasks. If such dimensions do not exist, however, any direction in stimulus space can become a novel differentiated dimension, insofar as the stimulus space is created through factorial combination of stimulus sequences (Folstein, Gauthier, & Palmeri, 2012).

In contrast to these reports, there have been some failures to find any effect of categorization training on dimension differentiation when the stimuli were novel shapes created by combining sinusoidal functions (Op de Beeck, Wagemans, & Vogels, 2003). Even so, other evidence suggests that the use of special categorization training procedures that are thought to produce learning of more “robust” categories, can lead to dimension differentiation using such novel shapes (Hockema, Blair, & Goldstone, 2005).

This line of research has been driven mostly by the hypothesis that category learning is accompanied by the learning of novel features and dimensions, but the question as to whether such dimensions are truly separable has remained unanswered. Although some results have been interpreted as supporting the hypothesis of separability learning (Goldstone and Steyvers, 2001, Hockema et al., 2005), no previous experiment has directly tested this hypothesis by actually assessing dimensional separability of the relevant dimensions before and after categorization training. The rotation test performed in some of these studies (Folstein et al., 2012, Goldstone and Steyvers, 2001) is suggestive of dimension learning, but it is not usually considered a test of dimensional separability. Instead, it is better described as a test of whether two dimensions are “primary axes” (Smith & Kemler, 1978) – that is, psychologically meaningful directions in stimulus space –, even though they might combine in an integral fashion (Grau and Nelson, 1988, Melara et al., 1993). The related concepts of acquired distinctiveness and acquired equivalence are also different from separability learning, as they refer to changes in discriminability of the category-relevant and category-irrelevant dimensions, respectively, while separability learning refers to changes in the interaction between both dimensions. Thus, tests of these two concepts are also different from tests of separability learning. As we have seen earlier, perceptually separable dimensions are processed in special ways that are not true of all stimulus dimensions. Thus, an important open question is whether categorization training increases the separability of a novel category-relevant dimension.

The goal of the present study was to evaluate whether categorization training increases dimensional separability of the category-relevant dimension, using traditional tests of separability and GRT-based analyses.

We studied separability of completely novel dimensions created through face morphing, as in the seminal work of Goldstone and Steyvers (2001). Using novel dimensions built through morphing is convenient because there is evidence suggesting that such dimensions are integral (Goldstone & Steyvers, 2001) and that there are no psychologically-meaningful directions in a space constructed this way (Folstein et al., 2012). Furthermore, morphing results in stimuli and dimensions that seem more ecologically valid than completely artificial stimuli.

We created a two-dimensional space of faces and trained participants in a categorization task that could be solved by selectively attending to only one of those dimensions. Next, we tested separability of the category-relevant dimension in the context of a completely novel dimension, never seen during training. We were interested in learning that is specific to the relevant training dimension, but not specific to the stimuli and irrelevant dimensions seen during training. We reasoned that when people are presented with new problems involving known dimensions, it is unlikely that such problems involve exactly the same stimuli and dimensions experienced earlier. Instead, new objects are likely to have properties that have never been seen before. Furthermore, finding that the separability of a dimension increases even when it is tested with a completely new dimension implies that there has been separability learning with the original dimensions, which generalizes across changes in the category-irrelevant dimension. This is a more general finding than observing increases in separability only for the originally-trained dimensions.

Two different tasks were used to test perceptual separability. In Experiment 1, we used the popular Garner filtering task and evaluated separability using a summary statistics approach to GRT analyses. In Experiment 2, we used an identification task and evaluated separability by directly estimating the parameters of a GRT model from the data using maximum likelihood estimation, followed by tests of separability performed on such estimates.