From natural geometry to spatial cognition

Computational cognitive models of spatial memory in navigation space: a review

Spatial memory refers to the part of the memory system that encodes, stores, recognizes and recalls spatial information about the environment and the agent's orientation within it. Such information is required to be able to navigate to goal locations, and is vitally important for any embodied agent, or model thereof, for reaching goals in a spatially extended environment. In this paper, a number of computationally implemented cognitive models of spatial memory are reviewed and compared. Three categories of models are considered: symbolic models, neural network models, and models that are part of a systems-level cognitive architecture. Representative models from each category are described and compared in a number of dimensions along which simulation models can differ (level of modeling, types of representation, structural accuracy, generality and abstraction, environment complexity), including their possible mapping to the underlying neural substrate. Neural mappings are rarely explicated in the context of behaviorally validated models, but they could be useful to cognitive modeling research by providing a new approach for investigating a model's plausibility. Finally, suggested experimental neuroscience methods are described for verifying the biological plausibility of computational cognitive models of spatial memory, and open questions for the field of spatial memory modeling are outlined.

Wild, free-living rufous hummingbirds do not use geometric cues in a spatial task

In the laboratory, many species orient themselves using the geometric properties of an enclosure or array and geometric information is often preferred over visual cues. Whether animals use geometric cues when relocating rewarded locations in the wild, however, has rarely been investigated. We presented free-living rufous hummingbirds with a rectangular array of four artificial flowers to investigate learning of rewarded locations using geometric cues. In one treatment, we rewarded two of four flowers at diagonally opposite corners. In a second treatment, we provided a visual cue to the rewarded flower by connecting the flowers with "walls" consisting of four dowels (three white, one blue) laid on the ground connecting each of the flowers. Neither treatment elicited classical geometry results; instead, hummingbirds typically chose one particular flower over all others. When we exchanged that flower with another, hummingbirds tended to visit the original flower. These results suggest that (1) hummingbirds did not use geometric cues, but instead may have used a visually derived cue on the flowers themselves, and (2) using geometric cues may have been more difficult than using visual characteristics. Although hummingbirds typically prefer spatial over visual information, we hypothesize that they will not use geometric cues over stable visual features but that they make use of small, flower-specific visual cues. Such cues may play a more important role in foraging decisions than previously thought.

Evidence of a relational spatial strategy in learning the centre of enclosures in human children (Homo sapiens)

Three- to five-year-old children were trained to localize a sensor hidden underneath the floor, in the centre of a square-shaped enclosure (1.5m×1.5m). Walking over the sensor caused a pleasant music to be played in the environment, thus engaging children in a playful spatial search. Children easily learned to find the centre of the training environment starting from random positions. After training, children were tested in enclosures of different size and/or shape: a larger square-shaped enclosure (3m×3m), a rectangle-shaped enclosure (1.5m×3m), an equilateral triangle-shaped enclosure (side 3m) and an isosceles triangle-shaped enclosure (base 1.5m; sides 3m). Children searched in the central region of the enclosures, their precision varying as a function of the similarity of the testing enclosure's shape to the shape of the training enclosure. This suggests that a relational spatial strategy was used, and that it depended on the encoding of geometrical shape. This result highlights a distinctive role of the geometric centre of enclosed spaces in place learning in children, as already observed in nonhuman species.

Wild hummingbirds rely on landmarks not geometry when learning an array of flowers

Rats, birds or fish trained to find a reward in one corner of a small enclosure tend to learn the location of the reward using both nearby visual features and the geometric relationships of corners and walls. Because these studies are conducted under laboratory and thereby unnatural conditions, we sought to determine whether wild, free-living rufous hummingbirds (Selasphorus rufus) learning a single reward location within a rectangular array of flowers would similarly employ both nearby visual landmarks and the geometric relationships of the array. Once subjects had learned the location of the reward, we used test probes in which one or two experimental landmarks were moved or removed in order to reveal how the birds remembered the reward location. The hummingbirds showed no evidence that they used the geometry of the rectangular array of flowers to remember the reward. Rather, they used our experimental landmarks, and possibly nearby, natural landmarks, to orient and navigate to the reward. We believe this to be the first test of the use of rectangular geometry by wild animals, and we recommend further studies be conducted in ecologically relevant conditions in order to help determine how and when animals form complex geometric representations of their local environments.

Scene analysis in the natural environment

The problem of scene analysis has been studied in a number of different fields over the past decades. These studies have led to important insights into problems of scene analysis, but not all of these insights are widely appreciated, and there remain critical shortcomings in current approaches that hinder further progress. Here we take the view that scene analysis is a universal problem solved by all animals, and that we can gain new insight by studying the problems that animals face in complex natural environments. In particular, the jumping spider, songbird, echolocating bat, and electric fish, all exhibit behaviors that require robust solutions to scene analysis problems encountered in the natural environment. By examining the behaviors of these seemingly disparate animals, we emerge with a framework for studying scene analysis comprising four essential properties: (1) the ability to solve ill-posed problems, (2) the ability to integrate and store information across time and modality, (3) efficient recovery and representation of 3D scene structure, and (4) the use of optimal motor actions for acquiring information to progress toward behavioral goals.

Functional and structural comparison of visual lateralization in birds - similar but still different

Vertebrate brains display physiological and anatomical left-right differences, which are related to hemispheric dominances for specific functions. Functional lateralizations likely rely on structural left-right differences in intra- and interhemispheric connectivity patterns that develop in tight gene-environment interactions. The visual systems of chickens and pigeons show that asymmetrical light stimulation during ontogeny induces a dominance of the left hemisphere for visuomotor control that is paralleled by projection asymmetries within the ascending visual pathways. But structural asymmetries vary essentially between both species concerning the affected pathway (thalamo- vs. tectofugal system), constancy of effects (transient vs. permanent), and the hemisphere receiving stronger bilateral input (right vs. left). These discrepancies suggest that at least two aspects of visual processes are influenced by asymmetric light stimulation: (1) visuomotor dominance develops within the ontogenetically stronger stimulated hemisphere but not necessarily in the one receiving stronger bottom-up input. As a secondary consequence of asymmetrical light experience, lateralized top-down mechanisms play a critical role in the emergence of hemispheric dominance. (2) Ontogenetic light experiences may affect the dominant use of left- and right-hemispheric strategies. Evidences from social and spatial cognition tasks indicate that chickens rely more on a right-hemispheric global strategy whereas pigeons display a dominance of the left hemisphere. Thus, behavioral asymmetries are linked to a stronger bilateral input to the right hemisphere in chickens but to the left one in pigeons. The degree of bilateral visual input may determine the dominant visual processing strategy when redundant encoding is possible. This analysis supports that environmental stimulation affects the balance between hemispheric-specific processing by lateralized interactions of bottom-up and top-down systems.

Navigation outside of the box: what the lab can learn from the field and what the field can learn from the lab

Space is continuous. But the communities of researchers that study the cognitive map in non-humans are strangely divided, with debate over its existence found among behaviorists but not neuroscientists. To reconcile this and other debates within the field of navigation, we return to the concept of the parallel map theory, derived from data on hippocampal function in laboratory rodents. Here the cognitive map is redefined as the integrated map, which is a construction of dual mechanisms, one based on directional cues (bearing map) and the other on positional cues (sketch map). We propose that the dual navigational mechanisms of pigeons, the navigational map and the familiar area map, could be homologous to these mammalian parallel maps; this has implications for both research paradigms. Moreover, this has implications for the lab. To create a bearing map (and hence integrated map) from extended cues requires self-movement over a large enough space to sample and model these cues at a high resolution. Thus a navigator must be able to move freely to map extended cues; only then should the weighted hierarchy of available navigation mechanisms shift in favor of the integrated map. Because of the paucity of extended cues in the lab, the flexible solutions allowed by the integrated map should be rare, despite abundant neurophysiological evidence for the existence of the machinery needed to encode and map extended cues through voluntary movement. Not only do animals need to map extended cues but they must also have sufficient information processing capacity. This may require a specific ontogeny, in which the navigator's nervous system is exposed to naturally complex spatial contingencies, a circumstance that occurs rarely, if ever, in the lab. For example, free-ranging, flying animals must process more extended cues than walking animals and for this reason alone, the integrated map strategy may be found more reliably in some species. By taking concepts from ethology and the parallel map theory, we propose a path to directly integrating the three great experimental paradigms of navigation: the honeybee, the homing pigeon and the laboratory rodent, towards the goal of a robust, unified theory of animal navigation.

Spatial integration of boundaries in a 3D virtual environment

Prior research, using two- and three-dimensional environments, has found that when both human and nonhuman animals independently acquire two associations between landmarks with a common landmark (e.g., LM1-LM2 and LM2-LM3), each with its own spatial relationship, they behave as if the two unique LMs have a known spatial relationship despite their never having been paired. Seemingly, they have integrated the two associations to create a third association with its own spatial relationship (LM1-LM3). Using sensory preconditioning (Experiment 1) and second-order conditioning (Experiment 2) procedures, we found that human participants integrated information about the boundaries of pathways to locate a goal within a three-dimensional virtual environment in the absence of any relevant landmarks. Spatial integration depended on the participant experiencing a common boundary feature with which to link the pathways. These results suggest that the principles of associative learning also apply to the boundaries of an environment.

Navigation by environmental geometry: the use of zebrafish as a model

Sensitivity to environmental shape in spatial navigation has been found, at both behavioural and neural levels, in virtually every species tested, starting early in development. Moreover, evidence that genetic deletions can cause selective deficits in such navigation behaviours suggests a genetic basis to navigation by environmental geometry. Nevertheless, the geometric computations underlying navigation have not been specified in any species. The present study teases apart the geometric components within the traditionally used rectangular enclosure and finds that zebrafish selectively represent distance and directional relationships between extended boundary surfaces. Similar behavioural results in geometric navigation tasks with human children provide prima facie evidence for similar underlying cognitive computations and open new doors for probing the genetic foundations that give rise to these computations.

Two-category place representations persist over body rotations

We explored a system that constructs environment-centered frames of reference and coordinates memory for the azimuth of an object in an enclosed space. For one group, we provided two environmental cues (doors): one in the front, and one in the rear. For a second group, we provided two object cues: a front and a rear cue. For a third group, we provided no external cues; we assumed that for this group, their reference frames would be determined by the orthogonal geometry of the floor-and-wall junction that divides a space in half or into multiple territories along the horizontal continuum. Using Huttenlocher, Hedges, and Duncan’s (Psychological Review 98: 352-376, 1991) category-adjustment model (cue-based fuzzy boundary version) to fit the data, we observed different reference frames than have been seen in prior studies involving two-dimensional domains. The geometry of the environment affected all three conditions and biased the remembered object locations within a two-category (left vs. right) environmental frame. The influence of the environmental geometry remained observable even after the participants’ heading within the environment changed due to a body rotation, attenuating the effect of the front but not of the rear cue. The door and object cues both appeared to define boundaries of spatial categories when they were used for reorientation. This supports the idea that both types of cues can assist in environment-centered memory formation.

Beacons and surface features differentially influence human reliance on global and local geometric cues when reorienting in a virtual environment

In the reorientation literature, non-geometric cues include discrete objects (e.g., beacons) and surface-based features (e.g., colors, textures, and odors). To date, these types of non-geometric cues have been considered functionally similar, and it remains unknown whether beacons and surface features differentially influence the extent to which organisms reorient via global and local geometric cues. In the present experiment, we trained human participants to approach a location in a trapezoid-shaped enclosure uniquely specified by global and local geometric cues. We explored the role of beacons on the use of geometric cues by training participants in the presence or absence of uniquely-colored beacons. We explored the role of surface features on the use of geometric cues by recoloring two adjacent walls at the correct location and/or adding a line on the floor which corresponded to the major principal axis of the enclosure. All groups were then tested in novel-shaped enclosures in the absence of unique beacons and surface features to assess the relative use of global and local geometric cues. Results suggested that beacons facilitated the use of global geometric cues, whereas surface features either facilitated or hindered the use of geometric cues, depending on the feature.

Psychology of spatial cognition

In this overview, focusing on memory and higher cognitive processes, we cover some of the most relevant results that emerged from research on spatial cognition in animals and in humans in the last 3 decades. In particular, we discuss how representations of distance and direction are used to localize oneself with respect to the external world, to determine the position of objects with respect to each other, and to compute the position of invisible goals. The role of landmarks and environmental geometry as cues for extracting spatial information in such abilities is compared, and the reliance upon self-centered and external frames of reference is discussed. Moreover, the contribution of working memory and processing strategies in forming representations of spatial relations in humans is presented. Finally, implications for some neighboring fields of the cognitive sciences will be outlined. WIREs Cogn Sci 2012. doi: 10.1002/wcs.1198 For further resources related to this article, please visit the WIREs website.

From objects to landmarks: the function of visual location information in spatial navigation

Landmarks play an important role in guiding navigational behavior. A host of studies in the last 15 years has demonstrated that environmental objects can act as landmarks for navigation in different ways. In this review, we propose a parsimonious four-part taxonomy for conceptualizing object location information during navigation. We begin by outlining object properties that appear to be important for a landmark to attain salience. We then systematically examine the different functions of objects as navigational landmarks based on previous behavioral and neuroanatomical findings in rodents and humans. Evidence is presented showing that single environmental objects can function as navigational beacons, or act as associative or orientation cues. In addition, we argue that extended surfaces or boundaries can act as landmarks by providing a frame of reference for encoding spatial information. The present review provides a concise taxonomy of the use of visual objects as landmarks in navigation and should serve as a useful reference for future research into landmark-based spatial navigation.

Mice recognize the center of an enclosure

In recent years, it has been shown that animals can localize the geometric center of an area by reference to the shape of the environment. We trained a group of mice (experimental group) to search for a pellet hidden under sand in the center of a square-shaped dry maze. Three weeks later, they were tested in a triangular enclosure half the size of the training area and a circular enclosure double the size of the training area to see transfer to these enclosures. We compared their searching behavior with that of subjects that had received no training. The results show that the experimental group searched the geometric center of each enclosure in both transfer tests, while the untrained control group walked along the walls. This indicates that the experimental group localized the center not by reference to the absolute distance from the corners but by equal distances from all walls (geometric center).

Core knowledge of object, number, and geometry: a comparative and neural approach

Studies on the ontogenetic origins of human knowledge provide evidence for a small set of separable systems of core knowledge dealing with the representation of inanimate and animate objects, number, and geometry. Because core knowledge systems are evolutionarily ancient, they can be investigated from a comparative perspective, making use of various animal models. In this review, I discuss evidence showing precocious abilities in nonhuman species to represent (a) objects that move partly or fully out of view and their basic mechanical properties such as solidity, (b) the cardinal and ordinal/sequential aspects of numerical cognition and rudimentary arithmetic with small numerosities, and (c) the geometrical relationships among extended surfaces in the surrounding layout. Controlled rearing studies suggest that the abilities associated with core knowledge systems of objects, number, and geometry are observed in animals in the absence (or with very reduced) experience, supporting a nativistic foundation of such cognitive mechanisms. Animal models also promise a fresh approach to the issue of the neurobiological and genetic mechanisms underlying the expression of core knowledge systems.

More than a feeling: incidental learning of array geometry by blind-folded adult humans revealed through touch

View-based matching theories of orientation suggest that mobile organisms encode a visual memory consisting of a visual panorama from a target location and maneuver to reduce discrepancy between current visual perception and this stored visual memory to return to a location. Recent success of such theories to explain the orientation behavior of insects and birds raises questions regarding the extent to which such an explanation generalizes to other species. In the present study, we attempted to determine the extent to which such view-based matching theories may explain the orientation behavior of a mammalian species (in this case adult humans). We modified a traditional enclosure orientation task so that it involved only the use of the haptic sense. The use of a haptic orientation task to investigate the extent to which view-based matching theories may explain the orientation behavior of adult humans appeared ideal because it provided an opportunity for us to explicitly prohibit the use of vision. Specifically, we trained disoriented and blind-folded human participants to search by touch for a target object hidden in one of four locations marked by distinctive textural cues located atop four discrete landmarks arranged in a rectangular array. Following training, we removed the distinctive textural cues and probed the extent to which participants learned the geometry of the landmark array. In the absence of vision and the trained textural cues, participants showed evidence that they learned the geometry of the landmark array. Such evidence cannot be explained by an appeal to view-based matching strategies and is consistent with explanations of spatial orientation related to the incidental learning of environmental geometry.