Which Neural Responses Can Intervention Data Validate?

Which variation should a neural response model explain to make a finite intervention experiment more informative? We study state-conditioned mean stimulation effects under randomized assignment and bounded responses, with finite-sample error control during sequential monitoring. A variance decomposition separates predictable common activity from effect heterogeneity and residual response noise. Matching null laws establish an inverse-margin validation lower bound and an exact information frontier with full, partial, and zero-adjustment regimes. In an eight-state model with asymmetric noise and heterogeneous effects, learned adjustment with accurate history at margin 0.01 reduces restricted correct-decision cost from 7,262 trials for a no-history oracle to 1,818, a 75.0% saving. All 256 learned runs answer correctly by 16,384 trials, compared with 244 for the oracle. With 70% history replacement, the advantage reverses: learned cost is 9,306 trials versus 7,778 without history. Across 256 population-history questions, improving observation increases optimal information by a median factor of 1.53; common-mean adjustment with the finer observation exceeds the coarse observation's information optimum in 253 questions. In a matched beta–binomial condition, a parametric likelihood-ratio test costs 60 trials, compared with 124 for the bounded-response oracle. These results identify when auxiliary prediction changes supported response conclusions and distinguish gains from fitting, observing state, and restricting the response class.