The Tracking Speed of Continuous Attractors
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 stimulus smoothly. In this study we investigate the tracking speed 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 input components perpendicular to the attractor space very quickly. We therefore project the network dynamics onto the tangent of the attractor space, and simplify it to be a one-dimension Ornstein-Uhlenbeck process. With this approximation we elucidate that the reaction time of a continuous attractor increases logarithmically with the size of the stimulus change. This finding may have important implication on the mental rotation behavior.
KeywordsNetwork Dynamic Neural System Mental Rotation External Input Neutral Stability
Unable to display preview. Download preview PDF.
- 3.Georgopoulos, A.P., Kalaska, J.F., Caminiti, R., Massey, J.T.: On the Relations between the Direction of Two-Dimensional Arm Movements and Cell Discharge in Primate Motor Cortex. J. Neurosci. 2, 1527–1537 (1982)Google Scholar
- 4.Maunsell, J.H.R., Van Essen, D.C.: Functional Properties of Neurons in Middle Temporal Visual Area of the Macaque Monkey. I. Selectivity for Stimulus Direction, Speed, and Orientation. J. Neurophysiology 49, 1127–1147 (1983)Google Scholar
- 5.Funahashi, S., Bruce, C., Goldman-Rakic, P.: Mnemonic Coding of Visual Space in the Monkey’s Dorsolateral Prefrontal Cotex. J. Neurophysiology 61, 331–349 (1989)Google Scholar
- 7.Zhang, K.C.: Representation of Spatial Orientation By the Intrinsic Dynamics of the Head-Direction Cell Ensemble: A Theory. J. Neuroscience 16, 2112–2126 (1996)Google Scholar
- 14.Trappenberg, T.: Continuous Attractor Neural Networks. In: de Castro, L.N., Von Zuben, F.J. (eds.) Recent Developments in biologically inspired computing, Idea Group Publishing, Hershey (2004)Google Scholar
- 17.Koriat, A., Norman, J.: Establishing Global and Local Correspondence Between Successive Stimuli: The Holistic Nature of Backward Alignment. J. of Experimental Psychology 15, 480–494 (1989)Google Scholar