Reservoir Subspace Injection for Online ICA under Top-n Whitening

Reservoir expansion can improve online independent component analysis (ICA) under nonlinear mixing, yet top-$n$ whitening may discard injected features. We formalize this bottleneck as \emph{reservoir subspace injection} (RSI): injected features help only if they enter the retained eigenspace without displacing passthrough directions. RSI diagnostics (IER, SSO, $ρ_x$) identify a failure mode in our top-$n$ setting: stronger injection increases IER but crowds out passthrough energy ($ρ_x: 1.00\!\rightarrow\!0.77$), degrading SI-SDR by up to $2.2$\,dB. A guarded RSI controller preserves passthrough retention and recovers mean performance to within $0.1$\,dB of baseline $1/N$ scaling. With passthrough preserved, RE-OICA improves over vanilla online ICA by $+1.7$\,dB under nonlinear mixing and achieves positive SI-SDR$_{\mathrm{sc}}$ on the tested super-Gaussian benchmark ($+0.6$\,dB).