Supplementary Methods

Template sequence construction The entire RUN session was divided into individual running laps. Laps were grouped into one of the two trajectories (leftright and rightleft). First, the two trajectories were linearized, and we computed a spatial firing rate curve ) ,..., 2 , 1 ( n i fi = for a cell at each spatial bin i (2 cm) on a linearized trajectory. Firing rate at a spatial bin was defined as number of spikes divided by total occupancy time in the bin. Secondly, the spatial firing rate curve was then transformed to a temporal firing rate curve , by converting each position point i to its average occupancy time during a single lap. The peak of the curve was taken as the cell’s firing time on the trajectory. Visual cells often had one or more fields, therefore one or more firing peaks. In this case, we used the dominant peak. Numbers (0, 1, ...) were assigned to the cells and were arranged to form a template sequence according to the order of the cells’ relative firing times. In order for a cell to be included in a template, first, the cell had to be active on the trajectory and had high spatial information (> 0.8 bit spike ) (t f