Population decoding schemes. A, In a place code, azimuth (red arrow) is read out from the location of greatest activity along a topographic map of azimuth. B, For the population-vector decoder, the activity of each neuron is represented as a vector with magnitude equal to its firing rate and direction equal to its best azimuth (black lines). Azimuth is estimated as the direction of the vector sum. C, For the two-channel difference decoder, azimuth is estimated from the difference between the summed firing rates on the left and right sides. D, For the population-pattern decoder, each azimuth is estimated from the pattern of activity across the population. This can be visualized as a second layer of neurons associated with each azimuth that sum population activity weighted by different synaptic strengths. Azimuth is estimated as that associated with the neuron in the second layer with greatest activity.