Fixed and resampled permutations are distinct controls in connectivity-augmented EEG decoding

Abstract

Fixed and independently resampled uniform permutations share an ex-ante one-presentation law but differ across repeated presentations. For a P-coordinate vector with coordinate variance sᵥ², expected squared displacement between two presentations of the same trial is zero under a fixed permutation and 2Psᵥ² under independent resampling. We test their practical consequences in connectivity-augmented EEG decoding using a protocol-locked rerun on four previously inspected evaluation partitions. Ten paired training replicates yield resampled-minus-fixed accuracy differences of +13.28, +0.26, +11.32, and +30.08 percentage points for BCI 2a, BCI 2b, Lee2019, and HGD. Removing auxiliary normalization reduces the matched five-replicate gaps on Lee2019 and HGD from 11.15 to 0.72 and from 29.62 to 2.75 points. An HGD finite-bank null approximately preserving node strengths retains a 17.20-point gap. A graph-convolutional extension shows small, uncertain schedule contrasts, restricting architecture-level generalization. Inference resampling and global relabeling meet a specified ±1-point mean-accuracy equivalence criterion. Large accuracy effects characterize the evaluated late-fusion procedure. Controls require explicit schedules, normalization, and evaluation rules.

Two controls that look alike

Shuffling connectivity values is a common way to ask whether a decoder relies on real structure. The shuffle can be fixed once for each trial, or drawn anew every time that trial is presented during training. Before training begins, the two procedures look the same for any single presentation; across repeated presentations, they feed the model different sequences of inputs.

This article first derives exact properties of these two permutation schedules. It then tests their practical consequences in one connectivity-augmented EEG decoding pipeline, an EEGNet late-fusion model using phase-locking value features, on four public datasets: BCI Competition IV 2a and 2b, Lee2019/OpenBMI, and the High-Gamma Dataset.

The accuracy gap between resampled and fixed controls ranged from near zero to about thirty percentage points across the datasets, and it depended strongly on auxiliary normalization. A graph-convolutional extension showed only small, uncertain differences, so the results describe the evaluated procedure rather than every architecture. The practical point: a control isn’t fully specified until you state its schedule, its normalization, and how it is evaluated.