We prove that population-averaged brain encoding models provably lose two distinct classes of neural information, with no linearity or distributional assumptions. Theorem 1 (Direction Erosion): for arbitrary nonlinear encoding functions, population averaging converges to the shared component, discarding all individual-specific computation. Theorem 2 (Variance Blindness): the MSE-optimal predictor is determined entirely by the conditional mean and is invariant to stimulus-dependent variance. Validated on 7T fMRI from eight Natural Scenes Dataset subjects across 12 ROIs with six novel empirical tests.
Karan Prasad (Tue,) studied this question.