Before revision: The grid cells in the mammalian medial entorhinal cortex exhibit striking hexagon firing patterns when the agent navigates in the open field. It is hypothesized that the grid cells are involved in path integration so that the agent is aware of its self-position by accumulating its self-motion.
After revision: The purpose of this paper is to understand how the grid cells may perform path integration calculations. We study a general representational model in which the self-position is represented by a vector formed by the activities of a population of grid cells, and the self-motion is represented by the change of this vector which is transformed by a general recurrent network for path integration. We identify an isotropic condition so that the agent is aware of its self-position by accumulating its self-motion.