Alignment De-Identifies Without Aligning: A Congruence-Invariant Relational Gap in Cross-Subject Neural Representations

Per-subject alignment is widely used to improve cross-subject transfer of neural decoders, yet it is typically evaluated only through decoding accuracy, which cannot determine whether aligned representations share greater task-related structure. We therefore distinguish two questions that accuracy conflates: whether alignment removes subject-specific information and whether it makes the relational organization of task conditions more similar across individuals. Using three motor imagery (MI) electroencephalogram (EEG) cohorts, trials are represented as covariance matrices and aligned by recentering each subject's mean covariance to a common reference. Subject-specific information is quantified with a subject-identification probe, whereas relational structure is assessed using representational dissimilarity matrices (RDMs) computed from condition means with the affine-invariant Riemannian distance. We show theoretically that recentering leaves this distance, and therefore the resulting RDMs, unchanged. Consistent with this result, recentering reduces subject identification accuracy from 0.96 to chance level across all cohorts, while altering RDMs only at numerical precision. Cross-subject agreement in relational structure remains significant but substantially below the measurement reliability ceiling. Introducing an explicit similarity regularizer during training also fails to increase held-out agreement: the apparent reduction in between-subject differences is explained by a decline in the reliability ceiling rather than improved alignment. These findings demonstrate that eliminating subject identity is not equivalent to aligning relational geometry. More broadly, claims about successful alignment must be interpreted with respect to the invariance properties of the metrics used to evaluate them.