Path Integration in a Continuous Attractor Network Model

The excerpt note is about path integration with continuous attractor network according to McNaughton B. L., et al., 2006.

McNaughton, Bruce L., Francesco P. Battaglia, Ole Jensen, Edvard I. Moser, and May-Britt Moser. “Path integration and the neural basis of the’cognitive map’.” Nature Reviews Neuroscience 7, no. 8 (2006): 663.


Mittelstaedt et al., 1980 present the first report of path integration in a mammal.

Mittelstaedt, M-L., and H. Mittelstaedt. “Homing by path integration in a mammal.” Naturwissenschaften 67, no. 11 (1980): 566-567.


McNaughton, B. L., et al., 1991 present an early version of the head direction path integrator model which formed the conceptual basis of subsequent continuous attractor models for path integration.

McNaughton, B. L., Chen L. L., and Markus E. J. “‘Dead reckoning’, landmark learning, and the sense of direction: a neurophysiological and computational hypothesis.” Journal of Cognitive Neuroscience 3, no. 2 (1991): 190-202.


Tsodyks M. & Sejnowski 1995 present one of the first papers to advance the concept of a system of continuous attractors.

Tsodyks, Misha, and Terrence Sejnowski. “Associative memory and hippocampal place cells.” International journal of neural systems 6 (1995): 81-86.

Tsodyks, Misha. “Attractor neural network models of spatial maps in hippocampus.” Hippocampus 9, no. 4 (1999): 481-489.

Battaglia, Francesco P., and Alessandro Treves. “Attractor neural networks storing multiple space representations: a model for hippocampal place fields.” Physical Review E 58, no. 6 (1998): 7738.


Zhang K. 1996 present a periodic continuous attractor model of head direction cell by angular velocity integration.

Zhang, Kechen. “Representation of spatial orientation by the intrinsic dynamics of the head-direction cell ensemble: a theory.” Journal of Neuroscience 16, no. 6 (1996): 2112-2126.


Samsonovich A. & McNaughton B. L. 1997 present the origin of the concept of periodic boundaries in the two-dimensional continuous attractor network that might underlie path integration and the medial entorhinal grid cells.

They proposed that the cell array in which the continuous attractor was represented had periodic boundaries, equivalent to a torus. The torus topology is the two-dimensional analogue of the ring topology suggested for the head direction system. The periodic boundary condition implies that, as the rat runs in a straight line, a given cell should activate periodically. So in a large, two-dimensional environment, each cell would have multiple place fields arranged in a square grid.

Samsonovich, Alexei, and Bruce L. McNaughton. “Path integration and cognitive mapping in a continuous attractor neural network model.” Journal of Neuroscience 17, no. 15 (1997): 5900-5920.