Spectral smoothing explains the offline gain from cross-order single-trial MEG movement decoding for non-invasive BCI

Objective. Acceleration, velocity, and position can be combined in non-invasive movement decoding, but in this dataset only acceleration is measured; velocity and position are deterministic transforms obtained by integration. We therefore tested whether cross-order decoder fusion improves estimation in position space and whether any apparent gain remains after matching the spectral consequences of those transforms. Approach. We analysed single-trial MEG recordings from nine participants (18 runs; 2,160 trials) using a deterministic five-fold split. The primary outcome was within-trial Pearson correlation in position-residual space after removing trial-invariant trajectory. Acceleration-, velocity-, and position-based routes were fused and compared with same-order bagging, decorrelation-matched controls, and a bandwidth-matched pseudo-fusion of filtered copies of the direct position decoder. We additionally tested implementation sensitivity, residual-space R², non-positive-lag and causal pipelines, artefact sensitivity, multi-task architectures, and between-run transfer. Main results. Cross-order fusion exceeded same-order bagging by +0.0389 per-trial r (95% CI [+0.0288, +0.0499]; 9/9 participants). The bandwidth-matched pseudo-fusion exceeded bagging by +0.0424 and reproduced 109.0% of the offline margin, leaving E_cross − E_spec = −0.0035 (95% CI [−0.0105, +0.0032]; upper one-sided 95% bound +0.003). A nested-cross-validated smoothed single decoder likewise matched the ensemble. On residual-space R² with a training-fitted gain, the ordering reversed (E_bag −0.099, E_cross −0.120), showing that the correlation gain did not improve amplitude fidelity. With non-positive lags only, bandwidth matching explained 79% of the margin; under a fully causal zero-look-ahead pipeline, a smaller residual persisted and its mechanism was underpowered to resolve. Between-run transfer within the same visit retained only about 18% of within-run accuracy. Significance. In the primary offline regime, cross-order fusion gains can arise from integration-induced spectral smoothing without additional cross-order neural information. A bandwidth-matched surrogate should precede mechanistic interpretation when decoder routes are linked by deterministic transforms. In the causal regime, the advantage remains available online, but its mechanism remains unresolved.