There is evidence, beginning with Cheng (1986), that mobile animals may use the geometry of surrounding areas to reorient following disorientation. Gallistel (1990) proposed that geometry is used to compute the major or minor axes of space and suggested that such information might form an encapsulated cognitive module. Research reviewed here, conducted on a wide variety of species since the initial discovery of the use of geometry and the formulation of the modularity claim, has supported some aspects of the approach, while casting doubt on others. Three possible processing models are presented that vary in the way in which (and the extent to which) they instantiate the modularity claim. The extant data do not permit us to discriminate among them. We propose a modified concept of modularity for which an empirical program of research is more tractable.

The medial temporal lobe (MTL) has been studied extensively at all levels of analysis, yet its function remains unclear. Theory regarding the cognitive function of the MTL has centered along 3 themes. Different authors have emphasized the role of the MTL in episodic recall, spatial navigation, or relational memory. Starting with the temporal context model (M.W. Howard and M. J. Kahana, 2002), a distributed memory model that has been applied to benchmark data from episodic recall tasks, the authors propose that the entorhinal cortex supports a gradually changing representation of temporal context and the hippocampus proper enables retrieval of these contextual states. Simulation studies show this hypothesis explains the firing of place cells in the entorhinal cortex and the behavioral effects of hippocampal lesion in relational memory tasks. These results constitute a first step towards a unified computational theory of MTL function that integrates neurophysiological, neuropsychological and cognitive findings.

The authors model the neural mechanisms underlying spatial cognition, integrating neuronal systems and behavioral data, and address the relationships between long-term memory, short-term memory, and imagery, and between egocentric and allocentric and visual and ideothetic representations. Long-term spatial memory is modeled as attractor dynamics within medial–temporal allocentric representations, and short-term memory is modeled as egocentric parietal representations driven by perception, retrieval, and imagery and modulated by directed attention. Both encoding and retrieval/imagery require translation between egocentric and allocentric representations, which are mediated by posterior parietal and retrosplenial areas and the use of head direction representations in Papez’s circuit. Thus, the hippocampus effectively indexes information by real or imagined location, whereas Papez’s circuit translates to imagery or from perception according to the direction of view. Modulation of this translation by motor efference allows spatial updating of representations, whereas prefrontal simulated motor efference allows mental exploration. The alternating temporal–parietal flows of information are organized by the theta rhythm. Simulations demonstrate the retrieval and updating of familiar spatial scenes, hemispatial neglect in memory, and the effects on hippocampal place cell firing of lesioned head direction representations and of conflicting visual and ideothetic inputs.

A computational model of how single neurons in and around the rat hippocampus support spatial navigation is reviewed. The extension of this model, to include the retrieval from human longterm memory of spatial scenes and the spatial context of events is discussed. The model explores the link between spatial and mnemonic functions by supposing that retrieval of spatial information from long-term storage requires the imposition of a particular viewpoint. It is consistent with data relating to representational hemispatial neglect and the involvement of the mammillary bodies, anterior thalamus, and hippocampal formation in supporting both episodic recall and the representation of head direction. Some recent behavioural, neuropsychological, and functional neuroimaging experiments are reviewed, in which virtual reality is used to allow controlled study of navigation and memory for events set within a rich large-scale spatial context. These studies provide convergent evidence that the human hippocampus is involved in both tasks, with some lateralization of function (navigation on the right and episodic memory on the left). A further experiment indicates hippocampal involvement in retrieval of spatial information from a shifted viewpoint. I speculate that the hippocampal role in episodic recollection relates to its ability to represent a viewpoint moving within a spatial framework.

Uncertainty coming from the noise in its neurons and the ill-posed nature of many tasks plagues neural computations. Maybe surprisingly, many studies show that the brain manipulates these forms of uncertainty in a probabilistically consistent and normative manner, and there is now a rich theoretical literature on the capabilities of populations of neurons to implement computations in the face of uncertainty. However, one major facet of uncertainty has received comparatively little attention: time. In a dynamic, rapidly changing world, data are only temporarily relevant. Here, we analyze the computational consequences of encoding stimulus trajectories in populations of neurons. For the most obvious, simple, instantaneous encoder, the correlations induced by natural, smooth stimuli engender a decoder that requires access to information that is nonlocal both in time and across neurons. This formally amounts to a ruinous representation. We show that there is an alternative encoder that is computationally and representationally powerful in which each spike contributes independent information; it is independently decodable, in other words. We suggest this as an appropriate foundation for understanding time-varying population codes. Furthermore, we show how adaptation to

In a continuous T-maze alternation task, CA1 complexspike neurons in the hippocampus differentially fire as the rat traverses overlapping segments of the maze (i.e., the stem) repeatedly via alternate routes. The temporal dynamics of this phenomenon were further investigated in the current study. Rats learned the alternation task from the first day of acquisition and the differential firing pattern in the stem was observed accordingly. More importantly, we report a phenomenon in which spatial correlates of CA1 neuronal ensembles gradually changed from their original firing locations, shifting toward prospective goal locations in the continuous T-maze alternation task. The relative locations of simultaneously recorded firing fields, however, were preserved within the ensemble spatial representation during this shifting. The within-session shifts in preferred firing locations in the absence of any changes in the environment suggest that certain cognitive factors can significantly alter the locationbound coding scheme of hippocampal neurons.

For many centuries, philosophers and scientists have pondered the origins and nature of human intuitions about the properties of points, lines, and figures on the Euclidean plane, with most hypothesizing that a system of Euclidean concepts either is innate or is assembled by general learning processes. Recent research from cognitive and developmental psychology, cognitive anthropology, animal cognition, and cognitive neuroscience suggests a different view. Knowledge of geometry may be founded on at least two distinct, evolutionarily ancient, core cognitive systems for representing the shapes of large-scale, navigable surface layouts and of small-scale, movable forms and objects. Each of these systems applies to some but not all perceptible arrays and captures some but not all of the three fundamental Euclidean relationships of distance (or length), angle, and direction (or sense). Like natural number (Carey, 2009), Euclidean geometry may be constructed through the productive combination of representations from these core systems, through the use of uniquely human symbolic systems.

ABSTRACT: One of the fundamental challenges of modern neuroscience is to understand how memories are acquired, stored, and retrieved by the brain. In the broadest terms, attempts to dissect memory can be broken down into four experimental disciplines: (1) identification of molecular components, (2) ex vivo and in vivo cellular analysis of neuronal function, (3) theoretical modeling approaches of neural systems, and (4) organ-

The geometric arrangement of surfaces in an environment plays an important role in navigation in vertebrate animals. In this line of research, an animal is typically disoriented and then presented the task of relocating a previously encountered goal. Aside from the geometric shape of the enclosure, other non-geometric (featural) cues are typically available, including colours of walls, objects serving as landmarks, or smells. Animals use both geometric and featural cues, but mammals sometimes rely solely on geometric cues. This has led to views that the processing of geometric information is modular, being the work of a geometric module. Recent work has started to address just what geometric properties are encoded. These current issues are commented on in this paper, and a tentative picture is drawn that both global and local geometry, each in limited ways, are used for navigation. A view of modularity is also presented in which spatial information is stored together (in non-modular fashion), but some computational processes are modular and operate on limited kinds of information.

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