Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hopfield, J.J.: Neurons with Graded Responses Have Collective Computational Properties Like those of Two-State Neurons. Proc. Natl. Acad. Sci. USA 81, 3088–3092 (1984)
Amari, S.: Dynamics of Pattern Formation in Lateral-Inhibition Type Neural Fields. Biological Cybernetics 27, 77–87 (1977)
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)
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)
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)
Wilson, M.A., McNaughton, B.L.: Dynamics of Hippocampal Ensemble Code for Space. Science 261, 1055–1058 (1993)
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)
Seung, H.S.: How the Brain Keeps the Eyes Still. Proc. Acad. Sci. USA 93, 13339–13344 (1996)
Ermentrout, B.: Neural networks as Spatial-Temporal Pattern-Forming Systems. Reports on progress in physics 61, 353–430 (1998)
Taube, J.S.: Head Direction Cells and the Neurophysiological Basis for A Sense of Direction. Prog. Neurobiol. 55, 225–256 (1998)
Deneve, S., Latham, P.E., Pouget, A.: Reading Population Codes: A Neural Implementation of Ideal Observers. Nature Neuroscience 2, 740–745 (1999)
Wang, X.J.: Synaptic Reverberation Underlying Mnemonic Persistrent Activitity. Trends in Neuroscience 24, 455–463 (2001)
Wu, S., Amari, S., Nakahara, H.: Population Coding and Decoding in A Neural Field: A Computational Study. Neural Computation 14, 999–1026 (2002)
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)
Wu, S., Amari, S.: Computing with Continuous Attractors: Stability and On-Line Aspects. Neural Computation 17, 2215–2239 (2005)
Tuckwell, H.: Introduction to Theoretical Neurobiology. Cambridge University Press, Cambridge (1988)
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)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wu, S., Hamaguchi, K., Amari, Si. (2007). The Tracking Speed of Continuous Attractors. In: Liu, D., Fei, S., Hou, ZG., Zhang, H., Sun, C. (eds) Advances in Neural Networks – ISNN 2007. ISNN 2007. Lecture Notes in Computer Science, vol 4491. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-72383-7_108
Download citation
DOI: https://doi.org/10.1007/978-3-540-72383-7_108
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-72382-0
Online ISBN: 978-3-540-72383-7
eBook Packages: Computer ScienceComputer Science (R0)