Reservoir Subspace Injection for Online ICA under Top-n Whitening

Wenjun Xiao; Yuda Bi; Vince D Calhoun

cs.LGMar 2, 2026

Reservoir Subspace Injection for Online ICA under Top-n Whitening

Authors: Wenjun Xiao, Yuda Bi, Vince D Calhoun

Organizations: Department of Computer Science, The George Washington University, Washington, DC 20052 USA · Tri-Institutional Center for Translational Research in Neuroimaging and Data Science (TReNDS), Georgia State University, Georgia Institute of Technology, and Emory University, Atlanta, GA 30303 USA · School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA 30332 USA

Abstract

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 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).

Figures & tables

Fig. 1: RE-OICA validation (

T{=}15{,}000

n{=}3

, 10 seeds). (a) Running unshifted SI-SDR (trailing 2 000): RE-OICA, vanilla, FastICA. (b) Steady-state SI-SDR sc across regimes (lag-compensated). (c) Nonlinear overlay (last 600): true vs. RE-OICA; corner labels show per-source unshifted SI-SDR.

Regime	Method	SI-SDR sc		Corr		Count
Static	RE-OICA	$-5.9$ $\,\pm\,$	$1.0$	$0.44$ $\,\pm\,$	$0.04$	6/10
	Vanilla	$-6.8$ $\,\pm\,$	$1.0$	$0.41$ $\,\pm\,$	$0.04$
Time-var.	RE-OICA	$-6.0$ $\,\pm\,$	$1.1$	$0.44$ $\,\pm\,$	$0.04$	7/10
	Vanilla	$-6.1$ $\,\pm\,$	$1.1$	$0.44$ $\,\pm\,$	$0.04$
Nonlinear	RE-OICA	$\mathbf{-7.0}$ $\,\pm\,$	$\mathbf{1.1}$	$\mathbf{0.41}$ $\,\pm\,$	$\mathbf{0.04}$	7/10
	Vanilla	$-8.7$ $\,\pm\,$	$1.0$	$0.35$ $\,\pm\,$	$0.03$

TABLE I: Last 5 000 samples (10 seeds, mean

\pm

SEM): SI-SDR sc (dB), mean

|r|

, count (RE-OICA

>

vanilla).

Branch	SI-SDR sc		IER	$\rho_{x}$	Count
RE-OICA-base ( $1/N$ )	$-7.0$ $\,\pm\,$	$1.1$	${<}0.001$	$1.00$	(ref)
RE-OICA-sqrt ( $1/\!\sqrt{N}$ )	$-8.7$ $\,\pm\,$	$1.0$	$0.016$	$0.94$	2/10
RSI-unguarded (counterfactual, $\mathrm{IER}^{\star}\!{=}0.25$ )	$-9.2$ $\,\pm\,$	$1.0$	$0.255$	$0.77$	2/10
RE-OICA-RSI (guarded, $\rho_{x}^{\star}\!{=}0.95$ )	$-7.1$ $\,\pm\,$	$1.1$	$0.007$	$0.98$	5/10

TABLE II: Nonlinear (10 seeds): SI-SDR sc (dB, mean

\pm

SEM), IER/

\rho_{x}

steady-state, count vs. RE-OICA-base.

Fig. 2: Ablation studies (10 seeds, mean

\pm

SEM). (a)

N

-sweep under nonlinear mixing across three scaling branches. (b) Architecture: ESN vs. RF vs. vanilla (time-varying). (c) Drift sweep:

\varepsilon\in\{0.1,0.3,0.8\}

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Independent Component Analysis

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Linear Independent Component Analysis (ICA) recovers jointly independent source signals from their linear mixtures. To achieve this, classical ICA algorithms attempt to maximize non-Gaussianity, measured by negentropy, which is linked to independence by information theory. Because exact negentropy optimization is intractable, they rely on proxy contrast functions, such as fourth-order cumulants and parametric log-likelihoods. We propose instead to use the squared

L_2

-Wasserstein distance to a standard Gaussian as the ICA contrast. We show that the Wasserstein distance between a standard normal distribution and linear projections of the data is maximized when the projection recovers an independent component, and that under a regularity condition on the sources this maximum is separated from every genuine mixture by an explicit margin. We uncover the advantageous properties of the resulting estimator: for sources with a smooth density it is

\sqrt{N}

-consistent and asymptotically normal with a closed-form variance, whereas for a source with an atom the contrast has a kink at the true direction, which makes the estimator exact with probability tending to one. The proposed OT-ICA algorithm finds this projection by gradient-based optimization. Empirical evaluation on simulated data shows that OT-ICA outperforms proxy-based methods and that the

W_2^2

contrast provides more robust signal than proxy contrasts in measuring non-Gaussianity for different distributional mixtures of the latent variables. Application to linear causal disentanglement and EEG artifact removal, along with further applications detailed in the appendix, confirms OT-ICA can be used for applied ICA tasks without distributional assumptions.

Abstract

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