Figure 1.

(a) Three possible compensation mechanisms following perturbation to population vector decoders (©2008 by National Academy of Sciences, adapted from Jarosiewicz B et al. PNAS 2008;105:19486-19491). A. Population vector before perturbation (black vector) pointing straight toward the target. B. After perturbation, some units will contribute differently to the population vector because of their rotated decoder coefficients (red vectors) and the resulting population vector does not point at the target. C. One possible re-aiming strategy based on a virtual target (dotted circle) that recruits a set of neurons with preferred directions that point toward the virtual target. The net vector sum is a population vector pointing toward the actual target. D. A re-weighting strategy. Down-modulating the firing rate of the rotated units makes the population vector straighten toward the target. E. A possible re-mapping strategy based on recruiting only unperturbed cells that point toward the target and perturbed cells that point 90° from the target to make the population vector point directly at the target.

(b) Conceptual illustration of redundancy using population vector addition where three of infinitely many solutions are depicted that give rise to the same population vector (blue vector).