One approach toinvariant object recognition employs a recurrent neural network as an associative memory. In the standard depiction of the network's state space, memories of objects are stored as attractive xed points of the dynamics. I argue for a modi cation of this picture: if an object has a continuous family of instantiations, it should be represented by a continuous attractor. This idea is illustrated with a network that learns to complete patterns. To perform the task of lling in missing information, the network develops a continuous attractor that models the manifold from which the patterns are drawn. From a statistical viewpoint, the pattern completion task allows a formulation of unsupervised learning in terms of regression rather than density estimation. A classic approach toinvariant object recognition is to use a recurrent neural network as an associative memory[1]. In spite of the intuitive appeal and biological plausibility of this approach, it has largely been abandoned in practical applications.

We study a partial integro-dierential equation dened on a spatially extended domain that arises from the modeling of \working" or short-term memory in a neuronal network. The equation is capable of supporting spatially localized regions of high activity which can be switched \on" and \o" by transient external stimuli. We analyze the eects of coupling between units in the network, showing that if the connection strengths decay monotonically with distance then no more than one region of high activity can persist, whereas if they decay in an oscillatory fashion then multiple regions can persist.

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.

According to a popular hypothesis, short-term memories are stored as persistent neural activity maintained by synaptic feedback loops. This hypothesis has been formulated mathematically in a number of recurrent network models. Here we study an abstraction of these models, a single neuron with a synapse onto itself, or autapse. This abstraction cannot simulate the way in which persistent activity patterns are distributed over neural populations in the brain. However, with proper tuning of parameters, it does reproduce the continuously graded, or analog, nature of many examples of persistent activity. The conditions for tuning are derived for the dynamics of a conductance-based model neuron with a slow excitatory autapse. The derivation uses the method of averaging to approximate the spiking model with a nonspiking, reduced model. Short-term analog memory storage is possible if the reduced model is approximately linear, and its feedforward bias and autapse strength are precisely...

Abstract. This work investigates whether population vector coding could be a principle mechanism for sensorimotor transformations. This paper presents a formal demonstration of how population vector coding can proceed arbitrary 3-dimensional rotations and translations. The model suggests that population coding could be a possible mechanism for frames of reference transformations across multiple sensori-motor systems. 1

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.

this paper, we will be basing our modeling efforts on the Blair et al. (1997) findings. The Taube and Muller findings were based on much shorter recording sessions: only 8 min as compared with 15--30 min in (Blair et al. 1997) and 15--90 min in (Blair and Sharp 1998). Thus because the tuning curve effects reported by Blair et al. are quite subtle, they may very well have been obscured in the 8-min sessions.

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Abstract. Motivated by experimental observations of the head direction system, we study a three population network model that operates as a continuous attractor network. This network is able to store in a short-term memory an angular variable (the head direction) as a spatial profile of activity across neurons in the absence of selective external inputs, and to accurately update this variable on the basis of angular velocity inputs. The network is composed of one excitatory population and two inhibitory populations, with inter-connections between populations but noconnections within the neurons of a same population. In particular, there are no excitatory-to-excitatory connections. Angular velocity signals are represented as inputs in one inhibitory population (clockwise turns) or the other (counterclockwise turns). The system is studied using a combination of analytical and numerical methods. Analysis of a simplified model composed of threshold-linear neurons gives the conditions on the connectivity for (i) the emergence of the spatially selective profile, (ii) reliable integration of angular velocity inputs, and (iii) the range of angular velocities that can be accurately integrated by the model. Numerical simulations allow us to study the proposed scenario in a large network of spiking neurons and compare their dynamics with that of head direction cells recorded in the rat limbic system. In particular, we show that the directional representation encoded by the attractor network can be rapidly updated by external cues, consistent with the very short update latencies observed experimentally by Zugaro et al. (2003) in thalamic head direction cells.

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