Auditing Gradient Retention under Hidden Conditions: Exact Cancellation, Objective-Dependent Alignment, and the Limits of Kappa

Learning systems often average gradients over hidden conditions: annotator groups with conflicting preferences, clients with different objectives, hidden teammates. When does averaging aggregate useful signal, and when does it suppress it? We show that gradient cancellation is governed by more than the presence of hidden heterogeneity. In an analytically tractable mirror model, elementwise parameter-independent weight fields cancel exactly under a symmetric condition mixture, while a differentiable-baseline field can retain a nonzero component away from uniform policies. For K-way mixtures retention depends on the mixture direction in the probability simplex at fixed distance from uniform, and objective-induced channels can interfere, making retention non-monotone in the entropy weight. A measurement protocol separates these structural effects from finite-sample noise: deterministic rollouts collapse retention into a weight ratio, and episode-noise readouts can understate it by an order of magnitude. Under a single bounded definition the retention score alone is ambiguous: a high score can be produced by condition-blindness rather than survival. In Overcooked the dynamic value field scores 0.998 while its condition contrast is only 0.1% of its shared mass; the differentiable-baseline advantage field carries a resolvable contrast (35–176x the estimation-noise floor, score 0.590) and the plain policy gradient's contrast sits at the noise floor (score 0.529). In 510K no field has a substantial condition contrast. The 30–65x value-policy gap suggested by noisy readouts is retired. A controlled capacity experiment shows that severe cancellation can coexist with poor worst-condition performance; in contrast, on a real three-group preference dataset the condition-contrast energy is dominated by item-level noise and group-conditioned capacity yields no gain. In a switching task, retention need not predict return when the measured condition is not the variable the task relies on. Retention is a structural audit of the specified condition signal, not a general performance metric, and it indicates when condition-aware capacity is likely worth its cost.