Reduced noise correlations improve coding efficiency for neurons with similar tuning and reduce coding efficiency for neurons with dissimilar tuning. (A) Heading discrimination thresholds a pair of neurons with various signal correlations. One neuron has a fixed heading preference of −90°, while the other cell’s heading preference varies from −90° (right inset) to 0° (middle inset) to 90° (left inset). (B) For each pair of MSTd neurons (each datum), we computed the ratio of discrimination thresholds for r_{noise}=0.1 and r_{noise}=0. A ratio of 1 (dashed line) indicates that correlated noise did not affect sensitivity. (C) Predicted discrimination thresholds for a population of 256 neurons with a variable distribution of heading preferences. From left to right, the range of heading preferences narrowed from a uniform distribution ([−180° 180°]) to only rightward headings near 90°. This generated varying distributions of signal correlations, as illustrated for 3 cases with proportions of positive r_{signal} values equal to 49% (heading preference range: [−180° 180°]), 75% ([0° 180°]), and 94% ([30° 150°]), as denoted by gray shading in insets. Blue, red, and black curves represent correlation structures corresponding to ‘naïve’, ‘trained’, and independent, respectively.