Preprocessing Sensitivity as a Signal in Brain Representations

We treat a brain representation's response to preprocessing as an observable feature in its own right. For fMRI, we measure how a joint time-delay spectral score changes when five selected aCompCor nuisance regressors are added to the same recording. The score measures excess concentration in two leading modes relative to channelwise phase-randomized references. In a post hoc analysis of 201 Alzheimer's Disease Neuroimaging Initiative participants, this paired response has an estimated adjusted slope of +0.472 percentage points per point of clinical severity (CDR-SB; HC3 standard error 0.247), while the original baseline score has no established association. The response coefficient remains similar when common temporal regressors change both pipelines' absolute scores, in a sensitivity analysis on the same cohort. We then characterize what this response can identify. A Gaussian construction shows that a related population statistic detects collective changes while every channel's complete univariate law remains fixed. Yet observation changes alone can produce a nonmonotone response at fixed latent dynamics. Observationally identical models further show that no decoder of the same inputs can resolve the latent source without additional assumptions. Five controlled simulation families connect these mechanisms to the finite-sample spectral measurement. Together, the findings make preprocessing response a concrete target for representation analysis, linking an estimated clinical association to explicit limits on latent interpretation.