Orientation map is necessary and sufficient for classification. *A*, Sufficiency. Gray symbols, the angular-position measurements were used to assign each voxel to one of a fixed number of angular-position bins, each corresponding to a different range of angular positions (“angular-position bin width”). Time series of all voxels within each bin were averaged, and classification was performed on the resulting averaged time series. Black symbols, voxels were assigned to bins randomly, not based on the angular-position map. Error bars, standard error of the mean across subjects (*n* = 3). Thick and thin gray lines indicate the median and 5th percentile of a one-sided null distribution (randomization test, see *Methods*). *B*, Necessity. Removing the coarse-scale map degraded classification of orientation. Left bar, baseline orientation decoding accuracy without removing any component from the map. Middle bar, decoding accuracy after projecting out, from each voxel's response, a sinusoid having phase equal to the angular position preference of that voxel as measured in the angular-position mapping experiment. Right bar, decoding accuracy after removing a sinusoid with random phase. Error bars, standard error of the mean across subjects (*n* = 3). Gray horizontal lines indicate the median (thick line) and 68% confidence interval (thin lines) of a null distribution for the residual decoding accuracy expected after map removal if decoding was driven entirely by the map. Specifically, this distribution was computed by removing the angular-position phases from a separate angular-position mapping experiment prior to measuring decoding accuracy for angular position (see *Methods*).

## PubMed Commons