The effect of correlated variability on the accuracy of a population code
Neural Computation
Population coding and decoding in a neural field: a computational study
Neural Computation
Computing with Continuous Attractors: Stability and Online Aspects
Neural Computation
Population Coding with Correlation and an Unfaithful Model
Neural Computation
Correlation and independence in the neural code
Neural Computation
Representations of continuous attractors of recurrent neural networks
IEEE Transactions on Neural Networks
Continuous Attractors of Lotka-Volterra Recurrent Neural Networks
ICANN '09 Proceedings of the 19th International Conference on Artificial Neural Networks: Part I
Continuous attractors of Lotka-Volterra recurrent neural networks with infinite neurons
IEEE Transactions on Neural Networks
Neural information processing with feedback modulations
Neural Computation
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Continuous attractor is a promising model for describing the encoding of continuous stimuli in neural systems. In a continuous attractor, the stationary states of the neural system form a continuous parameter space, on which the system is neutrally stable. This property enables the neutral system to track time-varying stimuli smoothly, but it also degrades the accuracy of information retrieval, since these stationary states are easily disturbed by external noise. In this work, based on a simple model, we systematically investigate the dynamics and the computational properties of continuous attractors. In order to analyze the dynamics of a large-size network, which is otherwise extremely complicated, we develop a strategy to reduce its dimensionality by utilizing the fact that a continuous attractor can eliminate the noise components perpendicular to the attractor space very quickly. We therefore project the network dynamics onto the tangent of the attractor space and simplify it successfully as a one-dimensional Ornstein-Uhlenbeck process. Based on this simplified model, we investigate (1) the decoding error of a continuous attractor under the driving of external noisy inputs, (2) the tracking speed of a continuous attractor when external stimulus experiences abrupt changes, (3) the neural correlation structure associated with the specific dynamics of a continuous attractor, and (4) the consequence of asymmetric neural correlation on statistical population decoding. The potential implications of these results on our understanding of neural information processing are also discussed.