  When choosing between options, we must solve an important binding problem.
The values of the options must be associated with information about the action
needed to select them. We hypothesize that the brain solves this binding
problem through use of distinct population subspaces. To test this hypothesis,
we examined the responses of single neurons in five reward-sensitive regions in
rhesus macaques performing a risky choice task. In all areas, neurons encoded
the value of the offers presented on both the left and the right side of the
display in semi-orthogonal subspaces, which served to bind the values of the
two offers to their positions in space. Supporting the idea that this
orthogonalization is functionally meaningful, we observed a session-to-session
covariation between choice behavior and the orthogonalization of the two value
subspaces: trials with less orthogonalized subspaces were associated with
greater likelihood of choosing the less valued option. Further inspection
revealed that these semi-orthogonal subspaces arose from a combination of
linear and nonlinear mixed selectivity in the neural population. We show this
combination of selectivity balances reliable binding with an ability to
generalize value across different spatial locations. These results support the
hypothesis that semi-orthogonal subspaces support reliable binding, which is
essential to flexible behavior in the face of multiple options.
