When Errors Cancel: Recovering Hidden Error Structure for Conformal Prediction

Locally adaptive conformal prediction normalises the nonconformity score by a learned scale, and essentially every construction learns this scale by regressing it on the observed absolute residual. We show that this default target is corrupted when the residual is a signed aggregate of latent elementary errors that partially cancel. Detection-based counting makes this exact. Over- and under-detections subtract, so the observed count error reports what survived cancellation rather than what the model got wrong. This corrupts the regression target used to fit the scale. The error’s predictable component, its latent magnitude, is masked by a survival factor that the input predicts far less well, and the intervals end up wider than they need to be. We propose cancellation-aware normalisation, which replaces the residual target by an exact factorisation into a latent error magnitude and a survival rate (the fraction of latent error mass that survives cancellation), fitted separately and multiplied. This preserves the coverage guarantee exactly, and shrinks the uncertainty intervals. Our central finding is about how this auxiliary information must enter the scale. Supplying it as an extra input feature, the standard practice in the literature, does not reproduce the gain. Fitting it as a factor of the regression target does. We verify the mechanism directly by intervening on the detector confidence threshold, which controls the survival rate, and evaluate it across three counting benchmarks at very different imaging scales.