Encoding Shape and Spatial Relations: The Role of Receptive Field Size in Coordinating Complementary Representations

An effective functional architecture facilitates interactions among subsystems that are often used together. Computer simulations showed that differences in receptive field sizes can promote such organization. When input was filtered through relatively small nonoverlapping receptive fields, artificial neural net-works learned to categorize shapes relatively quickly; in contrast, when input was filtered through relatively large overlapping receptive fields, networks learned to encode specific shape exemplars or metric spatial relations relatively quickly. Moreover, when the receptive field sizes were allowed to adapt during learning, networks developed smaller receptive fields when they were trained to categorize shapes or spatial relations, and developed larger receptive fields when they were trained to encode specific exemplars or metric distances. In addition, when pairs of networks were constrained to use input from the same type of receptive fields, networks learned a task faster when they were paired with networks that were trained to perform a compatible type of task. Finally, using a novel modular architecture, networks were not preassigned a task, but rather competed to perform the different tasks. Networks with small nonover-lapping receptive fields tended to win the competition for categorical tasks whereas networks with large overlapping receptive fields tended to win the competition for exemplar/metric tasks.     

Processing spatial relations with different apertures of attention

Neuropsychological studies suggest the existence of lateralized networks that represent categorical and coordinate types of spatial information. In addition, studies with neural networks have shown that they encode more effectively categorical spatial judgments or coordinate spatial judgments, if their input is based, respectively, on units with relatively small, nonoverlapping receptive fields, as opposed to units with relatively large, overlapping receptive fields. These findings leave open the question of whether interactive processes between spatial detectors and types of spatial relations can be modulated by spatial attention. We hypothesized that spreading the attention window to encompass an area that includes two objects promotes coordinate spatial relations, based on coarse coding by large, overlapping, receptive fields. In contrast, narrowing attention to encompass an area that includes only one of the objects benefits categorical spatial relations, by effectively parsing space. By use of a cueing procedure, the spatial attention window was manipulated to select regions of differing areas. As predicted, when the attention window was large, coordinate spatial transformations were noticed faster than categorical transformations; in contrast, when the attention window was relatively smaller, categorical spatial transformations were noticed faster than coordinate transformations. Another novel finding was that coordinate changes were noticed faster when cueing an area that included both objects as well as the empty space between them than when simultaneously cueing both areas including the objects while leaving the gap between them uncued.     

Effects of the global and local attention on the processing of categorical and coordinate spatial relations

Participants made categorical or coordinate spatial judgments on the global or local elements of shapes. Stimuli were composed of a horizontal line and two dots. In the Categorical task, participants judged whether the line was above or below the dots. In the Coordinate task, they judged whether the line would fit between the dots. Stimuli were made hierarchical so that the global patterns composed of a “global line” made of local dots-and-line units, and “global dot” made of a single dots-and-line unit. The results indicated that the categorical task was better performed when participants attended to the local level of the hierarchical stimuli. On the other hand, the coordinate task was better performed when they attended to the global level. These findings are consistent with computer simulation models of the attentional modulation of neuronal receptive fields’ size suggesting that (1) coordinate spatial relations are more efficiently encoded when one attends to a relatively large region of space, whereas (2) categorical spatial relations are more efficiently encoded when one attends to a relatively small region of space.     

Exogenous attention differentially modulates the processing of categorical and coordinate spatial relations

Carrasco and her colleagues have suggested that exogenous attention reduces the size of receptive fields at an attended location (Gobell & Carrasco, 2005; Yeshurun & Carrasco, 1998, 2000). Based on the hypothesis that categorical and coordinate spatial relations are more efficiently processed by smaller and larger receptive fields, respectively, we predicted that exogenous attention would be more beneficial to the processing of categorical spatial relations than coordinate spatial relations while it would disrupt the processing of coordinate spatial relations. To test these hypotheses, participants were tested using a variant of Posner's (1980) attentional cueing paradigm. Exogenous attention produced larger facilitative effects on categorical spatial processing than on coordinate spatial processing at a short cue-target stimulus onset asynchrony (100 ms, Experiment 1, N = 28), and this result was replicated regardless of cue size in Experiment 2 (N = 24). When the coordinate judgment was sufficiently difficult, exogenous attention disrupted the processing of coordinate spatial relations (Experiment 3, N = 28). These findings indicate that exogenous attention can differentially modulate the processing of categorical and coordinate spatial relations.     

Encoding Categorical and Coordinate Spatial Relations Without Input-Output Correlations: New Simulation Models

Cook (1995) criticized Kosslyn, Chabris, Marsolek & Koenig's (1992) network simulation models of spatial relations encoding in part because the absolute position of a stimulus in the input array was correlated with its spatial relation to a landmark; thus, on at least some trials, the networks did not need to compute spatial relations. The network models reported here include larger input arrays, which allow stimuli to appear in a large range of locations with an equal probability of being above or below a “bar,” thus eliminating the confound present in earlier models. The results confirm the original hypothesis that as the size of the network's receptive fields increases, performance on a coordinate spatial relations task (which requires computing precise, metric distance) will be relatively better than on a categorical spatial relations task (which requires computing above/below relative to a landmark).     

The relationship between allocentric and egocentric frames of reference and categorical and coordinate spatial information processing

We report two experiments on the relationship between allocentric/egocentric frames of reference and categorical/coordinate spatial relations. Jager and Postma (2003) suggest two theoretical possibilities about their relationship: categorical judgements are better when combined with an allocentric reference frame and coordinate judgements with an egocentric reference frame (interaction hypothesis); allocentric/egocentric and categorical/coordinate form independent dimensions (independence hypothesis). Participants saw stimuli comprising two vertical bars (targets), one above and the other below a horizontal bar. They had to judge whether the targets appeared on the same side (categorical) or at the same distance (coordinate) with respect either to their body-midline (egocentric) or to the centre of the horizontal bar (allocentric). The results from Experiment 1 showed a facilitation in the allocentric and categorical conditions. In line with the independence hypothesis, no interaction effect emerged. To see whether the results were affected by the visual salience of the stimuli, in Experiment 2 the luminance of the horizontal bar was reduced. As a consequence, a significant interaction effect emerged indicating that categorical judgements were more accurate than coordinate ones, and especially so in the allocentric condition. Furthermore, egocentric judgements were as accurate as allocentric ones with a specific improvement when combined with coordinate spatial relations. The data from Experiment 2 showed that the visual salience of stimuli affected the relationship between allocentric/egocentric and categorical/coordinate dimensions. This suggests that the emergence of a selective interaction between the two dimensions may be modulated by the characteristics of the task.     

The relationship between allocentric and egocentric frames of reference and categorical and coordinate spatial information processing

We report two experiments on the relationship between allocentric/egocentric frames of reference and categorical/coordinate spatial relations. Jager and Postma (2003) suggest two theoretical possibilities about their relationship: categorical judgements are better when combined with an allocentric reference frame and coordinate judgements with an egocentric reference frame (interaction hypothesis); allocentric/egocentric and categorical/coordinate form independent dimensions (independence hypothesis). Participants saw stimuli comprising two vertical bars (targets), one above and the other below a horizontal bar. They had to judge whether the targets appeared on the same side (categorical) or at the same distance (coordinate) with respect either to their body-midline (egocentric) or to the centre of the horizontal bar (allocentric). The results from Experiment 1 showed a facilitation in the allocentric and categorical conditions. In line with the independence hypothesis, no interaction effect emerged. To see whether the results were affected by the visual salience of the stimuli, in Experiment 2 the luminance of the horizontal bar was reduced. As a consequence, a significant interaction effect emerged indicating that categorical judgements were more accurate than coordinate ones, and especially so in the allocentric condition. Furthermore, egocentric judgements were as accurate as allocentric ones with a specific improvement when combined with coordinate spatial relations. The data from Experiment 2 showed that the visual salience of stimuli affected the relationship between allocentric/egocentric and categorical/coordinate dimensions. This suggests that the emergence of a selective interaction between the two dimensions may be modulated by the characteristics of the task.     

A Possible Connection between Categorical and Coordinate Spatial Relation Representations

Kosslyn (1987) theorized that the visual system uses two types of spatial relations. Categorical spatial relations represent a range of locations as an equivalence class, whereas coordinate spatial relations represent the precise distance between two objects. Data indicate a left hemisphere (LH) advantage for processing categorical spatial relations and a right hemisphere (RH) advantage for processing coordinate spatial relations. Although generally assumed to be independent processes, this article proposes a possible connection between categorical and coordinate spatial relations. Specifically, categorical spatial relations may be an initial stage in the formation of coordinate spatial relations. Three experiments tested the hypothesis that categorical information would benefit tasks that required coordinate judgments. Experiments 1 and 2 presented categorical information before participants made coordinate judgments and coordinate information before participants made categorical judgments. Categorical information sped the processing of a coordinate task under a range of experimental variables; however, coordinate information did not benefit categorical judgments. Experiment 3 used this priming paradigm to present stimuli in the left or right visual field. Although visual field differences were present in the third experiment, categorical information did not speed the processing of a coordinate task. The lack of priming effects in Experiment 3 may have been due to methodological changes. In general, support is provided that categorical spatial relations may act as an initial step in the formation of more precise distance representations, i.e., coordinate spatial relations.     

Dissociation between Categorical and Coordinate Spatial Computations: Modulation by Cerebral Hemispheres, Task Properties, Mode of Response, and Age

Kosslyn suggested a dissociation of two kinds of spatial representations: categorical and coordinate, the former computed by the left hemisphere and the latter by the right hemisphere. In addition, with practice, a “categorization” of the coordinate computation would appear. These suggestions resulted largely from an experiment, replicated by others, in which the subjects had to estimate the relative position of a dot and a line by giving an oral response, and feedback was provided. The present series of five experiments was an attempt to test whether this finding could be generalized, under several methodological manipulations, some of which have already been used by researchers in separate studies. In the five experiments, accuracy was a more contributive dependent variable than correct latencies, and practice effects on the task × field interaction were not verified. Experiments 1–3 concerned the kind of response. When a manual instead of an oral response was required (Experiment 1;n= 32 Ss), the expected dissociation was observed (as well as when the latency of responses made by the right hand were studied). When the number of oral responses was increased from two (a binary choice) to eight, the dissociation was still observed for accuracy but disappeared when a more liberal criterion of accuracy was used to reduce the considerable task effect (Experiment 2;n= 32 Ss), or when response requirements were equated for both tasks (Experiment 3;n= 32 Ss). In Experiment 4 (n= 32 Ss), a manual response was called but the feedback was removed and the task dissociation disappeared. Finally, the task dissociation observed in Experiment 1 was not verified when a sample of elderly subjects was enrolled (Experiment 5;n= 32 Ss). However, age per se was the source of an interesting additional dissociation since only the coordinate computation was age sensitive. Our results suggest that the dissociation proposed by Kosslyn between the computation of categorical vs coordinate spatial relationships is highly unstable and sensitive to subtle methodological factors (vocal vs manual response, presence vs absence of feedback, binary vs “continous” response, age) which could preclude its general application.     

Hemispheric specialization for categorical and coordinate spatial representations: A reappraisal

The purpose of the present study was to examine Kosslyn's (1987) claim that the left hemisphere (LH) is specialized for the computation of categorical spatial representations and that the right hemisphere (RH) is specialized for the computation of coordinate spatial representations. Categorical representations involve making judgements about the relative position of the components of a visual stimulus (e.g., whether one component is above/below another). Coordinate representations involve calibrating absolute distances between the components of a visual stimulus (e.g., whether one component is within 5 mm of another). Thirty-two male and 32 female undergraduates were administered two versions of a categorical or a coordinate task over three blocks of 36 trials. Within each block, items were presented to the right visual field-left hemisphere (RVF-LH), the left visual field-right hemisphere (LVF-RH), or a centralized position. Overall, results were more supportive of Kosslyn's assertions concerning the role played by the RH in the computation of spatial representations. Specifically, subjects displayed an LVF-RH advantage when performing both versions of the coordinate task. The LVF-RH advantage on the coordinate task, however, was confirmed to the first block of trials. Finally, it was found that males were more likely than females to display faster reaction times (RTs) on coordinate tasks, slower RTs on categorical tasks, and an LVF-RH advantage in computing coordinate tasks.     

Effect of an initiating action on the up-right/down-left advantage for vertically arrayed stimuli and horizontally arrayed responses

When up and down stimuli are mapped to left and right keypresses or "left" and "right" vocalizations in a 2-choice reaction task, performance is often better with the up-right/down-left mapping than with the opposite mapping. This study investigated whether performance is influenced by the type of initiating action. In all, 4 experiments showed the up-right/down-left advantage to be reduced when the participant's initiating action was a left response compared with when it was a right response. This reduction occurred when the initiating action and response were both keypresses, both were spoken location names, and one was a spoken location name and the other a keypress. The results are consistent with the view that the up-right/down-left advantage is due to asymmetry in coding the alternatives on each dimension, and a distinction between categorical and coordinate spatial codes seems to provide the best explanation of the advantage.     

知觉加工中存在颜色类别知觉效应的证据

对于颜色的辨别具有类别知觉效应：类间两种颜色的辨别能力比同等颜色空间距离的类内两种颜色的辨别能力更高。对于类别知觉效应的产生机制存在两种观点：知觉特性假设、语言标签假设。以往的研究范式由于实验任务涉及到工作记忆成分,被试在完成任务时会自动地对颜色命名以利于记忆,因此所得证据大多支持语言标签假设,而对知觉特性假设的支持证据则很少。本文利用目标觉察范式最大限度去掉了工作记忆成分,通过测量被试辨别两种颜色的反应时,得到了类别知觉效应。并通过语言干扰任务进一步证实在该实验范式下类别知觉效应与语言的无关性。从而,为知觉特性假设提供了证据     

Egocentric metric representations in peripersonal space: A bridge between motor resources and spatial memory

Research on visuospatial memory has shown that egocentric (subject-to-object) and allocentric (object-to-object) reference frames are connected to categorical (non-metric) and coordinate (metric) spatial relations, and that motor resources are recruited especially when processing spatial information in peripersonal (within arm reaching) than extrapersonal (outside arm reaching) space. In order to perform our daily-life activities, these spatial components cooperate along a continuum from recognition-related (e.g., recognizing stimuli) to action-related (e.g., reaching stimuli) purposes. Therefore, it is possible that some types of spatial representations rely more on action/motor processes than others. Here, we explored the role of motor resources in the combinations of these visuospatial memory components. A motor interference paradigm was adopted in which participants had their arms bent behind their back or free during a spatial memory task. This task consisted in memorizing triads of objects and then verbally judging what was the object: (1) closest to/farthest from the participant (egocentric coordinate); (2) to the right/left of the participant (egocentric categorical); (3) closest to/farthest from a target object (allocentric coordinate); and (4) on the right/left of a target object (allocentric categorical). The triads appeared in participants' peripersonal (Experiment 1) or extrapersonal (Experiment 2) space. The results of Experiment 1 showed that motor interference selectively damaged egocentric-coordinate judgements but not the other spatial combinations. The results of Experiment 2 showed that the interference effect disappeared when the objects were in the extrapersonal space. A third follow-up study using a within-subject design confirmed the overall pattern of results. Our findings provide evidence that motor resources play an important role in the combination of coordinate spatial relations and egocentric representations in peripersonal space.     

Neural Network Models as Evidence for Different Types of Visual Representations

Cook (1995) criticizes the work of Jacobs and Kosslyn (1994) on spatial relations, shape representations, and receptive fields in neural network models on the grounds that first-order correlations between input and output unit activities can explain the results. We reply briefly to Cook's arguments here (and in Kosslyn, Chabris, Marsolek, Jacobs & Koenig, 1995) and discuss how new simulations can confirm the importance of receptive field size as a crucial variable in the encoding of categorical and coordinate spatial relations and the corresponding shape representations; such simulations would testify to the computational distinction between the different types of representations.     

The nature of categorical and coordinate spatial relation processing: An interference study

Spatial relation information can be encoded in two different ways: categorically, which is abstract, and coordinately, which is metric. Although categorical and coordinate spatial relation processing is commonly conceived as relying on spatial representations and spatial cognitive processes, some suggest that representations and cognitive processes involved in categorical spatial relation processing can be verbal as well as spatial. We assessed the extent to which categorical and coordinate spatial relation processing engages verbal and spatial representations and processes using a dual-task paradigm. Participants performed the classical dot-bar paradigm and simultaneously performed either a spatial tapping task, or an articulatory suppression task. When participants were requested to tap blocks in a given pattern (spatial tapping), their performance decreased in both the categorical and coordinate tasks compared to a control condition without interference. In contrast, articulatory suppression did not affect performance in either spatial relation task. A follow-up experiment indicated that this outcome could not be attributed to different levels of difficulty of the two interference tasks. These results provide strong evidence that both coordinate and categorical spatial relation processing relies mainly on spatial mechanisms. These findings have implications for theories on why categorical and coordinate spatial relations processing are lateralised in the brain.     

Upper and lower visual field differences in categorical and coordinate judgments

Kosslyn (1987) theorized that the left and right hemispheres differ in processing categorical and coordinate spatial relationships, respectively. Previc (1990) hypothesized that the upper and lower visual fields are functionally specialized for visual search and visuomotor manipulations, respectively. Conceptual similarities between these two theories suggested possible upper visual field advantages for categorical judgments and lower visual field advantages for coordinate judgments. In the present two experiments, subjects made either categorical or coordinate judgments to stimuli in the upper left, upper right, lower left, or lower right visual fields. The first experiment manipulated categorical/coordinate judgments as a between-subjects variable. The second experiment manipulated categorical/coordinate judgments as a within-subjects variable. In the first experiment, reaction times (RTs) for categorical judgments were equal in all visual fields except the lower left, in which RTs were slower. For coordinate judgments, RTs were equal in all visual fields except the lower left, in which RTs were faster. In general, these effects were replicated in the second experiment. However, there appeared to be consequences associated with manipulating the categorical/coordinate variable in a within-subjects fashion. The requirements of visual search versus visuomotor processes appear to map onto the nature of categorical versus coordinate processing, respectively, suggesting possible upper-lower visual field differences in categorical versus coordinate processing.     

Differences in the coding of spatial relations in face identification and basic-level object recognition

The purpose of this investigation was to determine if the relations among the primitives used in face identification and in basic-level object recognition are represented using coordinate or categorical relations. In 2 experiments the authors used photographs of famous people's faces as stimuli in which each face had been altered to have either 1 of its eyes moved up from its normal position or both of its eyes moved up. Participants performed either a face identification task or a basic-level object recognition task with these stimuli. In the face identification task, 1-eye-moved faces were easier to recognize than 2-eyes-moved faces, whereas the basic-level object recognition task showed the opposite pattern of results. Results suggest that face identification involves a coordinate shape representation in which the precise locations of visual primitives are specified, whereas basic-level object recognition uses categorically coded relations.     

学前儿童近似数量系统敏锐度与符号数学能力的关系

选取杭州市122名学前儿童(3~6岁)为被试,以点数比较任务及点数异同任务测量幼儿的近似数量系统敏锐度,以数数测验、基数测验、符号数字知识测验及简单计算来测量幼儿的符号数学能力,以此考察学前儿童近似数量系统敏锐度的发展及与符号数学能力的关系。结果发现:(1)随年龄增长,学前儿童的近似数量加工的敏锐度逐渐提高;(2)点数比较任务与点数异同任务均适合测量学前儿童近似数量系统敏锐度,但儿童完成点数比较任务的正确率要高于点数异同任务的正确率;(3)在抑制控制、短时记忆、工作记忆和言语测验成绩被控制后,根据点数比较任务计算的韦伯系数能显著预测学前儿童的基数和符号数字知识测验分数,总正确率能显著预测学前儿童的数数、基数、符号数字知识测验分数;(4)点数异同任务中只有点数不同试次下的正确率能显著预测学前儿童的符号数字知识测验分数。     

Separating cue encoding from target processing in the explicit task-cuing procedure: are there "true" task switch effects?

Six experiments were conducted to separate cue encoding from target processing in explicitly cued task switching to determine whether task switch effects could be separated from cue encoding effects and to determine the nature of the representations produced by cue encoding. Subjects were required to respond to the cue, indicating which cue was presented (Experiments 1, 3a, and 4a) or which task was cued (Experiments 2, 3b, and 4b), before performing the cued task on the target. Cue encoding was successfully separated from target processing when the cue response indicated which task was cued but not when it indicated which cue was presented. Task switch effects were found when this separation was successful, suggesting that there are "true" task switch effects independent of cue encoding. Analysis of the conditions required for successful separation suggested that cue encoding results in a semantic categorical representation of the task to be performed rather than verbal or phonological representations of individual cues. Implications for the authors' past modeling of task-switching performance are discussed.