Understanding and Controlling Batch Normalization Statistics for Source-Free Cross-Subject Motor-Imagery EEG Decoding

Cross-subject motor-imagery electroencephalography (MI-EEG) decoders often lose accuracy on unseen users because intersubject distribution shifts affect both the input signals and the intermediate feature distributions. Although batch normalization (BN) is widely used in EEG decoders, the role of its running mean and variance in cross-subject generalization remains unclear. We isolate this role by decomposing a representative source-free test-time adaptation (TTA) procedure into target-statistics recalibration and affine-parameter optimization. Four strictly matched conditions and a source-statistics restoration intervention are evaluated on three datasets with three BN-based backbones. The target BN statistic recalibration alone reproduces nearly all of the composite adaptation gains at both the setting and matched-case levels. Disabling target statistic updates removes the mean gain, and restoring the source statistics largely eliminates the gain in all six settings for which restoration results are available. However, unconditional recalibration can still degrade individual target cases. We therefore treat BN recalibration as a selective deployment action and introduce a label-free risk gate calibrated by nested leave-one-subject-out (LOSO) evaluation. Using 23 target-time diagnostics, the gate selects either BN recalibration or source-only inference. It reduces exposure to negative transfer in all nine evaluated settings while retaining a setting-dependent proportion of the unconditional gain. The results identify target BN statistics as a measurable source of cross-subject adaptation gain and provide a practical means of controlling the associated risk.